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Delayed Output Feedback Control for Gait Assistance and Resistance Using a Robotic Exoskeleton
Bokman Lim, Junwon Jang, Jusuk Lee, Ryungjune Choi, Younbaek Lee, and Youngbo Shim
Abstract—In this study, we propose an interaction control framework for gait assistance and resistance using a robotic exoskeleton. We define a smoothed state variable that represents joint angle movements while walking. Furthermore, a self-feedback controller is designed with the delayed output state. By applying an appropriate time-delay and positive or negative feedback gain to the state variable, we can generate assistive or resistive torque stably without any gait phase or environment recognition. The time-delayed selffeedback controller reflects the movement of the wearer's joints at every moment of control, thereby stably coping with sudden task transitions (e.g., walk-stop-walk, forward-backward walking) as well as walking speed or environment changes. Case studies involved gait assistance with a knee exoskeleton and gait assistance and resistance with a hip exoskeleton. We performed various preliminary tests including metabolic energy measurements and a comparison of the positive or negative power of the generated torque profiles. The results show the flexibility and effectiveness of the proposed interaction control method for gait assistive or resistive training.
Index Terms—Prosthetics and exoskeletons, rehabilitation robotics, motion control.
I. INTRODUCTION
AIT training (or exercises) using a robotic exoskeleton can be an appropriate solution for those who need to improve their walking performance due to aging or disease. Hip and ankle assistance, for example, is expected to lessen the problem of excessive use of the hip muscles or a bent posture to compensate for weakened distal muscle strength and balance [1], [2]. It is expected that knee assistance can effectively improve a gait rehabilitation and training program in patients who suffer from arthritis [3] or have joint replacements.
To maximize the training effect using an exoskeleton device, interaction force should be applied naturally in accordance with the wearer's original walking pattern. Because the exoskeleton device's weight and motion constraints can distort the user's original gait pattern, reducing the device's weight and improving its wearability should take precedence. The device's usability, maintenance and manufacturing costs, and ease of wear are also key factors that cannot be overlooked.
Manuscript received February 24, 2019; accepted June 22, 2019. Date of publication July 10, 2019; date of current version July 24, 2019. This letter was recommended for publication by Associate Editor T. Lenzi and Editor P. Valdastri upon evaluation of the reviewers' comments. (Corresponding author: Bokman Lim.)
The authors are with the Samsung Advanced Institute of Technology, Suwon 16678, South Korea (e-mail: bokman.lim@samsung.com; jw526.jang@samsung.com; jusuk7.lee@samsung.com; bj81.choi@samsung.com; younbaek.lee@samsung.com; ddalbo.shim@samsung.com).
Digital Object Identifier 10.1109/LRA.2019.2927937
In addition, it is necessary to design an interactive controller capable of responding robustly and stably to changes in the wearer's movement. This is because of the irregular walking patterns of those who require rehabilitation, such as neuropathic patients, and those who have suffered strokes, and because training programs are conducted in a wide variety of conditions [4] (e.g., step/stair walking, walking over ground that entails navigating obstacles, walking at a self-selected fast speed, walking using a rail to walk forwards and backwards, and walking while completing a cognitive task). Patients who underwent joint replacement surgery must also achieve the rehabilitation goal of increasing the wearer's leg joint range of motion [5], such that fine assist strength control is possible.
Existing exoskeleton control methods based on walking phase/environment recognition with neural oscillators [6]–[9] or discrete gait events [10]–[12] cannot easily overcome the above problems because accuracy with irregular gait patterns in walking phase/environment recognition is more difficult to guarantee. To overcome this drawback (depending on the periodicity of the motion), Nagarajan et al. proposed an admittance control strategy based on modifying the dynamic response of a coupled human-exoskeleton system control [13].
Rehabilitation training programs are classified into two methods: applying assistive force and applying resistance. Recently, studies on the usefulness of walking resistance training have been reported [14], [15]. We expect that a variety of stimuli, including resistive interaction forces, will help balance training [16]. However, there are few examples of resistance torque control using exoskeletons [17] and it is difficult to find an interaction control method that can simultaneously cover assistive and resistive torque generation.
Thus, we present a novel interaction control framework for gait assistance and resistance to overcome many of the limitations described above. The interaction controller is based on delayed output feedback control known for stabil
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izing oscillatory systems under certain conditions [18]–[20]. By adding a timedelay buffer to the self-feedback control loop, we can generate assistive or resistive torque stably in the interaction between the user and exoskeleton. The proposed interaction controller can operate at various gait speeds and under environmental changes (e.g., stairs, up/down ramps) with only angular positions and without the need for gait phase or environment recognition. The proposed framework can appropriately handle non-uniform ground conditions, such as ramp–level–stair, sudden stopping, and forward–backward walking.
2377-3766 © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
Fig. 1. Hardware prototypes for gait training with the Gait Enhancing and Motivating System (GEMS), and an interaction control framework for gait assistance and resistance. GEMS-K is our knee exoskeleton and GEMS-H is our hip exoskeleton.
Previously, we proposed a hip assistance controller based on a time-delayed feedback control method [21]. In this study, we show that the proposed method can be applied not only to other types of exoskeletons, such as knee exoskeleton control, but also to resistive torque generation. The characteristics of the control parameters (viz., the time delay and feedback gain) are also analyzed and discussed. To my best knowledge, this is the first example of applying time delay control to walking resistance and knee assistance.
This letter is organized as follows: Section II describes the interaction control framework based on delayed output feedback control for knee and hip exoskeletons. Section III provides the experimental results under various walking conditions. Finally, we conclude with a summary of the study and suggestions on how to extend our framework into other types of exoskeletons, such as single joint driven assistance (e.g., an ankle exoskeleton device worn only on one foot).
II. FRAMEWORK AND ALGORITHM
A. Interaction Control for Gait Assistance and Resistance
Our interaction control framework for gait assistive or resistive training is shown in Fig. 1. The interaction control method is based on delayed output feedback control (DOFC). The DOFC-based controller design can be classified into two steps:
Step 1: Define an output state representing the current leg's motion with joint angular positions.
Step 2: Determine the smoothing rate, delay time, and feedback gain of the output state.
Once the value or range of the control parameters is determined, it is configured as a self-excited feedback control loop.
As shown in Fig. 1(c), the input of the interaction controller comprises the joint angular positions and the output is the interactive torque. The original state value $y_{raw}(t)$ is calculated as a function of the joint angles, $y_{raw}(t) = f(q(t))$ . Noisy sensing data $y_{raw}(t)$ is filtered through the state smoother. Delay due to state smoothing is not a problem because an additional time
delay is used in the next procedure. The smoothed state y(t) is delayed for some time by passing through the state delayer, $y(t) \rightarrow y(t-\Delta t)$ . This process is easily implemented by using a constant time delay buffer. Here, reducing the time delay value leads to an early assist (or response), while increasing the time delay value results in a late assist (or response). Finally, interaction control torque is generated by multiplying the delayed state $y(t-\Delta t)$ by the feedback gain $\kappa$ . The magnitude of the gain is proportional to the magnitude of the generated interaction torque, i.e., as the gain increases, the generated torque becomes more assistive or resistive. At this time, amplifying the state value using positive gain generates assistive torque, and, conversely, negative gain generates resistive torque.
B. Assistive or Resistive Torque Generation From Knee or Hip Joint Angles
The proposed interaction control framework can be expressed in a more detailed and concrete form, as shown in Fig. 2. We first define an output state $y_{raw}(t)$ as that representing the projected leg motion:
$$y_{raw}(t) = \sin q_r(t) - \sin q_l(t) \tag{1}$$
where $q_r$ and $q_l$ are the right and left joint angles, respectively. We use the sinusoidal projected joint angle difference for knee and hip exoskeleton control.
The original noisy sensor data is smoothed by passing through a simple first-order low-pass filter:
$$y^{i} = (1 - \alpha)y^{i-1} + \alpha y_{raw}^{i}, \ (0 < \alpha < 1)$$
(2)
where i denotes
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the current sample time and i-1 is the previous sample time. The current smoothed state $y^i$ is expressed as a weighted sum of the previous sample time state $y^{i-1}$ and the original state value of the current sample time $y^i_{raw}$ , and the smoothing rate can be adjusted by changing the smoothing factor $\alpha$ .
(a) Assistance for both knees with DOFC framework
(b) Left hip assistance/resistance with DOFC framework
Fig. 2. Examples of DOFC framework-based assistance or resistance for knee or hip exoskeleton. $q_r$ and $q_l$ are the right and left joint angles, respectively, and $\kappa$ is the feedback gain.
The assistive or resistive torque $\tau$ is then generated through a combination of appropriate time delays $\Delta t$ and positive or negative gains $\kappa$ :
$$\tau(t) = \kappa y(t - \Delta t) = \begin{cases} \text{if } \kappa > 0, \text{ assist mode} \ \text{if } \kappa < 0, \text{ resist mode} \end{cases}$$
(3)
1) Gait Assistance With a Knee Exoskeleton: Fig. 2(a) shows an example of DOFC-based walking assistance with a knee exoskeleton. Assistive torque for the left knee $\tau_{l,assist}$ is generated with a positive gain, and that for the right knee can be obtained by reversing the left assistance torque $(\tau_{r,assist} = -\tau_{l,assist})$ . This assistance strategy has advantages in terms of motion synergy for assisting both legs.
2) Gait Assistance and Resistance With a Hip Exoskeleton: Fig. 2(b) shows an example of DOFC-based walking assistance and resistance with a hip exoskeleton. Assistive torque for the left hip $\tau_{assist}$ is generated with a positive gain, and, conversely, resistive torque $\tau_{resist}$ is generated with a negative gain. The extent of the assistance or resistance can be gradually increased or decreased by gradually increasing or decreasing the positive or negative gain. Assistive or resistive torque for the right hip can also be obtained easily with a similar strategy (see Fig. 2(a) for an example with assistance to both knees).
III. CASE STUDIES: KNEE AND HIP EXOSKELETONS
This section considers two case studies: (i) gait assistance with a knee exoskeleton, and (ii) gait assistance and resistance with a hip exoskeleton. Fig. 1(a) and 1(b) show our latest knee and hip exoskeleton prototypes with the Gait Enhancing and Motivating System for a Knee and Hip (GEMS-K and GEMS-H). The weight of GEMS-K (knee-only actuated) and GEMS-H (hip-only actuated) is about 3.6 kg and 2.1 kg, respectively.
A. Gait Assistance With a Knee Exoskeleton
The basic assistance strategy (Fig. 2(a)) can be extended for both right/left and extension/flexion knee torque generations by
modifying the original torque equation in (3).
Right knee flexion, left knee extension:
$$\tau_{rk,des}(t) = -\tau(t)$$
$$\tau_{lk,des}(t) = \tau(t) \cdot \delta_K$$
(4)
Left knee flexion, right knee extension:
$$\tau_{lk,des}(t) = \tau(t)$$
$$\tau_{rk,des}(t) = -\tau(t) \cdot \delta_K$$
(5)
where $\delta_K$ denotes the knee extension/flexion torque ratio (if $\delta_K = 1$ , the knee flexion and extension torque strength is the same). The applied smoothing factor $\alpha_K$ for the knee exoskeleton in (2) is 0.04. This smoothing factor $\alpha_K$ is manually set for smooth interaction and torque generation.
Fig. 3 shows the joint angle and assistance torque values during walking task transitions from walking to stopping and stopping to walking (time-delay $\Delta t = 0.25$ s, feedback gain $\kappa = 10$ , extension/flexion ratio $\delta_K = 1$ ). The assistance controller and the output torque are directly affected by the knees range of motion, as shown in Fig. 3.
1) Effects on Metabolic Cost With Knee Assistance: Unlike ankle or hip assistance in walking, studies on the metabolic energy reduction in knee assists (or multiple-joint assists including the knee
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) are difficult to find. Rather, it is known that metabolic energy greatly increases due to increases in weight and motion constraints due to a rigid frame and actuator structure covering the knee [22]–[24]. The increase in metabolic energy during the device's operation implies that it is a burden to the user even to wear the device. Therefore, the effect and usefulness of the gait rehabilitation/training is significantly reduced. First, we need to at least prevent the increase in metabolic energy due to knee exoskeleton assistance.
Five male subjects participated in the experiment (age: $38 \pm 2.2$ ; weight: $68.4 \pm 6.3$ kg; height: $173 \pm 8.2$ cm; mean $\pm$ standard deviation). First the subjects stood for 5 minutes (as they did again at the end of the experiment) to obtain the average baseline from which to subtract the walking data
Fig. 3. Knee joint angle, velocity, torque, and power trajectories for the selected task transitions from walking to stopping and stopping to walking. The knee joint sensing data are obtained from the knee exoskeleton. The walk-stop-walk (time-delay $\Delta t=0.25$ s, feedback gain $\kappa=10$ , extension/flexion ratio $\delta_K=1$ , smoothing factor $\alpha_K=0.04$ ) is performed with exoskeleton assistance. In the torque plot, the gray dashed line represents the estimated torques (from current sensing), while the blue and red solid lines denote the generated desired assistance torque.
to obtain the net metabolic rate. Then they walked without the exoskeleton for six minutes (as they did again near the end of the experiment) to obtain the average metabolic rate under normal walking conditions. Then they wore the exoskeleton and walked on the treadmill with assistance. We took the median of the last three minutes of each condition to represent the metabolic rate expended under those conditions. The K5 "breath by breath" portable metabolic system (COSMED, Rome, Italy) was used to measure the metabolic energy expenditure. The treadmill speed was set to 4 km/h for all subjects. Knee control parameters were selected in advance as the most preferred values for the wearer. The applied assistance torque was mainly flexion rather than extension (extension/flexion ratio $\delta_K$ : 0.1 or 0.2; gain $\kappa$ : $10{\sim}13$ ; RMS torque: $3.4\pm0.6$ Nm; maximum flexion torque: $7.9 \pm 1.3$ ; maximum extension torque: $1.5 \pm 0.5$ Nm). The applied time-delay $\Delta t$ values were 0.2 or 0.25 s. Fig. 4 shows the knee exoskeleton sensing data and generated assistive torque and power applied to each subject.
As shown in Table I, the metabolic energy expenditure in knee assistance was $3.55 \pm 0.52$ W/kg, which increased by an average of 3.4% compared to normal walking state (without the exoskeleton) of $3.45 \pm 0.56$ W/kg. However, the difference was not statistically significant ( $^\dagger p$ – value = 0.4 > 0.05 for the paired t-test no exo vs. exo). In other words, there was no significant change in metabolic energy expenditure due to wearing the knee exoskeleton and its assistance during walking. This means that the increase in metabolic energy due to weight and the movement restriction due to wearing the knee exoskeleton was offset by knee assistance during walking.
Through this preliminary test, we showed that an increase in metabolic energy can be prevented through knee-only assistance for the five healthy subjects, and furthermore that it might
Fig. 4. Knee exoskeleton joint sensing data for five subjects. The joint torque represents the generated input assistance torque. The joint power is calculated by multiplying the joint torque by the joint velocity.
TABLE I
REDUCED METABOLIC COST WITH THE KNEE EXOSKELETON
| Subject | No Exo | Exo Assist | |
|------------|-------------|-----------------|-----------------------|
| No. | rNMR (W/kg) | NMR (W/kg) | rNMR (%) |
| 1 | 4.29 | 4.43 | -3.4 |
| 2 | 2.77 | 3.13 | -12.8 |
| 3 | 3.38 | 3.62 | -7.3 |
| 4 | 2.95 |
|
2.94 | 0.3 |
| 5 | 3.87 | 3.63 | 6.3 |
| Mean (±SD) | 3.45±0.56 | $3.55 \pm 0.52$ | -3.4±6.5 † |
NMR: net metabolic rate; rNMR: reduced net metabolic rate from free walking condition (No exo). $^\dagger p$ - value = 0.4 > 0.05 for paired t-test (No exo vs Exo). A negative value means that metabolic energy has increased compared to normal walking (with no exoskeleton).
be possible to reduce metabolic energy by tuning the control parameters and optimizing the extension/flexion assistance ratio, magnitude, and timing selection. (Notice that three of the five subjects had increased metabolic energy expenditure, while two had decreased metabolic energy.)
B. Gait Assistance and Resistance With a Hip Exoskeleton
The basic assistance strategy (Fig. 2(b)) can be extended for both right/left hip torque generation $\tau_{r,des}$ , $\tau_{l,des}$ by modifying the original torque equation in (3).
Right hip flexion, left hip extension:
$$\tau_{rh,des}(t) = -\tau(t)$$
$$\tau_{lh,des}(t) = \tau(t) \cdot \delta_H$$
(6)
Left hip flexion, right hip extension:
$$\tau_{lh,des}(t) = \tau(t)$$
$$\tau_{rh,des}(t) = -\tau(t) \cdot \delta_H$$
(7)
where $\delta_H$ denotes the hip extension/flexion torque ratio (if $\delta_H$ = 1, the hip extension and flexion torque strength is the same). In this study, we set the smoothing factor for the hip exoskeleton $\alpha_H$ to 0.05 in (2) and the hip extension/flexion ratio $\delta_H$ to 1. This smoothing factor $\alpha_H$ , like the knee exoskeleton case, was manually determined to produce smooth interaction torque.
Fig. 5. Generated mean positive/negative power and the RMS torque changes due to time-delay changes ( $\Delta t = 0.05, 0.15, 0.25, 0.35 \text{ s}, \kappa = 8$ ). Positive: mean positive power, Negative: mean negative power.
Fig. 6 shows the joint angle and assistance torque values during walking task transitions from forward-to-backward walking and backward-to-forward walking. The assistance controller and the output torque are directly affected by the hip motions, as seen in Fig. 6. For the forward-backward-forward walk transition task, the resulting mean positive and negative power values were $3.85~\mathrm{W}$ and $-0.13~\mathrm{W}$ , respectively. Lower negative power value compared to relatively large positive power supports the idea that the resistive torque generation was minimal.
With six male subjects (age: $41\pm3.2$ ; weight: $71\pm5.0$ kg; height: $174\pm8.2$ cm), we previously showed that hip assistance can reduce metabolic energy from walking by an average of 20% compared to normal walking state (without the exoskeleton) [21]. We also showed with same six male subjects how the proposed assistance algorithm can be generalized in assisting in various conditions (speed and environment changes) by showing the differently adapted torque and power profiles with fixed control parameters ( $\Delta t = 0.25, \kappa = 8$ ) [21]. The generated torque and power under fixed control parameters showed a consistent trend of change in walking speed/environment (except for small variance due to individual hip pattern differences). For this reason, experiments were conducted on a single subject and on a variety of situations.
1) Relationship Between Time-Delay and Generated Power/ Torque: We can adjust the assistance response (or timing) by adjusting the time-delay $\Delta t$ . Figure 5 shows the generated MP (mean power) and RMS (root mean square) torque for four selected time-delay values $\Delta t = 0.05, 0.15, 0.25, 0.35$ s. As shown in Fig. 2(b), the generated torque has a sinusoidal form, so the RMS torque value difference denotes the generated torque difference.
One male subject (age: 40; weight: 67 kg; height: 160 cm) wore the hip exoskeleton and walked with assistance. We used a fixed gain of $\kappa=8$ .
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The treadmill speed increased from 1 km/h to 5 km/h in 1 km/h increments. The torque and power generated in the hip joint were calculated with a sensor attached to the exoskeleton. As shown in Fig. 5(b), the time-delay $\Delta t$ affects the generated torque magnitude, even though it is a control variable related to assistance timing. The generated torque amplitude increases as the time-delay increases.
The positive and negative powers delivered to the subject is shown in Fig. 5(a). The magnitude of the positive power generated is likely to be highest at around a time-delay of
Fig. 6. Hip joint angle, velocity, torque, and power trajectories for the selected task transitions from forward-to-backward walking and backward-to-forward walking. The hip joint sensing data are obtained from the hip exoskeleton. A forward–backward–forward walk ( $\Delta t=0.25~\rm s, \kappa=8, \delta_H=1, \alpha_H=0.05)$ is performed with exoskeleton assistance. In the torque plot, the gray dashed line represents the estimated torque (from current sensing), while the blue and red solid lines denote the generated desired assistance torque.
$\Delta t=0.25$ s. If there is too much time delay, such as when $\Delta t=0.35$ s, this indicates that there is a problem with generating assistive (positive) power for high-speed walking. An increase in negative power generation means that the amount of work done by the wearer has increased due to a mismatch between the assist and the users movement. If the time-delay value is too small ( $\Delta t=0.05$ s), negative power generation does not increase even at high-speed gait, but there is also less positive power generation and assistive torque generation. It is therefore necessary to set an appropriate time-delay value.
2) Adjusting Transfer Power by Gain Change: We can adjust the assistance/resistance strength (strong or weak) by adjusting the feedback gain $\kappa$ . Same one male subject walked on the treadmill after wearing the device. The treadmill speed was fixed at 4 km/h. We set the time-delay $\Delta t$ to 0.25 s. From $\kappa=-5$ to $\kappa=10$ , we increased the gain value by 0.2 for every two steps (1 walking cycle). Fig. 7(a) shows the change in the torque and power profile when the gain gradually increased from -5 to 10.
Fig. 7. Generated torque and power changes due to gain changes. The feedback gain κ was increased from −5 to 10 (Δt = 0.25 s, 4 km/h walking speed). Positive: mean positive power, Negative: mean negative power.
Fig. 8. Raw metabolic rate data. The red line denotes the raw data. The black line denotes the filtered metabolic data shown for visual purposes. The horizontal black line denotes the median with respect to the last 3 minutes under each condition.
The resistance torque generated at the negative gain κ = −5 was inverted as the gain increased little by little and smoothly changed to the assistive torque (κ > 0). The generated power also shows a gradual change in response to the gain change.
Fig. 7(b) shows the gain and generated RMS torque and power relationships under given walking conditions (Δt = 0.25 s, 4 km/h walking speed). A linear proportional relationship between the generated torque/power and the gain κ is observed. In the plot on the right side of Fig. 7(b), when the gain is positive (κ > 0), mean negative power (MNP) generation is inhibited compared to mean positive power (MPP). On the other hand, when the gain is negative (κ < 0), MPP generation is effectively suppressed compared to MNP.
3) Effects on Metabolic Cost by Adjusting Gain: Fine control of power delivery can be extremely useful for gait rehabilitation or training. This is because customized rehabilitation is possible depending on the stage of the rehabilitation and the patients condition. Fig. 8 and Table. II show the resulting metabolic measurement for five selected gains κ = 8, 9.5, 11, 12.5, 14.
TABLE II REDUCED METABOLIC COST WITH THE HIP EXOSKELETON
| Condition | Exo-generated | | Human-reduced | |
|-------------------|-------------------|---------|---------------|----------|
| (gain) | $\tau_{RMS}$ (Nm) | MPP (W) | NMR (W/kg) | rNMR (%) |
| $\kappa_1 = 8.0$ | 3.86 | 7.48 | 3.49 | -3.1 |
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$\kappa_2 = 9.5$ | 4.30 | 8.29 | 3.24 | -10.1 |
| $\kappa_3 = 11.0$ | 4.78 | 9.30 | 3.07 | -14.8 |
| $\kappa_4 = 12.5$ | 5.22 | 10.36 | 2.98 | -17.1 |
| $\kappa_5 = 14.0$ | 5.70 | 11.34 | 2.85 | -20.9 |
τRMS : RMS torque; MPP: mean positive power; NMR: net metabolic rate; rNMR: reduced net metabolic rate from free walking condition (No exoskeleton).
Fig. 9. Generated torque and power changes due to cadence changes. The treadmill speed was increased from 2 to 6 km/h (Δt = 0.25 s, κ = 8). Positive: mean positive power, Negative: mean negative power.
Same one male subject walked on the treadmill at 4 km/h speed with assistance. We used the same protocol as that used to measure metabolic cost with knee assistance except for the exoskeletons settings. The subject wore the exoskeleton and walked on the treadmill under five different assistance conditions (κ1 < κ2 < ... < κ5).
The results from this preliminary test are shown in Fig. 8 and Table. II. The results demonstrate the possibility of stepwise intensity adjustment by controlling the gain value, and they are consistent with related studies which suggest that the assist power magnitude is proportional to the amount of reduced metabolic energy [25].
4) Assistance Adaptation to Variable Cadence Using Fixed Control Parameters: Our proposed control algorithm is stable enough to cope with cadence (or speed) changes. The control parameters were fixed (Δt = 0.25 s, κ = 8) under variable cadence. For the cadence change experiment, the same one subject walked on the treadmill with assistance at different walking speeds. The treadmill speed increased from 2 km/h to 6 km/h in 0.1 km/h increments for every step.
Fig. 9(a) shows the change in the torque and power profile when the cadence increased from 95 to 125 steps/m. The
Fig. 10. Resistance adaptation to gait speed and environment with fixed gain and delay ( $\Delta t = 0.25 \text{ s}, \kappa = -4$ ).
generated torque/power shows a gradual change in response to the cadence change. Negative power generation is very small compared to positive power generation. It means that the interference caused by mismatch during the cadence change is minimized. Fig. 9(b) shows the gain and generated RMS torque and power relationships under given walking conditions ( $\Delta t = 0.25 \text{ s}, \kappa = 8$ , variable cadence from 95 to 125 steps/m). A linear proportional relationship between the generated torque/power and the cadence (speed) is observed.
5) Generalizability of Resistance With Fixed Control Parameters: Same one male subject wore the exoskeleton and walked with resistance. The control parameters were fixed with the same values ( $\Delta t = 0.25 \text{ s}, \kappa = -4$ ) under various gait speeds and walking environments. For the speed change experiment, the subject walked on the treadmill at different walking speeds. The treadmill speed increased from 1 km/h to 5 km/h in 1 km/h increments. The subject walked for 1 minute at each speed. We took the last 30 s of each condition to calculate the generated mean positive/negative power. For the experiment regarding environmental changes, the subject walked at a self-selected speed on different ground levels (ramp ascent $\rightarrow$ ramp descent $\rightarrow$ level $\rightarrow$ stair ascent $\rightarrow$ stair descent). We took the section corresponding to each condition to calculate the generated mean positive/negative power. Through this experiment, we showed how the proposed interaction control algorithm can be generalized to resist under various conditions by showing the adapted torque and power profiles with fixed control parameters (time-delay $\Delta t$ and gain $\kappa$ ).
Fig. 10 shows the generated joint torque and positive and negative power. Fig. 10(a) illustrates how the generated torque
profile changed as the treadmill speed varied, all with the fixed control parameters ( $\Delta t = 0.25~\rm s$ , $\kappa = -4$ ). For the proposed controller, the interaction torque was determined by two factors: the control parameters (feedback gain $\kappa$ , time-delay $\Delta t$ ) and the gait motion state y. Since the control parameters were fixed, the hip
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motion (or range of motion) determines the output torque profile. As shown in Fig. 10(c), the generated torque trajectory changed with changes to the gait environment. Without changing the control parameters ( $\Delta t = 0.25~\rm s$ , $\kappa = -4$ ), the generated torque and power values varied with notable differences, except at a relatively high-speed walking (4, 5 km/h).
In Fig. 10(b) and Fig. 10(d), large negative power compared to small positive power indicates that the DOFC controller can operate under various conditions when resisting the user without assistance (pure interference). As shown in Fig. 7(a), maximum resistance torque is reached when the swing speed is high (when the legs cross) and the torque approaches zero when the swing speed is slow (when the swing direction of the leg changes). The above resistance strategy is advantageous because it may not be safe for a person who has difficulty walking to apply large resistance when changing the direction of the leg swing. (Normally at this time, even slight external force can be dangerous, because it passes through a zero point of human hip joint velocity.)
C. Discussion of Limitations
The proposed control method solely generates the assistance/resistance torque depending on the user's gait pattern. The interaction torque is limited to a sinusoidal shape as Fig. 7(a),
and only the peak magnitude can be adjusted for flexion or extension motion, right or left joints. Therefore, it might be not suitable when you want to generate specific torque pattern (not sinusoidal) only in certain gait phase. However, the physical therapist (or medical doctor) may need to apply a well-defined torque only at specific gait phase.
Another source of potential issues can derive from the fact that when you apply a significant amount of torque the angle joint profile is significantly affected by the interaction with the thigh/leg soft tissues. This problem could be reduced to some extent by smoothing the original angle sensor data, but there is still a possibility of instability when using large resistance torques. We have analyzed the stability of the DOFC controller under limited conditions in [21], but we need more rigorous theoretical/experimental studies on the stability of DOFC based assistance/resistance. Various parameter studies with a hip exoskeleton were performed on a single subject. This point should be considered as a limitation of this study.
IV. CONCLUSION
We presented an interaction control strategy for gait assistance and resistance. The DOFC-based controller stably handled gait pattern changes. By using the appropriate time-delay and feedback gain, we could generate assistive/resistive torque stably in the interaction between the user and exoskeleton. We showed the flexibility and effectiveness of the control method by measuring generated torque and power under various walking conditions and the metabolic energy expenditure from treadmill walking.
We plan to measure metabolic costs and stabilize aspects of the controller under various conditions to show the controller's effectiveness across a wide array of conditions. We will extend the application of our interaction control to other types of exoskeletons, such as single joint driven assistance (e.g., an ankle exoskeleton device worn only on one foot). We expect to be able to apply a similar strategy, provided we can define state variables that characterize ankle joint motion and assistive torque. To guarantee consistent control under extreme conditions, such as running, we also have a plan to use online parameter modification.
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MEDICAL ROBOTS
Human-in-the-loop optimization of hip assistance with a soft exosuit during walking
Ye Ding, 1,2* Myunghee Kim, 1,2* Scott Kuindersma, 1† Conor J. Walsh 1,2†
Wearable robotic devices have been shown to substantially reduce the energy expenditure of human walking. However, response variance between participants for fixed control strategies can be high, leading to the hypothesis that individualized controllers could further improve walking economy. Recent studies on human-in-the-loop (HIL) control optimization have elucidated several practical challenges, such as long experimental protocols and low signal-to-noise ratios. Here, we used Bayesian optimization—an algorithm well suited to optimizing noisy performance signals with very limited data—to identify the peak and offset timing of hip extension assistance that minimizes the energy expenditure of walking with a textile-based wearable device. Optimal peak and offset timing were found over an average of $21.4 \pm 1.0$ min and reduced metabolic cost by $17.4 \pm 3.2\%$ compared with walking without the device (mean $\pm$ SEM), which represents an improvement of more than 60% on metabolic reduction compared with state-of-the-art devices that only assist hip extension. In addition, our results provide evidence for participant-specific metabolic distributions with respect to peak and offset timing and metabolic landscapes, lending support to the hypothesis that individualized control strategies can offer substantial benefits over fixed control strategies. These results also suggest that this method could have practical impact on improving the performance of wearable robotic devices.
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American Association for the Advancement of Science. No claim to original U.S.
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INTRODUCTION
Wearable robotic devices have demonstrated the potential to enhance human economy and endurance (1-3). Recent breakthroughs in wearable robotics have substantially reduced energy expenditure in human walking using both passive (1) and active autonomous (2–4) or tethered (5-11) devices. In particular, advances in active devices provided flexibility to regulate assistance control parameters related to timing (5, 7, 10), magnitude (6, 12), or delivered power (12, 13). Studies have shown that control strategies can significantly affect performance (4-7, 10, 12), which raises questions about how to reliably and efficiently design optimal controllers. Assistive strategies have commonly been derived from simulations (14, 15) and biomechanical measurements (10, 16) or tuned manually based on average responses (11). Specifically, there is a growing interest in designing control strategies using musculoskeletal simulations (14, 17), and recently, this approach has shown promise in guiding assistive profiles for running (14, 18). However, physiological and neurological differences between individuals can cause divergent responses to an identical controller, that is, one participant's optimal control strategy may perform poorly on another (5-7, 10, 19). Thus, although generic musculoskeletal simulations may provide general guidelines on assistance, participant-specific models may be required when considering how to find optimal system parameters for individualized assistance.
Conventionally, discrete step (1,4-7) and continuous sweep (20,21) protocols have been used to investigate a participant's performance and to explore the landscape of control parameter settings for wearable robotic devices. With these approaches, metabolic cost is measured by varying a control parameter in either a discrete or a continuous manner. A curve fitting process is then followed to identify the optimal parameter value that results in the maximum metabolic benefit (1,5-7,20,21). Unfortunately, both continuous and discrete protocols involve a lengthy evaluation process, and the time required increases exponentially with
added control parameter dimensions. Long walking times in protocols may affect the accuracy of metabolic measurements due to high exertion or fatigue, which in turn leads to cardiopulmonary drift (22), especially for clinical populations who may not be able to sustain long walking bouts (23).
Human-in-the-loop (HIL) optimization aims to address the aforementioned challenges in protocol length by adjusting control parameters based on real-time measurements of human physiological signals, such as metabolic cost. This optimization is inspired by an observation of humans continuously adjusting their coordination pattern to minimize the metabolic cost of walking (24) and expands the concept to wearable devices. Some promising efforts in this domain have recently demonstrated the ability to optimize both single and multiple control parameters using ankle exoskeletons (8, 9). In these cases, substantial metabolic reductions were achieved with the optimal parameter settings identified by either a one-dimensional (1D) gradient descent method using a pneumatically actuated ankle exoskeleton for a fixed 50 min (9) or a 4D Covariance Matrix Adaptation Evolution Strategy (CMA-ES) with an electromechanically actuated ankle exoskeleton for $83 \pm 14 \text{ min (mean} \pm \text{SEM)}$ (8
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). Although these achievements are impressive, there remain opportunities to explore different wearable assistive hardware, control parameterizations, applications to other joints, and alternative optimization methods that could improve sample efficiency.
We developed an experimental method to rapidly identify optimal control parameters in a 2D space that minimized the metabolic cost of walking (Fig. 1). This was achieved through the use of Bayesian optimization, an efficient global optimization strategy that is well suited to find the minima of objective functions that are noisy and expensive to evaluate (25–27). In a previous HIL study that optimized step frequency, we found that Bayesian optimization converged in half the time of a gradient descent method (28). For the current HIL scheme, a participant walked with hip extension assistance applied via a soft exosuit (Fig. 2A), a textile-based wearable device designed to apply forces across joints in parallel with human muscles (10, 29). The assistive profile was configured by multiple control parameters that were iteratively updated by the optimization and applied to the participant using a tethered actuation system with admittance force control (29). The optimization was initialized by
<sup>1John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA. 2Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02115, USA.
*These authors contributed equally to this work.
†Corresponding author. Email: walsh@seas.harvard.edu (CJ.W.); scottk@seas.harvard.edu (CJ.W.);
Fig. 1. Experimental setup for HIL Bayesian optimization. Bayesian optimization was used to adjust the control parameters of an assistive device to minimize the metabolic cost of walking. The metabolic rate was estimated from respiratory measurements and used to compute a posterior distribution of metabolic rate with respect to the free control parameters. The posterior was initially generated by evaluating six prefixed control parameters. Given the posterior at the current iteration, the control parameters with maximum EI were chosen and applied to the wearable device. This process was repeated until convergence. During this process, the configured force profiles were delivered through a soft hip exosuit with a tethered actuation system.
Fig. 2. Soft exosuit and assistive hip force profile. (A) The hip soft exosuit. A hip extension moment was generated by pulling the inner cable to create a tension between two anchor points. (B) Parameterization of hip force profile. The hip force profile was chosen to be a combination of two parameterized sinusoidal curves joined at the peak. Peak force was set to 30% of body weight, and onset timing was fixed to the time of maximum hip flexion. Peak and offset timing were actively adjusted by the optimization to determine the shape of the force profile as a function of gait percentage. Shaded purple and blue bars represent the range of peak and offset timing, respectively. (C) Examples of feasible hip force profiles.
obtaining the metabolic cost of a prescribed number of assisted conditions with respect to pseudo-randomly selected control parameters from an evenly distributed parameter space. On the basis of this information, the optimization iteratively estimated the participant's metabolic cost distribution using a Gaussian process (fig. S1) (30) and selected control parameters for the next iteration by maximizing the expected improvement (EI) (25, 26). At each iteration, the metabolic cost was estimated by fitting a first-order dynamic model to 2 min of transient metabolic data (31). After a set number of iterations, the control parameters corresponding to the minimum value of the metabolic landscape (the mean of the metabolic cost distribution) represented the optimal values.
The hip assistive profile was a combination of two halves of sinusoidal curves joined at their peaks. This profile was defined by two fixed parameters (peak force and onset timing) and two free parameters (peak timing and offset timing; Fig. 2B) that were adjusted by the optimization method. We fixed peak force to 30% body weight to ensure comfort during the long walking test while still maintaining assistance high enough to achieve sufficient metabolic reduction. Previous work demonstrated that higher assistance magnitude resulted in larger metabolic benefits for both hip (10, 11) and ankle (6), and the forces we evaluated here were approximately within the range of previous evaluations. We also fixed the onset timing at the maximum hip flexion event based on previous hip studies, which showed the largest metabolic reductions with onset timing set close to maximum hip flexion (7, 10). Further, we found less intraparticipant variability of metabolic cost and lower signal-to-noise ratio when varying onset timing in our pilot testing (table S1). For the purposes of this study, we defined the start of the gait cycle using the maximum hip flexion event. Peak and offset timing were bounded within 15 to 40% and 30 to 55%, respectively, in this newly defined gait cycle. It is worth noting that the maximum hip flexion event was on average at 86
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.2% of the conventional gait cycle, defined with heel strike as 0% (table S2). The offset timing was constrained to occur at least 15% later than the peak timing. The range and constraint of peak and offset timing (Fig. 2C) were chosen by slightly extending the average range of the biological hip extension moment (32) while considering limitations on the ramp-up speed of assistance that our soft exosuit was capable of achieving. This configuration was able to shape our profiles similar to the hip assistive profiles used in previous assistive device studies (4, 7, 10, 11).
We conducted a single-day experiment on eight participants (table S3), optimizing the assistance timings as they walked on a treadmill at 1.25 m s-1. For the optimization, 6 iterations (six pairs of peak and offset timing) were evaluated for the optimization initialization and 14 iterations were followed to adjust the tuning. These numbers of iterations were chosen based on our simulation results (fig. S2). After optimization, we performed a validation test confirming the optimal condition found during the optimization process, then compared both optimal condition and validation test with a no-suit condition. The primary analysis included (i) the net metabolic cost of walking, defined as the gross metabolic rate during walking minus the rate measured during quiet standing; (ii) the convergence time across participants; (iii) participant-specific optimal timings; (iv) participant-specific optimal assistive profiles; (v) participant-specific metabolic landscape, defined as the mean of the metabolic cost distribution with respect to the peak and offset timing along with participant-specific probability of improvement landscape, interpreted as the likelihood of exceeding the largest metabolic reduction.
RESULTS
Metabolic rate
Participant-specific optimal assistance substantially improved energy economy for all participants by reducing the net metabolic cost of walking to $2.26 \pm 0.13 \text{ W kg}^{-1}$ and $2.27 \pm 0.18 \text{ W kg}^{-1}$ for the optimal and validation conditions, respectively, from $2.75 \pm 0.18 \text{ W kg}^{-1}$ for the nosuit condition (mean $\pm$ SEM). Net metabolic reduction of the validation condition ranged from 6.7 to 33.9%, with an average reduction of 17.4 $\pm$ 3.2% (mean $\pm$ SEM; paired t test, t = 0.003; Fig. 3A and table S4).
Convergence time
The optimization converged for all participants during the optimization process (fig. S3). The convergence time was on average $21.4 \pm 1.0$ min (mean $\pm$ SEM), ranging from 18 to 24 min.
Optimal timing
Participant-specific optimal peak and offset timings spread over about half of the feasible region of the control parameters (Fig. 3B). Most of the optimal timings were on the boundaries of the parameter ranges, with three participants having their optima at the latest peak and offset timing.
Fig. 3. Experimental results. (A) The net metabolic rate for each condition. Optimal: Minimum mean value of the posterior distribution (metabolic landscape). Validation: Metabolic rate of 5-min walking with optimized assistance. No-suit: Metabolic rate of 5-min walking with a regular pair of pants. Bars are means, error bars are SEMs, and asterisks denote statistical significance. (B) Feasible parameter region and optimal timing values for all participants. Optimal timings were varied across participants, and three participants shared the same optimal timings at the latest peak and offset timing. (C) Optimal assistive force profiles for participants 3, 4, and 6. Dashed and solid lines are reference and measured forces normalized by body mass, averaged across 10 strides during the last minute of the validation condition. The maximum hip flexion event was used to initialize the gait cycle in this study.
Optimal assistive force profile
For the validation condition, the averaged delivered peak force was $215.6 \pm 10.1 \text{ N} (2.84 \pm 0.02 \text{ N kg}^{-1}, \text{ mean} \pm \text{SEM})$ . The average root mean square error of the optimal assistive force tracking of the validation condition was 4.1%. For a clear representation, only three representative optimal force tracking samples with the most different optimal timings from the validation condition are shown in Fig. 4C, whereas all optimal force profiles are shown in fig. S4.
Metabolic landscape and probability of improvement landscape
The representative participant-specific metabolic landscapes (Fig. 4, A to C) further illustrated the interparticipant variability with respect to timings. The participants' metabolic landscapes, represented as Gaussian process posteriors, showed substantial visual differences.
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To quantitatively summarize the differences between the participants' metabolic landscapes, we computed the probability that each participant's optimal parameters would reduce the metabolic cost of other participants according to each participant's posterior landscape (Fig. 4, D to F). This analysis suggested that, in general, one participant's optimal peak and offset timing were likely to be suboptimal for another.
DISCUSSION
With the optimized hip extension assistance obtained from HIL Bayesian optimization, the average net metabolic reduction was 17.4% compared with walking without the device. Using a similar hip exosuit to assist loaded walking, our group previously showed an average reduction of 8.5% compared with an unpowered condition (10). Another study with a tethered hip exoskeleton using pneumatic actuators demonstrated
average metabolic reductions of 10.3 and 9.7% when assisting either hip extension or hip flexion, respectively, compared with an unpowered condition (7). Last, a recent study assisting both hip extension and flexion simultaneously with an autonomous electromechanical hip exoskeleton reported an average metabolic reduction of 21.1% when compared with walking without an exoskeleton (4). The result of this study suggests that substantial metabolic reductions can be achieved by solely assisting hip extension with optimized assistance and indicates the potential improvement of assisting both flexion and extension with hip assistive devices.
The average convergence time of our HIL Bayesian optimization was 21.4 min. Short convergence time could be important in some cases to mitigate widely observed inaccuracies stemming from cardiopulmonary drift and participant fatigue (22). This result also suggests that HIL Bayesian optimization could be applied to wearable devices designed for strenuous activities or clinical populations with limited physical strength—both cases where participant endurance is a limiting factor (23).
The variability shown in the optimized assistance profiles demonstrates the importance of individualization. The participant-specific metabolic landscapes and the probability of improvement generated by the Bayesian optimization further illustrate the interparticipant variability with respect to timings.
The nonparametric HIL Bayesian optimization was more effective than the model-based naïve grid search. We illustrated this problem by generating quadratic approximations with the first 10 iterations of the data from the optimization process, which was the average amount of data needed for the convergence of Bayesian optimization (table S5). The comparison showed that the model-based naïve grid search made unreasonable estimates of optimal parameter value in the high measurement noise environment.
Fig. 4. Participant-specific metabolic landscape and probability of improvement landscape. (A to C) Metabolic landscapes (the mean of the metabolic cost posterior distribution with respect to peak and offset timing) for participants 3, 4, and 6. Diamonds indicate the locations of participant-specific optimal timings. (D to F) Probability of improvement landscapes (capturing the probability of reducing metabolic cost beyond the identified optimal) for participants 3, 4, and 6.
The optimized assistance did not maximize the duration of force to maximize the positive mechanical power for the hip joint. This may be partially because assistance with a late offset timing may hinder hip flexion (32). However, most of the optimal timings for participants were on the boundaries of the parameter ranges, which may suggest that, with a larger parameter search area, further reductions in metabolic cost could be obtained. Currently, the selected parameter range was constrained by the limited ramp-up speed of assistance with our exosuit and a cautious approach to ensure that the assistance profile did not greatly exceed limits of the average range of biological hip extension moment (32). To reduce the likelihood that the optimal values are caught on the boundaries, future studies could expand the feasible parameter range by improving the exosuit stiffness to increase the ramp-up speed of the assistance and having participant-specific search areas based on training performance.
Another limitation of the current optimization is the lengthy sampling time for each measurement, which could prevent straightforward extension to higher dimensional parameterizations. It may be beneficial to add additional flexibility to the optimization not only to choose the exploration points but also to adjust the length of sampling time (33). In addition to adaptive sampling time, it may be useful to use musculoskeletal models to provide an initial estimation of the metabolic landscape, which could reduce the number of samples required to find low-cost parameters. In addition, the smoothness and regularity assumptions imposed by the Gaussian process kernel function may not be valid for all metabolic landscapes and wearable devices, but in our experiments, these landscapes were well approximated using a squared exponential kernel and a single global noise parameter. Last, because Bayesian optimization uses all available data to compute the posterior metabolic distribution and acquisition function, additional methods such as "data forgetting" would have to be used to deal with human adaption effects (34).
HIL optimization holds promise to improve the performance of wearable robotic devices for a wide range of tasks. The presented method shows a substantial metabolic reduction and suggests the possibility of optimizing wearable devices using low-dimensional control parameterization. The short convergence time would enable researchers to apply this method to individualize control parameters during strenuous tasks or for people with limited physical strength or endurance. Using
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a noisy respiratory signal as the objective function of the optimization indicates that this method can be applied to other alternate physiological or biological signals, such as using kinematic symmetry to optimize wearable devices for poststroke patients or using balancerelated measurements to optimize prostheses. The participant-specific metabolic landscapes and probability of improvement landscapes demonstrate the significant variability between participants and suggest that participant-specific optimal timing provides the highest probability of achieving the largest metabolic reduction, further highlighting the benefit of individualization.
MATERIALS AND METHODS
Experimental design
This was a single-day protocol without training sessions. To minimize the effects of adaptation, we recruited eight participants who had previous experience walking with the exosuit at least two times before. Participants walked without load on an instrumented treadmill (Bertec) at 1.25 m s−1 wearing a respiratory measurement device (COSMED; fig. S5). These conditions were chosen partially to lessen fatigue effects of the relatively long walking protocol, and the constant walking speed allowed the comparisons between studies (7, 10, 11). Each participant went through five conditions (fig. S6): (i) a 5-min quiet standing condition, (ii) a 5-min no-suit condition, (iii) a 40-min optimization condition intersected by two 3-min warm-up periods and 5-min rest periods, (iv) a 5-min validation condition with the optimal timing, and (v) a 5-min no-suit condition. Both warm-up periods were assisted walking with the same assistive profiles used in the follow-up iteration of the optimization condition. During the no-suit condition, participants walked with a regular pair of pants (mass, 715 g), which was chosen to assess the metabolic benefits from walking with active assistance to walking with normal clothes, similar to configuration in our previous hip assistance study (10). Resting breaks were given between all conditions besides the break during the optimization condition. Considering the relatively long walking time (61 min), two no-suit conditions were designed at both the beginning and the end of the protocol as a visual check of the possible fatigue reported by the participants.
Participants
Eight healthy male adults (n = 8; age, 30.3 ± 7.1 years; mass, 76.5 ± 8.9 kg; height, 1.77 ± 0.05 m; mean ± SD; table S3) participated in this study. Sample size was chosen based on the data from previous studies (10, 11). The study was approved by the Harvard Longwood Medical Area Institutional Review Board, and all methods were carried out in accordance with the approved study protocol. All participants provided written informed consent before their participation and after the nature and the possible consequences of the studies were explained.
Soft exosuit
The soft exosuit used in this study was designed to solely assist hip extension. The textile components of the hip exosuit consisted of a spandex base layer (mass, 181 g), a waist belt (mass, 275 g; fig. S7), two thigh braces (mass, 2 × 69 g; fig. S8), and two elastic straps (mass, 2 × 46 g) for mounting inertial measurement units (IMUs; mass, 2 × 13 g). Bowden cables and sensor wires including expandable braided cable sleeves for each leg (mass, 2 × 328 g) were tied together at the waist and connected to the actuation platform. The participant supported about half of the weight of the Bowden cable assembly. All textile components (size medium) and half of the weight of the Bowden cable assembly had a total mass of 0.859 kg. The stiffness evaluation of the soft exosuit used in this study is shown in (29).
Actuation platform
A tethered actuation system with two modular actuators was used to generate assistive forces. Each actuator consisted of one customized frameless brushless motor (Allied Motion), a customized spiroid gear set (ITW Heartland), a 90-mm-diameter pulley, and other supportive structures (29). Bowden cable was used to transmit the force from the actuator to the hip joint. On the actuator side, the Bowden cable sheath connected to the frame of the pulley cover and the inner cable attached to the pulley. On the exosuit side, the Bowden cable sheath connected to the anchor point on the bottom of the waist belt and the inner cable connected to the anchor point on the top of the thigh piece. When the actuator retracts, the distance between the two anchor points is shortened, generating a force to assist hip extension.
Sensing and control
Two IMUs (VN-100 Rugged IMU, VectorNav Technologies) attached to the front of each thigh detected the maximum thigh flexion angle to segment the stride (10, 35). Stride time was measured as the time between two consecutive maximum hip flexion events (35). By using the average stride time from
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the previous two steps, the reference force profile was scaled for each stride. The actual force signal was measured by two load cells (LSB200, FUTEK Advanced Sensor Technology) placed in series with the Bowden cables on each leg. Combined with the actuator position signals measured by the encoders (AS5134, Ams) mounted on the back of the customized brushless motors, an admittance controller with feedforward models was implemented to track the force profiles with different peak and offset timings. The detailed controller design, frequency response, and force tracking evaluation with different ramping speeds are presented in (29).
Instantaneous metabolic estimation
The metabolic rate was estimated by fitting a first-order dynamic model to 2 min of transient metabolic data (21). The mathematical representation in the frequency domain takes the form
$$Z(s) = H(s)R(s) \tag{1}$$
where Z(s) is the measured metabolic cost, R(s) is the instantaneous metabolic cost $f^{\text{inst}}$ in frequency domain, and H(s) is the first-order dynamic model $H(s) = 1/(\tau s + 1)$ with a time constant $\tau = 42$ s (31). In the discrete-time domain, Eq. 1 can be written as
$$z(i+1) = \frac{(\tau - dt(i))}{\tau} z(i) + \frac{dt(i)}{\tau} f^{\text{inst}}$$
(2)
where i is the number index of the measured breath and dt(i) is the time duration between the ith and (i+1)th breath. After measuring z and dt for 2 min, we obtained $f^{inst}$ by first calculating the change of the instantaneous metabolic rate from the last condition and then minimizing the error between the model estimation and measurements using least squares (21).
Bayesian optimization
Bayesian optimization is an efficient global optimization method that is particularly well suited to optimizing unknown objective functions that are expensive to evaluate (25–27, 36). It takes advantage of the information provided by the time history by computing a posterior distribution of cost as a function of the optimization variables and then using acquisition functions computed on this posterior to select the next points to evaluate. A prior belief over the objective function distribution is defined using mean and covariance functions. The posterior distribution of the objective function is iteratively computed in closed form when new data become available. Using this model, the algorithm balances exploitation with uncertainty reduction to guide exploration (37).
In our study, we initialized the optimization by evaluating instantaneous metabolic cost $f^{\rm inst}$ for six iterations with different pairs of prefixed peak and offset timing, which were pseudo-randomly selected from evenly spaced timing intervals (fig. S9). This initialization is a common practice to avoid biased sampling that could lead to premature convergence (25). After initial evaluation, the optimization calculated the metabolic landscape, $f(\mathbf{x})$ , using Gaussian processes (30, 34), where the parameter $\mathbf{x} = [x_p, x_o]$ consisted of peak and offset timing. Given the calculated landscape, the next sampling timing was selected by maximizing EI, which naturally balances exploration and exploitation (25, 26). With the metabolic rate of the newly sampled timing added to the data set, the metabolic landscape was refined again for selecting the next sampling timing.
This process was repeated for 14 iterations. In total, there were 20 iterations in the optimization process including 6 iterations of initialization, and fig. S10 shows one sample optimization process described above on iterations 6, 7, and 20.
The metabolic landscape, $f(\mathbf{x})$ , was modeled using a Gaussian process. The prior of the Gaussian process is represented by mean, $\mu(\mathbf{x})$ , and covariance, $k(\mathbf{x}, \mathbf{x}')$ , functions. As is standard practice, we used zero mean and the anisotropic squared exponential kernel for the covariance function (25),
$$k(\mathbf{x}, \mathbf{x}') = \sigma^2 \exp\left(-\frac{1}{2}(\mathbf{x} - \mathbf{x}')M(\mathbf{x} - \mathbf{x}')\right)$$
(3)
where $\sigma^2$ is the metabolic rate (signal) variance and M is a diagonal matrix consisting of the length scale parameters of peak and offset timing, $l_1$ and $l_2$ . Intuitively, the signal variance captures the overall magnitude of the cost function variation, and the length scales capture the sensitivity of the metabolic rate with respect to changes in peak and offset timing. Assuming that metabolic cost has an additive, independent, and identically distributed noise, the samples can be expressed as
$$f^{\text{inst}}(\mathbf{x}) = f(\mathbf{x
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}) + \varepsilon, \varepsilon \sim N(0, \sigma_{\text{noise}}^2)$$
(4)
where $\sigma_{\text{noise}}^2$ is the noise variance. Given the Gaussian process prior and data set D, the posterior metabolic cost distribution $f_^{\text{inst}}$ was calculated for a parameter $\mathbf{x}_$ as $f_^{\text{inst}}(\mathbf{x}_) \equiv f_^{\text{inst}} \sim N(E[f_^{\text{inst}}], s_*^2)$ . The mean and variance are calculated as
$$E[f_^{\text{inst}}] = \mathbf{k}_^T (K + \sigma_{\text{paise}}^2 I)^{-1} \mathbf{y}$$
(5)
$$s_^2 = k(\mathbf{x}_, \mathbf{x}') - \mathbf{k}_^T (K + \sigma{\text{noise}}^2 I)^{-1} \mathbf{k}_*$$
(6)
where $\mathbf{k} = [k(\mathbf{x}1, \mathbf{x}), ..., k(\mathbf{x}_n, \mathbf{x}*)]'$ and K is the positive definite kernel matrix, $[K]_{ij} = k(\mathbf{x}_i, \mathbf{x}_j)$ .
We optimized hyperparameters $(\theta = [\sigma \ l_1 \ l_2 \ \sigma_{\text{noise}}])$ at each iteration by maximizing log marginal likelihood of the data collected $(\mathbf{D} = {\mathbf{X}, \mathbf{y}}, \mathbf{X} = [\mathbf{x}_1, ..., \mathbf{x}_n]^T \in R^{N \times 2}, \mathbf{y} = [f_1^{\text{inst}}, ..., f_n^{\text{inst}}]^T \in R^N)$ using Matlab's fmincon function with 10 random initializations to avoid poor local minima
The peak and offset timing, $x_{\rm p}$ , $x_{\rm o}$ , were selected by maximizing the expected reduction in the metabolic cost over the best timing previously assessed $\max(f_{\rm best}-f_*^{\rm inst},0)$ (25). EI, which balanced between predictive minimum points and high uncertainty (25, 27), took the following form
$$EI[\mathbf{x}] = (f_{best} - E[f_^{inst}])\phi(u) + s_\phi(u_*)$$
(7)
where $f_{\text{best}} = \min_{i=1,\dots,N} \mathrm{E}[f^{\text{inst}}(\mathbf{x_i})], \ u_ = (f_{\text{best}} - \mathrm{E}[f^{\text{inst}}_])/s_, \text{ and } \phi(\cdot)$ and $\phi(\cdot)$ were the cumulative distribution function and probability density function of the normal distribution, respectively. The EI was set to zero when $s_$ was zero. At each iteration, the next sampling timing was selected by maximizing EI using Matlab's fmincon while enforcing the constraint that the offset timing be at least 15% later than the peak timing, $x_o - x_p \geq 15\%$ . We again used 10 random restarts to avoid poor local minima. We note that, as the dimensionality increases, the number
of random restart points required to reliably maximize EI would likely need to increase.
Metabolic measurement and analysis
Respiratory data were collected throughout the protocol. Metabolic rates from the quiet standing, first no-suit, validation, and second nosuit conditions were calculated from the last 2 min of carbon dioxide and oxygen rates using a modified Brockway equation (38). For the optimization process, the instantaneous metabolic estimations for each 2-min measurement period were also collected. Net metabolic rate and net metabolic landscape were obtained by subtracting the quiet standing metabolic rate, then normalizing by each participant's body mass. The metabolic reduction of the validation condition was obtained by subtracting the net metabolic rate of the validation condition from the net metabolic rate of the second no-suit condition and then dividing the result by the net metabolic rate of the second no-suit condition. The second no-suit condition was chosen for the comparison of metabolic reduction because it is the closest no-suit condition to the validation condition. The metabolic reduction of the optimal condition was obtained with the same calculation by replacing the net metabolic rate of the validation condition with the minimum value from the net metabolic landscape generated by the optimization. One participant's data were not included in the metabolic analysis because of fatigue reported by the participant during the
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protocol, where the net metabolic rate of the second no-suit condition increased by 32.4% compared with the first no-suit condition.
Convergence time analysis
The convergence time for each participant was calculated in a post hoc analysis (fig. S3 and table S4). We defined the convergence of the optimization with the following two conditions: (i) Two consecutive iteration-to-iteration changes of maximum metabolic reduction in percentage from the metabolic landscape fell below our preset convergence threshold ( $t_{\rm m}$ = 4%), and (ii) two consecutive iteration-to-iteration changes of hyperparameters from the Gaussian process fell below our preset convergence threshold ( $t_h = 3$ ). The convergence threshold for the changes of metabolic reduction $t_m$ was chosen based on the previous study (8), which has shown an average error of 4% on this instantaneous metabolic estimation. The convergence threshold $t_h$ was obtained from a separate simulation study. For this simulation, a generative model of metabolic landscape with added noise was first created. The noise was generated by Matlab's awgn function with a signal-to-noise ratio of 8.8 obtained from our pilot test (table S1). With this model, we ran Bayesian optimization for 50 iterations and calculated the iteration-to-iteration changes in the maximum metabolic reduction and the hyperparameters. The maximum changes for the metabolic reduction were set to 2% while evaluating the changes of all hyperparameters. We repeated the simulation 100 times and found that the metabolic reduction threshold was met when the threshold for all hyperparameters was set to 3.
Ground reaction force
Ground reaction forces (GRFs) were collected via the instrumented split-belt treadmill (Beltec) and synced with the actuation platform using the motion capture system (Qualisys AB). All the GRF force data were filtered with a zero-lag fourth-order low-pass Butterworth filtered with a 5- to 15-Hz optimal cutoff frequency that was selected using a custom residual analysis algorithm (32). A customized Matlab script was created using GRFs to segment the percentage of the gait cycle defined by the maximum hip flexion based on the detected heel strikes.
Statistics
Means and SEM of the net metabolic rate were calculated for each condition. According to the Jarque-Bera test (significance level $\alpha=0.05$ ; Matlab), the collected data followed the normal distribution (P>0.3). Therefore, we conducted a mixed-model, two-factor analysis of variance (ANOVA; random effect, participant; fixed effect, test condition to test the effect across different conditions including optimal, validation, and no-suit conditions (significance level $\alpha=0.05$ ; Matlab). For the outcome of the ANOVA test, it showed a significant difference of the net metabolic rate between conditions. We used paired t tests for the comparison between the conditions to identify which conditions exacted a significant change in the net metabolic rate (39).
SUPPLEMENTARY MATERIALS
robotics.sciencemag.org/cgi/content/full/3/15/eaar5438/DC1
Fig. S1. Illustration of 1D Gaussian process.
Fig. S2. Simulation results on the number of iterations needed for the optimization.
Fig. S3. Convergence analysis.
Fig. S4. Optimized hip extension force profiles for all participants.
Fig. S5. Experimental setup.
Fig. S6. Experimental protocol.
Fig. S7. Structure of the waist belt component.
Fig. S8. Structure of the thigh brace.
Fig. S9. Pseudo-randomly sampled timings for the initialization of Bayesian optimization.
Fig. S10. Optimization process.
Table S1. Signal-to-noise ratio and variations of metabolic cost of pilot tests.
Table S2. Onset timing.
Table S3. Participant characteristics.
Table S4. Metabolic rates, optimal timing, and convergence timing for each participant.
Table S5. Quadratic approximation of metabolic landscape.
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The Effect of Hip Assistance Levels on Human Energetic Cost Using Robotic Hip Exoskeletons
Inseung Kang ®, Hsiang Hsu ®, and Aaron Young, Member, IEEE
Abstract—In order for the lower limb exoskeletons to realize their considerable potential, a greater understanding of optimal assistive performance is required. While others have shown positive results, the fundamental question of how the exoskeleton interacts with the human remains unknown. Understanding the optimal assistance magnitude is not simply relevant for control, it is a critical knowledge for exoskeleton designers. An accurate understanding of assistance levels will enable the designers to minimize exoskeleton mass and improve the performance by avoiding excessive actuators and drivetrains. We explored the relationship between the assistance magnitude and the energetic cost benefits by using a series elastic actuator driven powered hip exoskeleton. The exoskeleton controller mimics a human biological hip moment to provide the assistance during the gait cycle. Ten able-bodied subjects walked using the exoskeleton with different magnitudes of assistance in both hip flexion and extension. Generally, the resulting metabolic cost across different assistance conditions showed a U-shape trend which was consistent across all subjects (p < 0.01). The interpreted optimal assistance point through the quadratic fit resulted in a 6% metabolic cost reduction with respect to the noassistance condition. The study validated that simply increasing the assistance level did not yield higher energetic return.
Index Terms—Wearable robots, human performance augmentation, robotic exoskeleton, energetic cost, hip orthosis.
I. INTRODUCTION
OWER limb exoskeleton technology has advanced greatly in the recent years and showed significant value in different applications [1]–[3]. Most of these technologies can be broken down into three main categories: industry settings, military purposes, and healthcare environments [1]. Several exoskeletons have been developed for industry usages where factory workers wear an exoskeleton suit to enhance physical strength to alleviate work load when lifting heavy weights [4], [5]. Another usage of exoskeleton technology is in the military settings where an exoskeleton can assist a soldier in safely and efficiently carry a
Manuscript received July 18, 2018; accepted December 14, 2018. Date of publication January 4, 2019; date of current version January 16, 2019. This letter was recommended for publication by Associate Editor R. V. Patel and Editor A. Young upon evaluation of the reviewers' comments. This work was supported in part by the Georgia Tech Research Institute (GTRI) IRAD funding, in part by the Institute for Robotics and Intelligent Machines (IRIM) Seed Grant at Georgia Tech, and in part by the NSF NRI Award #1830215. (Corresponding author: Inseung Kang.)
The authors are with the Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA (e-mail: ikang7@gatech.edu; hhsu24@gatech.edu; aaron.young@me.gatech.edu).
This letter has supplementary downloadable multimedia material available at http://ieeexplore.ieee.org, provided by the author. This includes a video file, which includes three parts about the powered hip exoskeleton device. This material is 41.1 MB in size.
Digital Object Identifier 10.1109/LRA.2019.2890896
heavy load over long such as when a solider would carry heavy loads while walking over long distances [6], [7]. Lastly, exoskeletons are used in the healthcare environment as an assistive device for patients with disabilities such as stroke, spinal cord injury, and muscular dystrophy [8]–[10]. Patients using these technologies in healthcare settings can not only regain mobility options, but also potentially benefit from long-term rehabilitation strategies [11]. Some of these exoskeletons such as Indego [8], Rewalk [9], and Ekso [12] have been commercialized in the market for medical applications. These devices frequently feature actuators at every joint, which makes the devices heavy and challenging to control. While these devices may benefit patients with a complete lower limb paralysis, their benefit for less impaired subjects remains less clear [13].
To accommodate such limitations of full body exoskeletons, several research and industry groups started to develop single joint actuated exoskeletons that are more suitable to both ablebodied humans and patients with partial gait disability (i.e., stroke survivors) [14]–[17]. Often these exoskeletons have targeted the ankle due to the joint providing a high mechanical power during walking. Several ankle exoskeletons were able to show positive results in achieving higher metabolic benefits when walking with assistance at the ankle joint [14], [18]. Recent literature studies have shown that the hip joint also plays a leading role in providing high mechanical power, up to 45%, during walking [19]. The ankle joint efficiently utilizes the Achilles tendon unit in
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storing the mechanical energy to perform positive joint power. However, due to different muscle characteristics and the lack of efficient elastic storage elements, the hip joint requires higher energetic cost for similar mechanical joint power [20]. Therefore, the hip joint represents an important area of exploration for engineers trying to increase human metabolic performance. Some of the hip exoskeletons that have been developed have shown positive outcomes [17], [21]–[25]. These exoskeletons are either autonomous with relatively low assistance levels or tethered to off board actuators to provide high magnitudes of assistance. Regardless, the majority of these devices have the same goal of achieving the best metabolic cost reduction. However, there is still a gap in understanding more in-depth relationships between energetic benefits and assistance
The three key parameters that may contribute to the exoskeleton controller are onset timing, assistance duration, and assistance magnitude. Utilizing the assistance duration from the literature study [26], our previous work optimized the assistance onset timing for hip flexion and extension to achieve best metabolic cost reduction [27]. However, as the study provided a fixed magnitude of torque applied at the hip joint, it did not capture the effect of assistance magnitude in respect to the metabolic cost benefits. Thus, an extended study was required
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Fig. 1. Powered bilateral hip exoskeleton design. (A) The orthotic thigh shells, pelvic band, and shoulder straps can be adjusted to accommodate different body sizes. (B) Exoskeleton device consists of multiple sensors and actuators. (C) The brushless DC motor drives a timing belt pulley to extend and retract the ball screw transmission (orange) where the motor housing (red) pivots around the hinge to create torque around the output hip joint (green). Deflection at the fiberglass spring provides corresponding measurement of the output torque.
to understand the effect of magnitude changes when providing assistance during walking using a hip exoskeleton.
This letter provides three core contributions to the field of assistive lower limb robotics. This letter presents a novel hip exoskeleton (Fig. 1A) utilizing a ball screw driven series elastic actuator (SEA) for power assistance at the hip joint in both hip flexion and extension along the sagittal plane. The device achieves a high fidelity closed loop torque control with a measurement of fiberglass spring deflection. This device presents an excellent test-bed for understanding assistance levels. Secondly, this letter presents a novel controller design that mimics a human biological hip torque profile during the gait cycle. The proposed controller is capable of applying different control parameters such as assistance onset timing, duration, and magnitude with the aid of different mechanical sensors on the device. Thirdly, this letter rigorously tests the design and controller through a ten human subject test to determine the effects of assistance level on energetic cost savings. These results highlight the experimental value of our test-bed system and illustrate that an optimal assistance magnitude indeed exists.
The overall goal of our work is to determine the optimal assistance level applied at the hip joint using a powered exoskeleton during walking. The in depth understanding of relationship between the hip assistance levels and energetic cost savings using an exoskeleton will aid the field to move forward in developing an optimal exoskeleton device. We hypothesize that the increase of exoskeleton assistance provided at the hip joint will off load the work done by the hip flexor/extensor hence, reducing the metabolic cost of walking.
II. POWERED HIP EXOSKELETON DESIGN
We designed a bilateral hip exoskeleton device (Fig. 1B) to apply torque at the user's hip joint during walking. The overall mass of the device is around 7 kg where the main components of the device are actuators (1.5 kg each), main frame structure (2 kg), orthosis (1.5 kg for both waist band and thigh cuffs), and the on board electronics (0.5 kg). The device is capable of providing a peak torque of 60 Nm and a maximum continuous torque of 30 Nm with an angular velocity up to 180 °/sec. The desired exoskeleton peak and maximum continuous torque parameters were derived using Eq. 1 and Eq. 2 based on the biomechanic data [28]–[30] where $\tau(v)$ is the human biological hip moment over one gait cycle, v is the walking speed, m is the subject's body mass, and n is the number of moment data
points over one gait cycle.
$$\tau(v){peak} = \frac{m}{2} \left( |\tau{\min}(v)| + \tau_{\max}(v) \right) \tag{1}$$
$$\tau(v){cont} = m\sqrt{\frac{\sum{i=1}^{n} \tau(v)_i^2}{
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n}}$$
(2)
Using the both equations, our device can support approximately 90% of peak and maximum continuous torque for an average body mass of 70 kg subject walking at 1.2 m/s. The device allows 100° and 30° range of motion in the sagittal plane for maximum hip flexion and extension respectively. Additionally, a passive hinge joint allows for 15° of movement for both hip ab/adduction along the frontal plane. The entire device has three different attachment points to the user: orthotic thigh shell, pelvic band, and shoulder straps. Each attachment point can be adjusted to accommodate different body sizes.
A. Mechatronic Design
The powered bilateral hip exoskeleton consists of two ball screw driven series elastic actuators (SEAs) (Fig. 1C). The motor torque is initially speed reduced with a 2:1 timing belt transmission where the output torque is converted into a linear force with the ball nut travelling along the ball screw shaft with a carbon fiber tube attached to it. The ball screw transmission was chosen because it provides high efficiency and back drivability in a light weight package [31]. The entire actuator rotates along the pivot point located at the motor housing as the actuator extends or retracts. Lastly, the carbon fiber actuator is coupled in series with a fiberglass leaf spring where the deflection of the spring is measured with a set of strain gauges mounted in a form of full Wheatstone bridge. The use of a fiberglass spring enables reduced mass [32]. Each SEA is mounted to a main C-shaped frame made of carbon fiber, which ensures the orientation of the device is upright when the user is fitted. The user interface, which includes the thigh orthosis, the pelvic band, and the polycarbonate back plate, is attached to the main frame. The back plate holds the electronics as well as shoulder straps.
The 200 W brushless DC motor rated at 36 V (EC 30, Maxon Motor) is controlled with a single board computer (myRIO, National Instrument). The myRIO is equipped with a FPGA chip for a closed loop torque control with a PD controller using the spring deflection reading measured with from the strain gauge (Omega Engineering). A servo driver (ESCON 50/5 Module, Maxon Motor) operates in current control mode and uses a Hall
Fig. 2. Control system architecture of the exoskeleton device. On board computer interacts with different mechanical sensors on the device for high level control and commands the desired torque in currents to a servo driver for a low level closed loop torque control.
effect sensor and an incremental motor shaft encoder for commutation. Both actuators are powered by two 18.5 V lithium polymer batteries (Venom Power) connected in series. A 14-bit absolute magnetic encoder (Orbis, Renishaw) is used to measure the hip joint angle. Three inertial measurement units (IMUs) (Micro USB, Yost Lab) are also mounted on the device. Two IMUs are placed bilaterally on each thigh and one is on the back unit to measure the limb and trunk orientation during walking. Lastly, force sensitive resistors (FSRs) are placed on each heel of the user to detect the heel contact during walking. An additional custom made printed circuit board is used for reading and filtering the analog sensor signals such as strain gauge amplifier for spring measurements. All of the on board mechanical sensor data are collected by myRIO for high and mid-level control such as estimating the gait phase and generating the torque assistance profile.
B. Controller Design
The exoskeleton device control layer is broken down into three tiers for its purpose: high, mid, and low-level layers (Fig. 2). The high-level layer implements an algorithm to estimate the user's state such as gait phase. This aspect is critical as it provides information regarding the timing for power assistance. While it is mainly used for estimating the gait phase in this study, this layer can be enhanced with additional control algorithms such as classifying the user's intent with machine learning
Fig. 3. Example of a commanded torque profile for a biological torque controller. Control profile (shown in purple) emulates a percentage of human biological hip moment (shown in green) over a gait cycle. Hip flexion (red region) and extension (blue region) assistance onset timing, duration, and magnitude (shown with different type of arrows) can be tuned for a desired profile.
techniques. The mid-level layer dictates the device dynamic performance. This layer can implement different dynamic controllers used in the literature such as admittance, position, and myoelectric control [22], [33], [34]. For this study, our exoskeleton incorporates a torque controller where the commanded torque profile is generated with given timing and magnitude parameters with additional user state information computed from the high-level layer. Lastly, the low-level layer ensures that the output torque meets the desired torque by applying a closed loop torque control.
Our biological torque controller mimics the human biological hip moment profile (Fig.
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3). Over a gait cycle, the controller can generate a torque assistance for both hip flexion and extension with predefined control parameters. The three key parameters that dictate the assistance profile are onset timing, assistance duration, and assistance magnitude. The onset timing parameter was used with values found from our previous work [27] which was 45% and 90% of the gait cycle for hip flexion and extension respectively (where 0% is defined as heel contact). Assistance duration was optimized with an initial pilot test. Lastly, assistance magnitude can be changed relative to percentage of peak human biological hip moment during the gait cycle [29]. The peak biological hip moment value was normalized to the user's bodyweight to provide appropriate assistance magnitude.
The biological torque controller (Eq. 3) intakes a gait phase percentage, x, as an input and outputs a commanded torque, f(x), where of and oe are flexion and extension onset timing respectively and d is the assistance duration all relative to the gait phase.
$$f(x) = \begin{cases} -g\left(x - o_f\right), & o_f \le x < \operatorname{mod}\left(\left(o_f + d\right), 100\right) \ g\left(x - o_e\right), & o_e \le x < \operatorname{mod}\left(\left(o_e + d\right), 100\right) \ 0, & \text{otherwise} \end{cases}$$
(3)
g(z)represents a function generating a single trapezoidal profile (Eq. 4) with a desired assistance magnitude u, input phase z, assistance u starting and ending set point $s_1$ and $s_2$ respectively, all relative to the gait phase. The assistance magnitude u (Eq. 5) is computed using the desired assistance level a (%) and the peak human biological hip moment, $\tau(v)_{peak}$ , calculated from Eq. 1.
$$g(z) = \begin{cases} \frac{uz}{s_1}, & 0 \le z < s_1 \ u, & s_1 \le z < s_2 \ -\frac{u(z-s_2)}{d-s_2} + u, & s_2 \le z < d \end{cases}$$
(4)
$$u = a\tau(v)_{peak} \tag{5}$$
During the gait cycle where the assistance is not provided, the device is put into zero impedance mode which is simply generating the interaction torque that is measured between the user and the actuator output. Due to the gear reduction stage in the mechanical transmission in the SEA, it exerts non-negligible interaction torque to the user when walking which hinders natural movement. To minimize this resistance, the device outputs an equal amount of torque to allow the user to move the limb freely, hence called zero impedance mode. A video of a subject walking in both assistance and zero impedance mode is included in the supplemental material.
As the biological torque controller is heavily dependent on the gait cycle for generating the correct assistance profile, it is critical to estimate the gait phase accurately in real time. We utilized the FSR sensor to estimate the user's gait phase during walking. While walking, the myRIO stores the timestamp when the heel contact occurs through the FSR sensor readings. From this, a stride time was calculated by taking the time difference between the heel strikes. Using the previous five stride times, we calculated the average stride duration. Finally, the time since the most recent heel contact was divided by this average stride duration in order to compute the current gait phase in percentage [35].
III. INITIAL HUMAN CHARACTERIZATION
An initial study was conducted to characterize the device performance. During this process, several key factors contributing to the device performance were observed: the device impedance in terms of actuator interaction torque, controller performance in terms of zero impedance mode compensating the interaction torque, and the low-level controller performance regarding torque tracking of the closed loop torque control.
A. Exoskeleton Human Performance Characterization
We conducted a pilot test where three able-bodied subjects (body mass of 71.3 $\pm$ 5.5 kg) walked on a treadmill at 0.4 m/s with the exoskeleton to analyze the controller's capability in compensating the interaction torque during zero impedance mode. During this testing, we collected the user's metabolic cost of walking to observe the zero impedance mode performance in terms of human energetics. The low treadmill speed was mainly due to the limitations of walking with the device powered off. When the device is powered off, the actuator has a certain impedance (interaction torque), mainly from the gear transmission and friction, which impedes the user's hip movement. The treadmill speed was chosen carefully so that the user could still easily walk normally. Overall, the user walked in four different conditions: exoskeleton powered off, actuator off (exos
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keleton without the SEA), exoskeleton in zero impedance mode, and no exoskeleton condition. We have added the actu-
Fig. 4. Initial human characterization results of the exoskeleton device. (A) Actuator interaction torque compensation. When the actuator operates with zero impedance mode, the interaction torque (shown in purple) that is exerted due to mechanical impedance of the transmission in the SEA was greatly reduced compared to the unpowered mode. (B) Hip joint kinematics across different actuator conditions. Actuator off condition is where the spring is disconnected from the output hip joint to allow the user to freely move the hip joint without any impedance.
ator off condition where the spring linkage was disconnected from the transmission so that the actuator output does not exert any interaction torque to the user. This condition can provide an additional baseline information (along with no exoskeleton condition) to compare the controller performance with the exoskeleton mass added to the user (but not the impedance). The average metabolic costs of walking, after subtracting out the resting metabolic cost, were measured to be 1.92 $\pm$ 0.25 W/kg, $1.33 \pm 0.13$ W/kg, $1.59 \pm 0.13$ W/kg, and $0.75 \pm 0.04$ W/kg for exoskeleton powered off, actuator off, exoskeleton in zero impedance mode, and no exoskeleton condition respectively. It was observed that the powered off condition can increase the net metabolic cost nearly twice compared to the no exoskeleton condition. According to the literature studies, theoretical increase of metabolic cost of walking can be evaluated with the exoskeleton mass added [36], [37]. Since the exoskeleton mass added to the user can be represented as the actuator off condition, metabolic cost result comparison between zero impedance mode and the actuator off condition could validate whether the zero impedance mode can be used as a baseline condition. While the zero impedance mode did not yield the same metabolic cost
Fig. 5. Torque tracking of the assistance torque profile of the gait cycle. A 10 Nm torque was assisted to the user during walking with predefined control parameters (onset timing and assistance duration). The overall mean RMS error was calculated to be 2.15 Nm over a gait cycle.
reduction as the actuator off condition (mainly due to the residual torque in zero impedance mode), it was capable of reducing the metabolic cost vastly and compensated the impedance caused from the actuator. While these metabolic cost measurements cannot be utilized directly in the main experiment mainly due to difference in walking speed, this validation process allowed to quantify the exoskeleton actuator performance in terms of metabolic cost.
The metabolic cost compensation from the zero impedance mode aligned well with the kinetic compensation results (Fig. 4). The RMS interaction torque between the exoskeleton and the human user was reduced from 4.66 Nm to 0.94 Nm using the zero impedance controller during walking (Fig. 4A). During this pilot experiment, more in depth characterization of the actuator behavior was investigated by observing how the interaction torques affect the human gait biomechanics during walking, specifically the hip joint angle (Fig. 4B). The pilot results showed that the actuator output produces non-negligible interaction torque to the user. Moreover, this interaction torque showed that it impedes the user significantly and causes them to reduce the hip joint's range of motion. This was demonstrated in that the peak hip flexion and extension angles were both reduced by 5° each. However, with zero impedance mode, the user's kinematics were closely consistent with the actuator physically disconnected. This illustrates the importance of effective zero impedance mode.
Another preliminary assessment of the device design was to quantify torque tracking of the desired torque with the actual interface torque (Fig. 5). This can be validated by observing the low-level control performance with torque tracking during assistance mode. During the pilot testing, a user was assisted with 10 Nm for both flexion and extension with prechosen controller parameters (onset timing and assistance duration) while walking on a treadmill at 0.4 m/s for 2 minutes. The assistance profile in terms of actual torque measured followed the desired torque correctly validating that the desired torque was assisted. Overall, the RMS error over the 2 minute trial compared to the desired torque profile was 2.15 Nm. A video displaying the low-level torque tracking with hip assistance is included in the supplemental material.
Fig. 6. Experimental setup of the exoskeleton device testing. The user is fitted with a metabolic mask to measure the energy expenditure while wearing the hip exoskeleton.
B. Assistance Duration Optimization Characterization
A pilot test was conducted to determine the optimal duration of hip flexion and extension for the controller. The subject walked on the treadmill with 0.8 m/s walking speed for six minutes with 26% of the subject's bodyweight for assistance magnitude for both hip flexion and extension. The
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assistance duration window length was swept from 20% to 35% of the gait cycle with a 5% increment. The metabolic cost reduction for each condition was 6.2% for 20%, 14.6% for 25%, 11.2% for 30%, and 11.0% for 35% all relative to metabolic cost of walking in zero impedance mode. As the 25% window length achieved the highest metabolic cost reduction, the value was used for both hip flexion and extension assistance duration for the main experiment.
IV. HUMAN SUBJECT TESTING
A. Experimental Design
The study was approved by the Georgia Institute of Technology Institutional Review Board, and informed written consent was obtained for all subjects. Ten healthy subjects (seven males and three females) with an average age of 22.4 $\pm$ 2.0 years, body mass of $70.6 \pm 8.6$ kg, and height of $1.73 \pm 0.1$ m were recruited. The subjects were asked to walk on the treadmill (TuffTread) for six minutes at 0.8 m/s walking speed in four different assistance conditions where one of them was the zero impedance mode (Fig. 6). The other three assistance conditions are 13%, 26%, and 40% of the peak hip flexion/extension moment based on subject's bodyweight at 0.8 m/s walking speed [29]. The walking speed was set as 0.8 m/s due to device limitation in providing high torque at faster walking speeds. Other control parameters such as onset timing (45% and 90% of flexion and extension) and assistance duration (25% of the gait cycle) were fixed throughout the entire experiment for assistance conditions. During all walking conditions, metabolic cost of walking was measured using an indirect calorimetry system. Before subjects began walking, we measured their resting metabolic rate for 3 minutes while they stood still wearing the exoskeleton. The metabolic cost was calculated using the modified Brockway equation [38] for the last 3 minutes of each six-minute trial to determine the metabolic energy expenditure. Each walking measurement was subtracted with the metabolic cost of a
| AssistanceLevel (%) | Joint Kinematic | | | | Joint Torque | | | |
|-------------------------|---------------------|-----------------------|---------------------|--------------------------|----------------------------|-------------------------|---------------------------|------------------------------------------|
| | Peakflexion (°) | Peakextension (°) | Range of motion (°) | Peak flexion torque (Nm) | Peak extension torque (Nm) | RMS flexion torque (Nm) | RMS extension torque (Nm) | Net RMS torque overa gait cycle (Nm) |
| 0 | 32.07 | -5.06 | 37.13 | 1.41 | 0.95 | 0.76 | 0.61 | 0.55 |
| 13 | 33.37 | -5.43 | 38.8 | 4.82 | 4.14 | 3.41 | 2.31 | 2.87 |
| 26 | 35.37 | -4.24 | 39.62 | 8.95 | 8.73 | 6.95 | 6.23 | 6.04 |
| 40 | 36.33 | -4.16 | 40.5 | 12.81 | 13.37 | 10.24 | 9.83 | 8.89 |
TABLE I
KINEMATIC AND KINETIC RESULTS ACROSS DIFFERENT EXOSKELETON ASSISTANCE LEVELS
All of the joint kinematic and kinetic results are represented with an averaged value across 10 subjects. Flexion and extension joint torques were decoupled by computing the torque during flexion ( $45\% \sim 70\%$ ) and extension ( $90\% \sim 15\%$ ) region of the gait cycle. For zero impedance mode, flexion and extension torque were computed respect to 0 Nm to calculate the residual interaction torque.
Fig. 7. Metabolic cost result with different assistance magnitude during walking. Generally, increase of assistance magnitude achieved decrease in net metabolic cost of walking except for the highest assistance condition (40% condition) where the metabolic cost increased. The quadratic fit of the metabolic result computed that the maximum metabolic cost can be benefited with 6% reduction from the zero impedance mode with 20% assistance magnitude. Error bar in the graph represents +/- 1 SEM.
resting condition. Additional biomechanic data such as the hip joint torque and angle were
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measured using the device's SEA and encoder during walking in each condition.
All of the joint kinematic and kinetic results are represented with an averaged value across 10 subjects. Flexion and extension joint torques were decoupled by computing the torque during flexion ( $45\% \sim 70\%$ ) and extension ( $90\% \sim 15\%$ ) region of the gait cycle. For zero impedance mode, flexion and extension torque were computed respect to 0 Nm to calculate the residual interaction torque.
A regression analysis was run to the overall metabolic cost of all subjects across different assist conditions to observe a general trend. Both linear and quadratic fits were run where each coefficient of determination $(R^2)$ was calculated to evaluate the goodness of fit. Furthermore, a pairwise t-test was conducted by calculating the goodness of fit for both linear and quadratic fit to observe if this trend is repeatable across all subjects by setting $\alpha$ to 0.05.
V. RESULTS
Across the different assistance conditions, general trend showed that there was a U-shaped trend where the global optima for the lowest metabolic cost were in between the 13% and 26% conditions (Fig. 7). For the average metabolic cost results, a quadratic and a linear fit had the $R^2$ value of 0.869 and $9.38 \times 10^{-5}$ respectively. A pairwise t-test result showed a
Fig. 8. Average hip kinematics across subjects during different magnitude of assistance levels. Darker shades represent increase of assistance level. With higher assistance magnitude, peak hip flexion angle increased.
statistical significance of the $R^2$ of a quadratic fit to linear fit (p < 0.01). Using the quadratic fit to the metabolic cost model, theoretical maximum reduction of metabolic cost was computed to be 6% reduction compared to zero impedance mode. The RMS torque that was applied to the user during the flexion and extension region linearly scaled with different assistance levels while maintaining relatively constant residual interaction torque and showed that similar amount of assistance were provided for both regions during the gait cycle (Table I). Additionally, a post hoc analysis was conducted to compute the continuous torque that was applied to the user over a gait cycle for each assistance levels (normalized by the walking speed) which was 3.59 Nm/m·s-1 for 13%, 7.55 Nm/m·s-1 for 26%, and 11.11 Nm/m·s-1 for 40% respectively. Using the computed torque values, normalized continuous torque over a gait cycle at 20% was found to be $5.62 \,\mathrm{Nm/m \cdot s^{-1}}$ , which is what the study supports as the optimal continuous torque level for exoskeleton design.
Hip joint kinematics changed with varying levels of assistance magnitude (Fig. 8 and Table I). During the first part of stance phase (from 0% to 15% of the gait cycle), there was an excessive hip extension with the increase of assistance magnitude. The average RMS error of hip kinematic deviation in the early stance across subjects was 1.21° for 13%, 2.57° for 26%, and 3.96° for 40% compared to the zero impedance mode. For the remaining early stance (up to 30% of the gait cycle), the hip kinematics returned to the normal hip joint trajectory. In late stance (right before the push off), the hip kinematic started to deviate again where the increase of assistance resulted in higher
hip flexion. Especially when transiting to the mid swing (around 80% of the gait cycle), the peak hip flexion angle increased significantly with higher assistance. The average peak hip flexion across subjects increased 4% for 13%, 10.7% for 26%, and 15% for 40% assistance compared to zero impedance mode where the peak flexion occurred at approximately 85% of the gait cycle. Moreover, the average hip joint range of motion across subjects increased 4.49% for 13%, 6.71% for 26%, and 18.93% for 40% assistance compared to zero impedance mode. The quadratic fit best represented the resulting hip range of motion with different assistance levels (R2 = 0.962).
Additionally, the excessive hip flexion (Especially in the 40% assistance condition) caused the subject to walk in a marching gait pattern. This gait pattern increased the overall stride frequency linearly with the increase of assistance levels. The average stride frequency across subjects was 0.75 stride/sec for zero impedance, 0.78 stride/sec for 13%, 0.81 stride/sec for 26%, and 0.84 stride/sec for 40% assistance. The linear regression showed that the assistance level and stride frequency indeed have a linear
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relationship (R2 = 0.999). The stride frequency in zero impedance mode correlated well with human biomechanics data with the same walking speed [28]. A video of a subject walking in a marching gait pattern with hip assistance at maximal levels is included in the supplemental material.
VI. DISCUSSION
Overall, our exoskeleton was able to show a positive result in achieving metabolic cost benefits with the increase of assistance level. Our study resulted in a similar metabolic cost reduction (6% when optimized) compared to other recent exoskeleton studies [21], [25], [39]. For example, Seo et al. utilized an adaptive oscillator controller that generated a torque profile similar to our biological torque controller and was able to achieve a substantial amount metabolic cost reduction (∼13%) compared to no exoskeleton condition using a lightweight hip exoskeleton [21]. Ding et al. was also able to achieve a considerable amount of metabolic cost reduction (between 5.7∼8.5%) with cable driven hip extension assistance compared to unpowered condition [25]. The range of metabolic cost benefit differences across the studies were mainly due to other confounding factors such as the device structure and controller architecture.
While providing hip assistance resulted a metabolic cost reduction, our initial hypothesis was rejected in that increase of assistance level did not yield higher metabolic cost reduction. The resulting U-shaped trend of metabolic cost provides an important information that there is an optimum for exoskeleton assistance to attain the best metabolic cost benefits. Our study resulted in a similar quadratic trend as the relevant literature study using the ankle exoskeleton [40]. While the study may not directly correlate with our work (as the ankle joint has different musculotendon structure than the hip joint), the general results aligned that excessive assistance at the joint may penalize both mechanically and biologically. Similar to the literature studies on assistance timing study [26], [27], the assistance magnitude should be optimized for best energetic savings rather than just being set as high as physically possible. Moreover, while it was outside the scope of this study, a possible future work can observe the energetic effect of hip assistance when the magnitude ratio of extension to flexion varies to fully optimize the hip assistance levels.
Mainly we observed that larger assistance magnitudes biased the hip kinematics in the flexion direction during swing phase (Fig. 8). This excessive hip flexion induced a marching gait which increased the user's stride frequencies. Generally, increased stride frequencies in marching gait will direct the user to take shorter steps. Considering the stance phase as an inverted pendulum motion, positive work at the center of mass is required to restore the energy lost during the collision occurring at the heel contact [41], [42]. As increase in the exoskeleton assistance decreases the user's step length, overall negative work done through the collision gets reduced hence, higher metabolic cost reduction.
On the other hand, the increase of stride frequencies in higher assistance levels penalize the net metabolic cost. Along with stride frequencies, results showed that the hip joint range of motion exhibited quadratic growth with increase of assistance levels which will force the subject to have a faster leg swing. Literature studies have shown that increase in the stride frequencies correlates with faster swinging leg motion where muscle fibers are required to produce larger forces at short durations. Overall, this will result in a higher metabolic cost due to the low economy muscle generating the required force over short time [43], [44]. Two main factors relating to increase in assistance, stride frequencies and collision time, direct the metabolic cost in an opposite direction which explains the reason for achieving a general U-shaped trend for the resulting metabolic cost where ideally the cross over point of two factors is the optimal assistance magnitude that attains highest metabolic cost reduction.
Our findings in regard to optimal assistance levels provide valuable information about the exoskeleton design. For example, computed continuous torque to achieve the best metabolic cost benefits can help future exoskeleton designers to optimize the actuator specification. Furthermore, the non-negligible energy loss through the user interface should be investigated more as it may have affected the result. The hip kinematic deviation occurring at the early stance phase occurred due to the soft tissue of the limb segment. This dampening effect in the limb limits the exoskeleton by delaying the assistance applied at the skeletal structure. Lastly, further exploration in the interaction between control parameters such as integrating the human-inthe-loop optimization may be useful [18], [24]. This approach can improve the exoskeleton controller by having the control parameter scale to the user's state such as the user's stride frequencies. Through this, the dynamic controller may be able to accommodate the assistance in a stride by stride basis.
VII. CONCLUSION
Our powered hip exoskeleton showed that the metabolic cost reduction does not correlate linearly with assistance magnitude. The underlying biomechanical effects in the user during exoskeleton assistance resulted in a U-shaped trend in the metabolic cost. The exhibited exoskeleton behavior illustrated the importance of understanding human robot interaction. Moreover, as our result showed that additional levels of support are undesirable, there are clear ramifications for system design
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. Future exoskeleton designers can utilize our findings to further investigate to optimize the mechatronic design for a more robust and versatile exoskeleton. Lastly, implementation of an integrated controller capable of scaling parameters dynamically may aid the exoskeleton technology to be translated to more realistic settings such as outdoor environments.
ACKNOWLEDGMENT
The authors would like to thank Dr. G. Kogler for his insights in designing the orthotic interface, C. Kilpatrick and S. E. Lee for their help in fabricating the interface, and J. Li and R. Hong for data collection. The authors would also like to thank C. Bivens and M. Mayo at Georgia Tech Research Institute for their contributions.
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RESEARCH ARTICLE
Comparing optimized exoskeleton assistance of the hip, knee, and ankle in single and multi-joint configurations
Patrick W. Franks\* , Gwendolyn M. Bryan, Russell M. Martin , Ricardo Reyes, Ava C. Lakmazaheri and Steven H. Collins
Department of Mechanical Engineering, Stanford University, Stanford, California, USA
*Author for correspondence: Patrick W. Franks, Department of Mechanical Engineering, Stanford University, Stanford, California, USA. Email: pwfranks23@gmail.com
Received: 11 May 2021; Revised: 13 September 2021; Accepted: 20 October 2021
Key words: biomechanics; exoskeleton; human-in-the-loop optimization
Abstract
Exoskeletons that assist the hip, knee, and ankle joints have begun to improve human mobility, particularly by reducing the metabolic cost of walking. However, direct comparisons of optimal assistance of these joints, or their combinations, have not yet been possible. Assisting multiple joints may be more beneficial than the sum of individual effects, because muscles often span multiple joints, or less effective, because single-joint assistance can indirectly aid other joints. In this study, we used a hip–knee–ankle exoskeleton emulator paired with human-in-the-loop optimization to find single-joint, two-joint, and whole-leg assistance that maximally reduced the metabolic cost of walking. Hip-only and ankle-only assistance reduced the metabolic cost of walking by 26 and 30% relative to walking in the device unassisted, confirming that both joints are good targets for assistance (N = 3). Knee-only assistance reduced the metabolic cost of walking by 13%, demonstrating that effective knee assistance is possible (N = 3). Two-joint assistance reduced the metabolic cost of walking by between 33 and 42%, with the largest improvements coming from hip-ankle assistance (N = 3). Assisting all three joints reduced the metabolic cost of walking by 50%, showing that at least half of the metabolic energy expended during walking can be saved through exoskeleton assistance (N = 4). Changes in kinematics and muscle activity indicate that single-joint assistance indirectly assisted muscles at other joints, such that the improvement from whole-leg assistance was smaller than the sum of its single-joint parts. Exoskeletons can assist the entire limb for maximum effect, but a single well-chosen joint can be more efficient when considering additional factors such as weight and cost.
Impact Statement
Exoskeletons could make walking easier for people, from military personnel to older adults. They can reduce the energetic cost of walking, but we still do not know the best way to assist walking. Which leg joints should exoskeletons assist? What torques should they apply? What is the greatest improvement we could expect? To study this, we optimized hip–knee–ankle exoskeleton assistance for each joint individually, for two-joint combinations, and for the whole leg. We found that assisting the whole leg reduced the energy cost of walking by 50%, double the state-of-the-art. We also found that while assisting the whole-leg was most effective, assisting a single joint may be more efficient when considering device mass. These findings will help exoskeleton designers choose which joints to assist.
© The Author(s), 2021. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Introduction
Lower limb exoskeletons can assist human locomotion by reducing the metabolic cost of walking. These devices have the potential to restore ambulatory ability lost from age or disability, and increase maximum performance for high-activity users like first responders, military personnel, or athletes. One important way exoskeletons can help is by reducing the metabolic cost of walking, which is the amount of biochemical energy consumed to produce walking at a given speed (Das Gupta et al., 2019). Humans tend to move in ways that minimize metabolic cost (Zarrugh et al., 1974; Bertram and Ruina, 2001; Donelan et al., 2001; Sanchez et al., 2020), indicating its importance. Reducing the metabolic cost of walking is considered the gold standard for evaluating performance-augmenting exoskeletons (Young and Ferris, 2017; Sawicki et al., 2020). By reducing metabolic cost, exoskeletons could help achieve related mobility outcomes like increasing the user's walking speed or decreasing fatigue.
Exoskeletons have improved walking by reducing metabolic cost, but larger improvements may be necessary for widespread adoption of exoskeleton products. Reductions in metabolic cost have been demonstrated from assisting one or two joints with both tethered and mobile exoskeletons (Malcolm et al., 2013; Mooney
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et al., 2014; Collins et al., 2015; Seo et al., 2016; Quinlivan et al., 2017; Zhang et al., 2017; Ding et al., 2018; Lee et al., 2018; Malcolm et al., 2018; Lim et al., 2019; MacLean and Ferris, 2019; Cao et al., 2020; Sawicki et al., 2020). The largest metabolic cost reductions have been around 18% relative to walking in no exoskeleton using hip-only assistance on a mobile device (Ding et al., 2018; Lim et al., 2019) and 24% relative to walking in an exoskeleton with no torques applied using tethered bilateral ankle assistance (Zhang et al., 2017). Despite demonstrated improvements, exoskeletons are in a nascent stage of commercial development, and widespread adoption has not yet occurred (Young and Ferris, 2017). To promote adoption, devices may need larger improvements that offset the negative impacts of exoskeletons, such as worn mass, bulkiness, or cost. The added mass of wearing a device, which can vary with device design, imposes a metabolic penalty, which could eliminate small benefits. Users may not be able to sense if the exoskeleton is assisting them because the largest improvements in the field are similar to the just-noticeable difference for metabolic cost (around 20%, Medrano et al., 2020). Improving our scientific and engineering understanding of exoskeleton assistance could deliver larger benefits that may lead to widespread adoption of these devices.
Whole-leg exoskeleton assistance could produce the largest improvements to walking performance. Assisting all of the lower-limb joints simultaneously seems likely to yield the largest energy savings because the hips, knees and ankles all significantly contribute to biological energy consumption during walking (Winter, 1991; Farris and Sawicki, 2012). Simulations of exoskeleton assistance also indicate that whole-leg devices should be most effective (Uchida et al., 2016; Dembia et al., 2017; Franks et al., 2020). Unfortunately, there has been limited testing of whole-leg assistance for able-bodied users (Zoss et al., 2006), and these devices have not yet reduced metabolic cost (Gregorczyk et al., 2010). With improvements to exoskeleton hardware and control, larger benefits might be realizable.
While whole-body assistance may produce larger benefits, single-joint assistance may be more efficient. Assisting just one joint could lead to a smaller, lighter and more cost-effective device, which could result in better net improvements. While a variety of single-joint devices have been tested, there has not been a well-controlled comparison between them owing to differences in actuator capabilities and control. Each device has had different limits on torque and power (Bryan et al., 2020), many below previously identified optimal values (Zhang et al., 2017), and larger torque and power capacity are associated with larger reductions in metabolic cost (Quinlivan et al., 2017; Ding et al., 2018). Most devices have not used control that has been systematically optimized for the participant, which can improve performance by as much as a factor of five (Jackson and Collins, 2015; Zhang et al., 2017) and has led to the largest improvements in the metabolic cost of walking (Zhang et al., 2017; Ding et al., 2018). A direct comparison of optimized single-joint assistance in a high-torque, high-power exoskeleton would be useful to designers as they choose which joint, and how many joints, to assist.
A comparison of single-joint and multi-joint assistance would also provide scientific insights into the biomechanics of walking. A large portion of human leg musculature is biarticular (van Ingen Schenau et al., 1987), comprising muscles that span two joints. Biarticular muscles might be more effectively assisted by multi-joint exoskeletons, leading to a total benefit beyond the sum of assisting each joint individually. Some experiments have suggested that multi-joint assistance might be more effective than single-joint assistance (Ding et al., 2017; Malcolm et al., 2018). Alternatively, adding assistance at other joints may have diminishing returns. Users might adapt their walking pattern to maximize the benefit from assistance at a single-joint, thereby indirectly benefiting muscles at other joints, which may make it relatively less effective to assist additional joints. Some experiments have shown indications of such indirect assistance (Lenzi et al., 2013; Mooney and Herr, 2016; Jackson et al., 2017). A well-controlled comparison allowing observations of how users respond to different types of assistance would help us to develop improved models of biomechanical and neural adaptation to exoskeletons.
The purpose of
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this study was to find the single-joint, two-joint, and whole-leg exoskeleton torques that minimized the metabolic cost of walking and to understand how effective each device architecture is at assisting walking. We used a tethered hip–knee–ankle exoskeleton emulator that can assist hip flexion and extension, knee flexion and extension, and ankle plantarflexion of both legs (Bryan et al., 2020). This labbound device uses off-board motors and power to apply large torques to the user while minimizing worn mass. This allows for comparison of different actuation schemes without the difficulty of designing product-like mobile devices, which enables us to identify optimal actuation parameters to inform design specifications of future untethered exoskeletons. We paired this tool with human-in-the-loop optimization, a process where the control of the exoskeleton is updated in real time based on biomechanical measurements of the user (Felt et al., 2015; Koller et al., 2016; Kim et al., 2017; Zhang et al., 2017). We performed experiments optimizing and comparing assistance at the hips, knees, and ankles, individually, in pairs, and with all three joints assisted simultaneously. We optimized each assistance pattern to reduce the measured metabolic cost of walking and compared it to walking without assistance and walking without the exoskeleton. We measured changes in kinematics and muscle activity to see how users adapted to assistance and to gain insights into the potential biomechanical mechanisms that brought about reductions in metabolic cost. By finding and comparing optimized assistance for different potential device architectures, we expect these results to inform models of human adaptation to exoskeletons and lead to the design of more effective exoskeletons.
Methods
Participants
Four healthy participants were included in this study (P1: M, 26 years old, 90 kg, 187 cm; P2: F, 26 years old, 61 kg, 170 cm; P3: M, 19 years old, 82 kg, 176 cm; P4: M, 23 years old, 62 kg, 171 cm). We were limited to four participants because of the extensive time required to complete the protocol (Supplementary Material, Sections 11 and 12). Each participant completed at least 50 hr of experiments in total. These participants were also authors of the study (P.W.F., G.M.B., R.M.M., and R.R.) as these were the people who could spend such time as a participant for the study. All four participants completed the whole-leg optimization, but due to external factors related to the COVID-19 pandemic, three participants completed one-joint (P1, P2, and P3) and two-joint (P1, P3, and P4) optimization. With three participants, we have a statistical power of 0.8 to detect metabolic reductions greater than 24%, assuming metabolic reductions have a standard deviation of 7.4% (Zhang et al., 2017; Supplementary Material, Section 12). With four participants, the 50% reduction detected from whole-leg assistance has a statistical power of 0.999.
All four participants were experienced with the device at the time of optimization. P1 and P2 had previous experience walking in the exoskeleton before this experiment. P3 and P4 completed a training protocol prior to optimization to get accustomed to wearing the exoskeleton and walking with torques. More details on the training protocol are included in Supplementary Material, Section 1.
Experimental Protocol
We optimized single-joint, two-joint, and whole-leg assistance using a hip–knee–ankle exoskeleton (Figure 1; Bryan et al., 2020). We used human-in-the-loop optimization (Zhang et al., 2017), a strategy where the control of the exoskeleton is updated in real-time based on measurements of the user. For this study, the cost function to be minimized was the measured metabolic cost of walking at 1.25 m/s. First, we optimized single-joint assistance for P1, P2, and P3 in the order of ankle-only, hip-only, and then kneeonly assistance. We then optimized whole-leg assistance for all four users, meaning we optimized assistance of the hip, knee and ankle simultaneously. Finally, for P1, P3, and P4, we optimized two-joint assistance, in the order of hip–ankle, knee–ankle, and hip–knee assistance.
After optimization, we performed validation experiments to compare the optimized assistance to the control conditions of walking without the exoskeleton and walking in the exoskeleton with no torque applied. During these validations, we measured metabolic cost, applied torques, kinematics, and muscle activity.
Exoskeleton Hardware
Assistance was applied using a hip–knee–ankle exoskeleton emulator (Figure 1; Bryan et al
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., 2020). This device can apply large torques using offboard motors and Bowden cable transmissions to actuate an end effector worn by the user, enabling laboratory tests of different assistance strategies without actuation limits (Caputo and Collins, 2014). The device has a worn mass of 13.5 kg. It has carbon fiber struts along the length of the legs that are designed to minimize restriction of the user by being stiff in actuated directions but compliant in out-of-plane bending. The exoskeleton was fit to each user by adding boots for their foot size, by adjusting the length of the shank, thigh, and torso segments of the exoskeleton, and by adjusting the width of the exoskeleton at the knees, thighs, and hips. Straps were adjusted to fit the user at the shanks, thighs, hips, and torso.
Exoskeleton Control
The exoskeleton is controlled by commanding a desired torque for each joint (Bryan et al., 2020). When the desired torque is zero, the exoskeleton tracks the user's joint angles and applies no torques. During walking, we define these desired torque profiles as a function of percent stride. We consider heel strike, measured by ground reaction forces on the treadmill, to be the start of a stride. We calculate percent stride
Figure 1. Overview of exoskeleton emulator system. (Left) Overview of exoskeleton emulator. Ten powerful off-board motors actuate a lightweight end effector worn by a user who walks on a treadmill. Metabolic cost is measured using a respirometry system and muscle activity is measured using electromyography (EMG). (Center) Isometric photo of experimental setup. (Right) Side view of exoskeleton. The exoskeleton can apply torques in hip flexion and extension, knee flexion and extension, and ankle plantarflexion.
as the time since heel strike divided by the average stride time over the past 20 strides. The hip profile starts at 84% of stride after heel strike because hip extension torque is active during heel strike. Resetting the hips' stride time at heel strike caused discrete jumps in hip extension torque during pilot testing. The desired torque profile for each joint is made up of a spline (piecewise cubic hermite interpolating polynomial) anchored by nodes. Each node can be set in advance by an operator, or it can be updated in real time by an algorithm. For the knees, torque was also commanded as a function of joint state. Along with a torque-time profile, knee torque had one spring-like phase during stance, and one damping-like phase during late swing.
Our exoskeleton accurately applied desired torques using closed-loop proportional control with iterative learning and joint-velocity compensation (Zhang et al., 2015; Bryan et al., 2020). Root-meansquare (RMS) error for tracking desired torques was 0.6 Nm at the hips, 3.0 Nm at the knees, and 0.4 Nm at the ankles during whole-leg assistance (Supplementary Material, Section 13). Error was highest at the knees because the state-based control allowed for discontinuous jumps in desired torque that were not possible for our device to track, and the desired torque would change step to step making it harder to track. When zero torque was commanded it was realized effectively, with an RMS applied torque of less than 1 Nm.
Controller Parameterization
The optimization algorithm varied parameters that affected the desired torque control of the exoskeleton (Figure 2). These parameters are mostly related to the timing and torque magnitude of the nodes that define our splines.
We chose these parameters by considering previously successful human-in-the-loop optimizations (Zhang et al., 2017; Ding et al., 2018), considering biological torques during walking (Winter, 1991), and by pilot
Figure 2. Desired torque profiles defined by the controller for the hips, knees, and ankles. Hip-only assistance was defined by 8 parameters, knee-only assistance was defined by 10 parameters, and ankleonly assistance was defined by 4 parameters, meaning whole-leg assistance was optimized using 22 parameters. For the hips (left) and ankles (right), torque (black) was commanded as a function of time, defined as a spline fit to nodes (red) that were optimized during the experiment. For the knees (center), torque was commanded both as a function of time (black), joint angle, and joint velocity. During stance, the knee torque was a function of knee angle to mimic a spring (red), where the spring's stiffness was optimized. During late swing, torque was a function of knee joint velocity to mimic a damper (red). The red curves shown for these periods of state-based control are the average applied torque at the knees from whole-leg assistance, but the applied torque could vary based on the user's kinematics. The steep increases and decreases in applied torque during knee extension assistance were due to the
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impedance controller being turned on and off as a function of percent stride defined by the nodes while the knee angle was nonzero, resulting in discrete jumps in desired torque.
testing. Before this, one participant completed a 9-parameter whole-leg optimization pilot study (Supplementary Material, Section 14), which indicated the need for more degrees of freedom in our controller.
For these optimizations, we included 8 parameters for the hips, 10 for the knees, and 4 for the ankles (Figure 2). For optimization of whole-leg assistance, the optimizer could adjust all 22 parameters. Each parameter had a minimum and maximum allowed value. The allowed parameter ranges were based on user testing to ensure all tested profiles would be sufficiently comfortable for the user to walk in. The optimization tended not to optimize to these limits. However, ankle torque was often as large and as late in stride as possible, which meant the fall time was minimized to prevent torque application during swing. During single-joint assistance, ankle torque magnitude was limited to 1 Nm/kg. After single-joint optimization concluded and multi-joint optimization began, participants noted that these torques were too large to walk in comfortably. Participants noted that the ankle assistance felt like it was extending the ankle too quickly, and it is possible that kinematic adaptations during ankle-only assistance that mitigated this discomfort were not possible when assistance was also present at the hip and knee. To prevent discomfort, the torque magnitude limit was reduced to 0.8 Nm/kg for ankle torque during multi-joint assistance. Tables with the parameter ranges, as well as their initial and optimized values, are available in Supplementary Material, Section 5.
The hip profile was defined by eight parameters. Hip extension was defined by the rise time, peak time and peak magnitude while hip flexion was defined by the peak time, peak magnitude and fall time. There was a period of no torque in between the two peaks defined by the midpoint timing and its duration. The period of no torque dictated the hip extension fall time and the hip flexion rise time.
Knee torque was defined by 10 parameters. Knee torque was commanded both as a function of percent stride and of joint state. The first phase of knee torque was knee extension defined as a virtual spring, with torque proportional to knee angle, which was zero when the knee was straight. Knee extension was defined by the virtual spring onset timing, stiffness, and offset timing. If the joint angle reached zero degrees before the offset time, the knee torque would stay at zero torque for the remainder of the stiffness period. During knee flexion around toe-off, torque was defined as a function of time similar to the hips. This torque was determined by the rise time, peak torque magnitude, peak time, and fall time. Late in swing, knee flexion torque was commanded as a virtual damper, so torque was proportional to a filtered measurement of knee joint velocity. The damping period was defined in a similar way to knee stiffness, with optimization of the onset timing, the damping coefficient, and the offset timing. As the knee joint angle and velocity were not necessarily zero at the start of the state-based controllers, desired torque could instantaneously change at the onset.
Ankle torque was defined using four parameters, which were previously effective for optimization of ankle assistance (Zhang et al., 2017). Torque was defined by rise time, peak torque magnitude, peak time, and fall time. To ensure large torques were not applied too late in the stride, torque was set to be zero by 65% of stride, so if peak time optimized to its latest allowed value (55% of stride), the fall time would be set to the minimum allowed fall time (10% of stride).
Human-in-the-Loop Optimization Protocol
To optimize assistance, we used the covariance matrix adaptation evolutionary strategy (CMA-ES) (Hansen, 2006), which has previously been effective for human-in-the-loop optimization of exoskeletons (Zhang et al., 2017; Witte et al., 2020). CMA-ES samples a "generation" of conditions from a distribution defined by parameter means and a covariance matrix, ranks the performance of the samples, and uses those results to update the mean and covariance before sampling the next generation. The optimizer's goal was to minimize metabolic cost, which was estimated for each condition after 2 min of walking using a first-order dynamical model (Selinger and Donelan, 2014), similar to previous work (Zhang et al., 2017; Witte et al., 2020). More details about the optimization, including hyperparameters and numbers of conditions per generation, are included in Supplementary Material, Section 15.
The initial parameter values for each optimization were carefully selected to try to reduce convergence time. For the single-joint optimizations for P1, initial parameter values were based on previously optimized assistance (Zhang et al., 2017; Ding et al., 2018), hand-tuning, and a 9-
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parameter pilot study (Supplementary Material, Section 14). For whole-leg optimization for P1, initial values were based on the optimized values for single-joint assistance. For P2, P3, and P4, initial values for optimization were based on the optimized values for P1. Finally, for the two-joint assistance optimizations, initial parameters were based on each participant's previously optimized whole-leg assistance values. The initial values for all parameters are included in Supplementary Material, Section 5.
The optimization time was intended to balance being long enough to ensure convergence while short enough to be experimentally feasible. P1 underwent a longer optimization to ensure convergence, to estimate expected reductions, and to inform our understanding of how the optimizer would perform (Supplementary Material, Sections 11 and 16). Ankle-only optimization was conducted for 12 generations over 3 days, and hip-only, knee-only and whole-leg were conducted for at least nine generations over 3 days. Each two-joint assistance optimization was conducted for six generations over 2 days. For all participants, single-joint and whole-leg optimization each occurred over at least 3 days, which seemed sufficiently long for P1 to reach metabolic reductions that were consistent in future sessions and that matched previous studies for previously assisted joints (Zhang et al., 2017) (Supplementary Material, Section 11). For whole-leg assistance for P3, the optimization was restarted because the user had an abnormally high stride frequency that had high metabolic cost, indicating a maladaptation to assistance similar to some users in a previous optimization study. The exact number of generations and days for each optimization is included in Supplementary Material, Section 11. Participants were permitted but not required to take breaks between generations. While walking, participants were allowed to listen to podcasts using wireless headphones.
Validation Protocol
We conducted validation experiments to evaluate the effectiveness of the optimized assistance. Metabolic reductions were validated for each assistance strategy after each optimization. After all the single-joint and whole-leg optimizations were completed, torques, kinematics, and muscle activity were compared between assistance strategies on the same day. Finally, the two-joint assistance strategies were validated after each optimization.
After each optimization was completed, a validation experiment was used to accurately assess the metabolic cost of walking and calculate the percent reduction. This collection was on a separate day, before optimization of the next assistance strategy began. Users walked in longer bouts for the exoskeleton conditions to ensure accurate measurements of steady-state metabolics and to ensure users were acclimated to the device and assistance. We recorded the user standing quietly for 6 min, walking without the exoskeleton for 6 min, walking in the exoskeleton with no torque applied for 10 min, and walking with the optimized assistance torques for 20 min, in a double-reversed order (ABCDDCBA). This order was not randomized due to the time it takes to get in and out of the exoskeleton, as well as to maximize acclimation to the device by presenting progressively more novel conditions. Users rested for at least 3 min between walking conditions, and at least 5 min before a quiet standing condition, to ensure their metabolics returned to baseline. For the no exoskeleton condition, users wore the same brand and model of boots that are included in the exoskeleton (McRae 8189).
After all single-joint and whole-leg optimizations were completed, we evaluated all these optimized strategies in one data collection to directly compare conditions. We measured applied torque, kinematics, muscle activity, power, and vertical ground reaction forces. For this validation, we recorded the user standing quietly for 6 min, walking without the exoskeleton for 6 min, walking in the exoskeleton with no torque applied for 10 min, and then walking for 10 min in each of the four optimized assistance conditions (hip-only, knee-only, ankle-only, and whole-leg) in a random order, and then the no torque, no exoskeleton, and quiet standing conditions a second time (ABCDEFGCBA).
For the three users who completed optimization of two-joint assistance, a validation day was completed after each optimization similar to the protocol following the single-joint and whole-leg optimizations. We recorded the user standing quietly for 6 min, walking without the exoskeleton for 6 min, walking in the exoskeleton with no torque applied for 10 min, and walking with the optimized assistance torques for 20 min, in a double-reversed order (ABCDDCBA), so each condition was evaluated twice. For these validations, we measured metabolics, torques, kinematics, muscle activity, power, and vertical ground reaction forces.
Measured Outcomes
We collected biomechanical data of the user when walking in the different conditions during the validation. We calculated the average of these measurements over the last 3–5 min of walking of each condition to ensure the user's metabolics and gait had reached steady-state.
Metabolic cost
Metabolic cost
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was calculated using indirect calorimetry. We measured volumetric carbon dioxide expulsion, oxygen consumption, and breath duration on a breath-by-breath basis (Quark CPET, COSMED). For each condition, we calculated metabolic rate using a modified Brockway equation (Brockway, 1987) similar to previous studies (Zhang et al., 2017; Witte et al., 2020). Average metabolic cost was calculated for each condition using the last 3 min for quiet standing and walking with no exoskeleton, and using the last 5 min for walking with no torque and walking with optimized assistance. Because each condition was evaluated twice in the double-reversed order, the average was calculated across both measurements of the condition. The cost of quiet standing was subtracted from the measured cost of all the other conditions to calculate the cost of walking. Users fasted for at least 2 hr before optimizations and at least 4 hr before validations to minimize the possible thermal effects of food on metabolic cost measurements. Two-tailed paired t-tests were used to evaluate if the metabolic cost of walking with exoskeleton assistance was significantly different from walking in the control conditions.
For all two-joint optimizations except P3 hip-ankle, participants wore a cloth mask underneath the metabolics mask to comply with COVID-19 safety protocols. This mask did affect the metabolics measurements, by seeming to cause an underestimation of measured metabolic cost (Supplementary Material, Section 17). While this disrupted the accuracy of the absolute measurements, we expected the percent reductions in metabolic cost to be accurate, because we are comparing between conditions. We excluded these affected measures when calculating the average absolute measurements reported for standing quietly, walking with no exoskeleton, and walking with no torque.
Torques and kinematics
Applied torques were measured using load cells and strain gauges on the exoskeleton. Exoskeleton joint angles were recorded to estimate user kinematics, meaning that we could not calculate kinematics for walking without the exoskeleton. Stride frequency was calculated using vertical ground reaction forces measured by the instrumented treadmill (Bertec). Measurements were averaged over the last 3 min of the condition for walking with no exoskeleton, and averaged over the last 5 min for walking with no torque and walking with each assistance condition. Measurements were averaged across both legs. For conditions that were evaluated twice (walking with no exoskeleton and walking with no torque), results were averaged across the two conditions.
Biological torques reported for reference (Figure 4) were from a separate study. Reference walking data is from three able-bodied male subjects (Arnold et al., 2013), different from the participants included in this study. Walking data was collected from three gait cycles of motion capture data during treadmill walking at 1.25 m/s including marker trajectories, ground reaction forces, and EMG measurements (Arnold et al., 2013). Biological joint torques during walking were calculated using the Inverse Dynamics tool in OpenSim (Seth et al., 2018), as described in Franks et al. (2020).
Muscle activity
Muscle activity was measured using surface EMG (Delsys Trigno). We applied a third-order bandpass filter of 40–450 Hz, rectified, then applied a third-order low pass filter of 10 Hz (De Luca et al., 2010). Muscle activity was averaged for a stride over the last 5 min of the device conditions and over the last 3 min for the no device conditions. We subtracted the baseline noise offset then normalized to the maximum of the no torque condition profile. The sensor locations are similar to the protocol of previous gait analysis experiments (Winter, 1991) with adjustments to avoid interfering with the device structure and straps.
Results
Metabolic Cost
The metabolic cost of walking was reduced in all assistance conditions (Figure 3). To evaluate the metabolic cost of walking, we subtracted the metabolic cost of standing quietly (1.52 W/kg on average, Supplementary Material, Section 2) from the metabolic cost measured in each walking trial. The metabolic cost of walking without wearing the exoskeleton was 2.86 W/kg on average. The cost of walking in the exoskeleton with no torque applied was 3.92 W/kg on average, which was higher than the no-exoskeleton condition because of the added mass and impedance to the user. Percent reductions in metabolic cost were calculated in comparison to this no-torque condition to assess the effect of the designed torque assistance specifically without the effect of device mass, allowing for best comparisons between assistance conditions, which could require different device architectures as mobile systems.
Single-joint assistance at each joint reduced metabolic cost, with the largest improvements coming from the ankles and hips. Hip-only assistance reduced the metabolic cost of walking by 26% relative to walking with no torque (N = 3, range of reductions: 24–30%, p = .005). Knee-only
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assistance reduced metabolic cost for each participant, with an average reduction of 13% relative to walking with no torque, although this was not statistically significant (N = 3, range of reductions: 5–18%, p = .07). Ankle-only assistance performed best of the single-joint strategies, reducing metabolic cost by 30% relative to walking with no torque (N = 3, range of reductions: 28–31%, p = .004). When assisting a single joint, exoskeleton designers should consider the ankles or the hips.
Two-joint assistance outperformed single-joint assistance. Two-joint assistance reduced metabolic cost of walking relative to no torque by 33% for hip–knee (N = 3, range of reductions 29–37%, p = .008), 37% for knee–ankle (N = 3, range of reductions 35–40%, p = .02), and 42% for hip–ankle assistance
Figure 3. Metabolic cost of walking. Average metabolic cost (bar) of each condition reported as a percentage of walking in the exoskeleton with no torque. Individual participant values are shown with symbols (P1 X, P2 O, P3 Δ, and P4 þ). Metabolic cost of walking was calculated by subtracting out quiet standing. The percent reduction relative to walking with no torque is shown above each bar. For each participant, the cost of walking without the exoskeleton (No exo., gray) was averaged over all validations. Whole-leg assistance (blue, N = 4) provided the largest improvement to metabolic cost of walking, reducing it by 50% relative to walking in the exoskeleton without assistance.
(N = 3, range of reductions: 36–49%, p = .03) (Supplementary Material, Section 3). Hip–ankle assistance provided the most benefit, mirroring single-joint reductions and aligning with expectations based on biological power.
Whole-leg exoskeleton assistance led to the greatest reductions in metabolic cost of any condition. Whole-leg assistance (hips, knees, and ankles simultaneously) reduced the metabolic cost of walking by 50% relative to walking with no torque (N =4, range of reductions: 46–53%, p= .003), corresponding to a reduction of 33% relative to walking without wearing the exoskeleton (N = 4, range of reductions: 17– 41%, p = .016). This shows that about half of the metabolic energy expended during walking can be saved through exoskeleton assistance, and suggests that whole-leg assistance could provide large net benefits in untethered systems, even after accounting for the effects of added mass.
Optimized Exoskeleton Torque
Optimized torques differed from biological torques in both timing and magnitude (Figure 4, Supplementary Material, Sections 4–6). Optimized torque magnitudes were smaller than biological torques, with peak exoskeleton torques ranging from about 15 to 60% of biological peaks. Ankle torque magnitudes were largest and optimized to the comfort-limited parameter constraints in all but two cases. The timing of the optimized assistance only partially aligned with biological torque. For example, the peak of optimal hip flexion assistance occurred later than peak biological flexion torque. Sometimes, assistance torque opposed typical biological torques. For example, knee flexion assistance around 60% of stride opposed biological knee extension torque for normal walking. These optimized magnitudes indicate the design requirements for mobile devices and show that optimized assistance is not a scaled version of biological torques.
The shape and timing of optimized assistance was consistent across conditions and participants, but optimal magnitudes differed. For example, the optimal timing of peak hip extension assistance was about 11% of stride for all joint combinations and participants, while optimal magnitudes ranged from 0.24 Nm/ kg (hip-only) to 0.5 Nm/kg (hip–knee). One exception to the consistency of optimal timing was ankle torque rise time, which was shorter during single-joint assistance, possibly due to adjustments for comfort
Figure 4. Optimized exoskeleton torques. Optimized single-joint (green, purple, and pink), two-joint (orange, yellow, and red) and whole-leg (blue) exoskeleton assistance torques at the hips (left), knees (center), and ankles (right). Lines are the average of the measured applied torque profiles across both legs and all participants (N =3 for single-joint and two-joint, N =4 for whole-leg), with the range of optimized profiles shown with their respective clouds for each type of assistance. Biological joint torques for unassisted walking without an exoskeleton (black) are included from a different study with different participants (Arnold et al., 2013; Franks et al., 2020) for reference; gray clouds indicate standard deviation of biological torques. For the hips and
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knees, whole-leg assistance optimized to smaller magnitudes than single-joint assistance. For the ankles, maximum torque had to be constrained to find comfortable profiles for walking. Ankle torques were limited to 1 Nm/kg for single-joint assistance, and 0.8 Nm/kg for two-joint and whole-leg assistance.
in multi-joint conditions (Supplementary Material, Section 5). Optimized assistance torques were typically larger when acting alone at a joint, and smaller when acting in a multi-joint configuration. For example, for P1, applied knee flexion torque peaked at 0.25 Nm/kg for knee-only assistance and at 0.14 Nm/kg for whole-leg assistance. The consistency of optimal timing parameters suggests that optimization could occur in a lower-dimensional parameter space of torque magnitudes, and that a generalized assistance profile could be almost as effective as a customized one.
Kinematics
Kinematics varied between assistance conditions, indicating that the user's walking pattern is not fixed and adapts to best utilize assistance (Figure 5, Supplementary Material, Sections 7 and 8). These changes were beyond the deviation measured during walking with no torque (gray cloud, Figure 5). In some cases, assistance shifted joint angles in the direction of the applied torque. For example, peak ankle plantarflexion angle increased with whole-leg assistance, and increased even more during ankle-only assistance, which had larger ankle torques. However, some kinematic changes were not the direct result of applied torques. For example, the indirect effects of hip-only and ankle-only assistance on the knee during stance were larger than the direct effect of knee assistance. These kinematic adaptations indicate the user adjusts their walking strategy to maximize the benefit they get from the exoskeleton, and that these adaptations do not always match intuition.
Muscle Activity
Muscle activity decreased with assistance, but it was not completely eliminated (Figure 6; Supplementary Material, Section 9). Typically, reductions in activity were seen in muscles that crossed assisted joints and acted in the same direction as assistance. For example, soleus activity decreased during all conditions that applied ankle assistance. Sometimes activity increased during opposing assistance, such as in the vastus lateralis during periods of knee flexion torque. Some reductions in muscle activity occurred during assistance at other joints. For example, gluteus maximus activity decreased when the hip was assisted directly, but also decreased during ankle-only assistance. This is consistent with the observation that exoskeleton assistance at one joint can indirectly assist muscles that cross other joints. The indirect assistance could be from the complex dynamics of the leg during walking, or could be facilitated by the
Figure 5. Average joint kinematics. Average joint angle as a percentage of stride at the hips (left), knees (center), and ankles (right) for each assistance condition (denoted by color). Shown here are the average for both legs across all participants (N = 3 for single-joint and two-joint, N = 4 for whole-leg). All singlejoint and whole-leg conditions for P1, P2, and P3 were tested on the same day to reduce changes in alignment between user and device. Two-joint and P4's three-joint conditions were each collected individually. For walking in the exoskeleton with no torque (black), the standard deviation of angles is shown (gray cloud) to contextualize the magnitude of changes between conditions.
Figure 6. Muscle activity. Muscle activity measured during walking using surface EMG for each condition. Lines shown are the average across all participants (N = 3 for single-joint, hip–knee, and hip– ankle, N = 2 for knee–ankle due to a technical difficulty with P3's EMG collection, and N = 4 for wholeleg). The EMG signal was filtered, averaged, had baseline activity removed to eliminate noise, and normalized to the peak value of walking in the exoskeleton without assistance (black). Gluteus maximus activity (second row, third column) decreased for hip-only, hip–knee, hip–ankle, and whole-leg assistance as expected, and also decreased during ankle-only and knee–ankle assistance, indicating that the gluteus was indirectly assisted by ankle exoskeleton torque. This effect was less pronounced for the soleus (top row, first column), where hip-only and hip–knee assistance only slightly reduced muscle activity.
kinematic adaptations to maximize the effectiveness of each type of assistance. Optimized assistance did not cause users to eliminate muscle activity, suggesting that either some amount of activity is still useful or further advancements to control architecture would be needed to reduce energy expenditure further.
Discussion
With capable devices, optimization, and training, exoskeletons can provide very large improvements in locomotor performance. Whole-leg assistance reduced the metabolic cost of walking by 50% relative to walking with no torque, a substantial improvement over the state-of-the-art (17–24%) (Zhang et al., 201
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7; Ding et al., 2018; Lim et al., 2019). This corresponded to a 33% reduction relative to walking with no exoskeleton, much greater than the just-noticeable difference in metabolic cost (20%) (Medrano et al., 2020), indicating that participants could feel the reduction in effort compared to walking normally. Because whole-leg assistance produced the largest benefit of all assistance conditions, exoskeleton designers who want to maximize performance should consider assisting the whole leg.
Among single-joint assistance strategies, ankle-only assistance was most effective, followed closely by the hip, with smaller reductions possible at the knee. Hip and knee assistance resulted in greater metabolic cost reductions than previous lower-torque exoskeletons assisting these joints (Ding et al., 2018; Lim et al., 2019; MacLean and Ferris, 2019), while ankle assistance resulted in similar improvements as found with high-torque exoskeletons and human-in-the-loop optimization (Zhang et al., 2017; Jackson and Collins, 2019). Knee-only assistance reduced the metabolic cost of walking, although the reduction was not statistically significant for our sample size and significance level. Knee-only assistance may be more effective for walking up inclines (MacLean and Ferris, 2019; Haufe et al., 2020), considering the increased positive power requirements from the knee (Montgomery and Grabowski, 2018). Devices designed to assist just one joint during level walking should target the ankle or hip, which showed reductions of 30 and 26%, respectively. With similar metabolic reductions, designers could compare between the ankle or hip based on other aspects of the design. For example, it may be easier to interface with the ankle using a simple device, while a hip exoskeleton places the mass more proximally on the body where it is easier to carry (Browning et al., 2007).
The best-performing two-joint assistance strategy, hip-ankle assistance, reduced metabolic cost by 42%, nearly as much as whole-leg assistance. With 37% and 33% reductions for knee–ankle and hip–knee assistance, the small added benefit of knee-assistance may not be worth the added device complexity compared to ankle-only or hip-only assistance for level ground walking. The inclusion of knee assistance may be more effective for different walking conditions such as incline walking or during sit-to-stand, where the knee is expected to contribute more to movement.
Assisting multiple joints results in larger net benefits, but smaller benefits per joint, possibly because of the way people adapt to exoskeleton assistance. Whole-leg assistance led to the largest metabolic cost reduction (50%), but it was smaller than the sum of the reductions of the single-joint assistance strategies (26% þ 13% þ 30% = 69%). During single-joint assistance, users may have been able to adapt the kinematics of their unassisted joints to take most advantage of the single-joint assistance. During wholeleg assistance, their subconscious walking strategy could have been to maximize metabolic benefit overall from assistance of the whole-leg, while not getting maximal benefit from any joint in particular. This adaptation might also explain why optimized torque magnitudes during single-joint assistance were larger than whole-leg torque magnitudes. It was previously hypothesized that multi-joint assistance may be more effective at assisting biarticular muscles, but the relative benefit of single-joint assistance indicates that indirectly assisting muscles at other joints from single-joint assistance leads to larger benefits on a perassisted-joint basis. The reduction in metabolic cost per joint assisted (Table 1) could be helpful for designers when considering potential device architectures.
These results suggest ways of designing better exoskeleton products. Optimized torques did not mimic biological torques, with magnitudes smaller than biological for all joints and peak torques later than biological peaks for the hips and ankles (Figure 4). Optimized torque magnitudes were within the range of reported capabilities of some existing mobile devices for the lightest participant (61 kg) (Mooney et al., 2014; Shepherd and Rouse, 2017; Lee et al., 2018) but not for the heaviest participant (90 kg) (Bryan et al., 2020). Exoskeletons could be designed in different sizes (e.g., small, medium, and large) that meet the optimized torque magnitudes for different sized users while minimizing worn mass. The similar timing parameters across users and across assistance strategies suggest that these optimized profiles could translate well to existing devices with lower capabilities and could be generalizable to a wide range of users. Device designers could consider control strategies that allow for kinematic adaptations because they seem to be useful to maximize device effectiveness. We also recommend considering state-based control at the knees, which was more effective than pilot tests of strictly torque-time control. This strategy may have facilitated adaptation to knee extension assistance during stance, because the torques grew as the
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user bent more into flexion, allowing for a "stabilizing" effect that prevented buckling of the knee. In this study, we used a tethered exoskeleton emulator to compare assistance, but future work should attempt to recreate this assistance on mobile exoskeletons. We reported our improvements primarily relative to walking in the exoskeleton unassisted, and we expect these relative improvements to be consistent for mobile systems, but future mobile device development will need to focus on keeping worn mass low to ensure a good benefit relative to no exoskeleton as well. These findings should translate well to a wholeleg mobile device because the worn mass (13.5 kg) is similar to the expected mass of a mobile device
Table 1. Metabolic reduction per joint assisted, relative to walking in the exoskeleton with no torque
| Condition | Ankle-only(%) | Hip-only(%) | Hip–ankle(%) | Knee–ankle(%) | Whole-leg(%) | Hip–knee(%) | Knee-only(%) |
|--------------------------|-------------------|-----------------|------------------|-------------------|------------------|-----------------|------------------|
| Reduction per | 30 | 26 | 21 | 18 | 17 | 16 | 13 |
| jointTotal reduction | 30 | 26 | 42 | 37 | 50 | 33 | 13 |
capable of the optimized torque magnitudes (10 kg) based on published torque densities (Pratt et al., 2004; Zoss et al., 2005; Meijneke et al., 2014; Mooney et al., 2014; Giovacchini et al., 2015; Seo et al., 2016; John et al., 2017; Shepherd and Rouse, 2017; Bryan et al., 2020; Supplementary Material, Section 10).
These results can be used to improve our models of human coordination, especially when using assistive devices. The larger metabolic cost reductions we saw from hip and ankle assistance support the idea that the hips and ankles are primary energy consumers during walking (Farris and Sawicki, 2012). Unlike some simulations (Franks et al., 2020), muscle activity did not go to zero even when assisted without hitting torque limits, indicating the user is optimizing for more than just metabolic cost for an average steady-state stride. Simulations could capture that more complicated objective function, including control required for balance. These results show that kinematic adaptations to assistance are important and should be considered in simulations. Biomechanical models could also be used to study the kinematic adaptations and relative metabolic benefits seen in this study. Muscle-level simulations of single-joint and multi-joint assistance could better understand how assistance at one joint could be indirectly assisting muscles at another joint, facilitated by the user's kinematic adaptations. This work could also try to understand how single-joint and multi-joint assistance compare in assisting biarticular muscles specifically.
This study could have been improved by testing more participants, providing additional training, or testing additional controller parameterizations. This was an extremely arduous experiment with long optimization times, with each participant having completed over 50 hr of experiments. It was then interrupted by difficult external conditions (the COVID-19 pandemic). As such, we were only able to complete three participants for the single-joint and two-joint optimizations, and four participants for the whole-leg optimizations. However, given the magnitude of the changes and the consistency of the responses across participants, this sample size is sufficient to identify the efficacy of the joint combinations tested. Given three participants and a desired statistical power of 0.8, and assuming metabolic reductions have a standard deviation of 7.3% (Zhang et al., 2017), we can confidently detect metabolic reductions of 24% and larger. Although we gave our users substantial training and optimization time, more time may have improved the outcomes. Longitudinal studies with mobile devices that can be worn daily could show greater improvements to walking as users adapt. During optimization, torque magnitudes reached the comfort-based limits at the ankles, which were set due to discomfort at the biological ankle joint, possibly from extending the ankles too quickly or too far during torque application at push-off. If we were able to apply larger torque magnitudes comfortably, we could unconstrain the optimization of assistance and allow the torques to converge on the magnitude that provides the greatest benefit, which could be larger than 1 Nm/kg for the ankles. Using a more sophisticated control approach to ensure user comfort while allowing the largest possible exoskeleton torques might also lead to larger benefits. Due to the COVID-19 pandemic interrupting our protocol, participants had to wear cloth masks during optimization and validation of two-joint assistance, which could have impacted the accuracy of the metabolic cost measurements. While we believe the percent reductions should still be accurate, future work
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studying two-joint exoskeleton assistance could confirm the results found here.
These results suggest that new cost functions, gait environments, and user populations could be exciting topics for future studies. Future work could optimize metabolic cost alongside other costs that are important for gait, such as walking speed, balance, or user satisfaction (Ingraham et al., 2020). In our study, we did not rigorously collect user feedback, but participants often provided similar feedback, such as noting that the exoskeleton felt like it was making them march if torques were too large, or that they noticed how beneficial assistance was right after it was turned off. Future work could collect user feedback in an organized way and incorporate it in the design of exoskeleton assistance, possibly through humanin-the-loop optimization. Our study did not penalize high torques or powers, but future work could try to maintain sufficient metabolic cost reductions while minimizing actuator requirements, which can be costly to mobile devices. While our study assisted walking at a fixed speed on level-ground, future work can explore optimized assistance for walking in different conditions such as at different speeds, on inclines, or with worn loads. Our study was restricted to a treadmill due to our tethered device, but this work could be extended to unstructured environments by translating the paradigm to mobile devices. Our findings for assisting young, able-bodied users could be a starting point to optimize assistance for older adults and people with disabilities, hopefully speeding the discovery of effective assistance strategies.
Acknowledgments. We would like to thank K. Gregorczyk, G. Kanagaki, M. O'Donovan, and the NSRDEC for their input on experimental design, N. Bianco for assistance in controller development and reference biological torques, and all of the Stanford Biomechatronics Lab for their feedback and support. We would also like to thank the staff and administrators who were able to reopen the lab during the COVID-19 pandemic.
Funding Statement. This work was supported by the U.S. Army Natick Soldier Research, Development and Engineering Center (Grant number W911QY18C0140), by the National Science Foundation Graduate Research Fellowship Program (Grant number DGE-1656518), and by the Stanford Vice Provost for Undergraduate Education STEM Fellowship.
Competing Interests. The authors declare no competing interests exist.
Authorship Contributions. P.W.F. and G.M.B. designed and constructed the exoskeleton and developed the controllers. P.W.F. developed the optimization strategy and the experimental protocol, conducted experiments, and drafted and edited the manuscript. G.M.B., R.M.M., R.R., and A.C.L. conducted experiments and edited the manuscript. S.H.C. conceived and managed the project, provided design, controls and testing support, and edited the manuscript.
Data Availability Statement. The data that support the findings of this study are available on request from the corresponding author, P.W.F., and will be made available online at biomechatronics.stanford.edu following publication.
Ethical Standards. All user experiments were approved by the Stanford University Institutional Review Board and the US Army Medical Research and Materiel Command (USAMRMC) Office of Research Protections. All participants provided written informed consent before their participation as required by the approved protocol.
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Task-agnostic exoskeleton control via biological joint moment estimation
https://doi.org/10.1038/s41586-024-08157-7
Received: 17 October 2023
Accepted: 4 October 2024
Published online: 13 November 2024
Dean D. Molinaro1,2,5,8 ⋈, Keaton L. Scherpereel1,2,6,8, Ethan B. Schonhaut1, Georgios Evangelopoulos3,7, Max K. Shepherd4 & Aaron J. Young1,2
Lower-limb exoskeletons have the potential to transform the way we move1-14, but current state-of-the-art controllers cannot accommodate the rich set of possible human behaviours that range from cyclic and predictable to transitory and unstructured. We introduce a task-agnostic controller that assists the user on the basis of instantaneous estimates of lower-limb biological joint moments from a deep neural network. By estimating both hip and knee moments in-the-loop, our approach provided multi-joint, coordinated assistance through our autonomous, clothing-integrated exoskeleton. When deployed during 28 activities, spanning cyclic locomotion to unstructured tasks (for example, passive meandering and high-speed lateral cutting), the network accurately estimated hip and knee moments with an average $R^2$ of 0.83 relative to ground truth. Further, our approach significantly outperformed a best-case task classifier-based method constructed from splines and impedance parameters. When tested on ten activities (including level walking, running, lifting a 25 lb (roughly 11 kg) weight and lunging), our controller significantly reduced user energetics (metabolic cost or lower-limb biological joint work depending on the task) relative to the zero torque condition, ranging from 5.3 to 19.7%, without any manual controller modifications among activities. Thus, this task-agnostic controller can enable exoskeletons to aid users across a broad spectrum of human activities, a necessity for real-world viability.
Lower-limb exoskeletons promise to reinvent human mobility by augmenting our capability and increasing longevity15,16. However, within powered exoskeleton technology lies a critical limitation: the controllers—which in many cases were optimized through extensive experimentation—only work for a single task or small set of tasks, offering little adaptability beyond passive devices17,18. Switching between tasks typically requires a 'high-level' task classification (for example, level walking, incline walking and stair ascent) often toggled manually or in some cases by an autonomous classifier1,19-24. Within each class, a 'mid-level' controller computes desired exoskeleton assistance, which is often tuned on a user- and task-specific basis3,11,25. For highly repetitive cyclic tasks, assistance is often designed as a function of time or phase3,10,12,24. For some gravity-fighting non-cyclic tasks, such as squats or sit-to-stand, impedance controllers assist, removing any dependence on time26-28. Although this approach has worked well for many laboratory-based experiments, this highly constrained discretization contrasts with the fluidity of natural human movement; we shuffle and side-step as we navigate a busy kitchen, stop our jog to take in a scenic view and regather our balance to again try the door that was heavier than we had anticipated. Our median walking bouts are a mere four steps29. Unstructured, non-cyclic and transitory tasks make up a large portion of our movements and interactions with the environment, but current exoskeleton controllers are incapable of recognizing or assisting these tasks. In fact, the expansion of traditional classification-based high-level control architectures to encompass these unstructured movements is intractable owing to the sheer number of movements that must be defined.
We have developed a task-agnostic exoskeleton controller that short-circuits the need for high-level task classification or gait phase estimation by basing assistance on a fundamental, continuous physiological state: the human's biological joint moment (Fig. 1a and Supplementary Video 1). Biological moment can be calculated using optical motion capture and high-fidelity force plates to measure interactions with the ground30 but cannot be measured or solved for analytically through available wearable sensors, owing to sensor noise and incomplete information (particularly shear forces with the ground). Instead, biological joint moments can be estimated from wearable sensor data, often by including optimization or learning methods to account for incomplete sensor information 13,14,31-36, but very few studies have begun to explore the implications of using this technology in the control loop13,14,35,36. In these previous works, however, using instantaneous biological joint moment estimates in the control loop has shown substantial promise. Gasparri et al.13 developed a joint moment-based ankle exoskeleton controller, which has shown large metabolic benefits across inclines and declines, stairs and mixed terrain in both unimpaired individuals and those with cerebral palsy $^{
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13,37-39}$ . Additionally,
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA. Institute for Robotics and Intelligent Machines, Georgia Institute of Technology, Atlanta, GA, USA. 3X, The Moonshot Factory, Mountain View, CA, USA. 4College of Engineering, Bouvé College of Health Sciences, and Institute for Experiential Robotics, Northeastern University, Boston, MA, USA. 5 Present address: Boston Dynamics Al Institute, Cambridge, MA, USA. 6 Present address: Skip Innovations, San Francisco, CA, USA. 7 Present address: Google Mountain View, CA, USA. 8These authors contributed equally: Dean D. Molinaro, Keaton L. Scherpereel. ™e-mail: molinarodean@gmail.com
$\label{Fig.1} \textbf{Fig.1}| \textbf{Task-agnostic exoskeleton control with a clothing-integrated} \ \textbf{exoskeleton. a}, \textbf{The proposed approach continuously and seamlessly provides} \ assistive torque to the hip and knee using an estimate of the user's biological joint moments from a deep neural network. By basing assistance off a continuous physiological variable, no task classification is required; the same control law can effectively assist across the full range of human movement. The time series shown illustrates the average performance of our control approach with representative participant-averaged curves on the tasks shown. ext., extension. \textbf{b}, \textbf{A} \textbf{n} \textbf{autonomous hip-knee exoskeleton system was constructed to} \$
capture a rich set of sensing modalities and then assist across a wide range of mobility tasks. $\mathbf{c}$ , The hybrid design consists of both soft textiles and semirigid structural components to efficiently transmit exoskeleton assistance to both the hip and knee joints. The human interface consisted of zero-stretch woven fabric to efficiently transmit forces, whereas low-stretch knitted fabrics covering joints helped avoid restrictions in the user's range of motion. $\mathbf{d}$ , Structural compliance and a passive translational degree of freedom between the hip and knee allowed hip ab- or adduction and rotation while maintaining actuator alignment across movements.
energy shaping methods35,36 promise joint moment-based control agnostic to a specific lower-limb joint. Further, our previous work14 presented a deep learning-based approach that significantly reduced user metabolic cost during both level and incline walking using a hip exoskeleton; this approach demonstrated similar or even better outcomes than using previously optimized, spline-based assistance (that is, the previous standard of exoskeleton control) depending on the condition.
Although these past studies demonstrate the efficacy of exoskeleton control using real-time biological joint moment estimates, they do not yet realize the key benefit of this approach: the potential for generalizability across the broad spectrum of human movement. In fact, these previous studies are almost entirely limited to the domain of level walking, ramps and stairs (domains that have been studied in exoskeleton control for decades15,16) aside from the sit–stand task investigated by Lin et al.35. Further, this approach could autonomously coordinate assistance across many lower-limb joints, a key component of generalizing exoskeleton technology across tasks that depend on different joints; however, significant augmentation of user energetics using a multi-joint exoskeleton controlled by joint moment estimates remains
to be demonstrated. In this study, we introduce a task-agnostic controller enabled by a neural network-based joint moment estimator, which runs onboard an autonomous, hip-knee exoskeleton. By training the network on a diverse dataset of time-synced exoskeleton sensor data and ground-truthjoint moments, we found that it accurately estimated user joint moments during 28 cyclic and non-cyclic human activities when deployed online (corresponding dataset released with this study). Further, we found that the resulting controller significantly reduced metabolic cost (four activities tested) and lower-limb biological joint work (six activities tested) relative to a no-assistance condition in all tested activities without any manual user or experimenter intervention between activities. This work provides a path to generalizing assistance across human behaviour, a critical link for the adoption of exoskeleton technology in the real world.
Clothing-integrated robotic exoskeleton
We developed a new exoskeleton with the capacity to assist an extensive range of movements, with a particular focus on under-appreciated functional movements that are critical to independence, but can be difficult
for many populations, such as older adults. The clothing-integrated research exoskeleton presented here (Fig. 1b–d), was designed at X, The Moonshot Factory and combines the advantages of rigid exoskeletons with the comfort of soft textiles for the human–exoskeleton interface16,40 (Fig. 1c). Compact quasi-direct drive actuators (AK80-9 T-Motor
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, Nanchang) mounted coaxially with the hip and knee provided up to 15 N m of assistance at each joint. The semirigid structure consisted of carbon fibre and 3D printed nylon orthotics on which the actuators and sensors were mounted. Six inertial measurement units (IMUs), joint encoders on the hips and knees, and a pair of wireless force-sensitive insoles provided real-time human movement data for the joint moment estimator (Fig. 1b) with the IMUs being the most important for joint moment estimation (Extended Data Fig. 1). Sagittal-plane actuation is provided at the hip and knee whereas passive degrees of freedom at the hip (translation and rotation) provide flexibility (Fig. 1d). This new exoskeleton architecture gave the user the flexibility and range of motion needed to perform a diverse range of structured and unstructured activities and represents a vital step forward in designing exoskeleton interfaces that are compliant, comfortable and adjustable.
Lower-limb joint moment estimation
To train the joint moment estimator, we collected exoskeleton sensor data time-synced with motion capture and ground reaction forces (GRFs) while users performed a wide range of tasks. Standard Open-Sim inverse dynamics (detailed in the Supplementary Information) were used to calculate hip and knee moments41,42, providing the ground-truth labels (Fig. 2a). To achieve both task generalizability and user-independence, our extensive dataset consisted of 15 healthy participants performing 28 different activities consisting of 66 total conditions (Extended Data Fig. 2). We categorized the 28 activities as cyclic (Supplementary Video 2), impedance-like (Supplementary Video 3) or unstructured (Supplementary Video 4) on the basis of normative joint biomechanics43 (Fig. 2b). Using this dataset, we trained a temporal convolutional network (TCN) with optimized hyperparameters (see Extended Data Table 1) to estimate hip and knee moments from 19 of the 28 tasks, with the 19 tasks chosen by a forward selection algorithm to promote task generalization within the model (Fig. 2c and Extended Data Fig. 3a). The most helpful data for model generalization (aside from the seed task of level-ground walking whose importance cannot be assessed) was a series of static standing poses, allowing the model to learn the static characteristics of the human body (for example, standing upright requires near zero moment), which is critical for generalization (Extended Data Fig. 3b). Other critical tasks, such as jump and cut, are extremely high-effort tasks that probably helped establish the bounds of the system dynamics and thus are also important for generalization. These previously understudied activities in the exoskeleton domain, many of which are not suitable for gait phase or impedance control, were the most critical for training a model to infer joint moments across real-world tasks.
The joint moment estimates were mapped to applied exoskeleton torque by a continuous transformation (Fig. 2a). Hip and knee moments were scaled to 20 and 15% of the total estimated biological moments, respectively. These scaling factors were established in pilot experiments and provided comfortable assistance while preventing substantial saturation and overheating of the motors during high-torque movements. Hip moment estimates were delayed by 100 ms to maximize positive work done by the exoskeleton44 and to potentially minimize user metabolic cost14. Furthermore, the delay between knee moment estimates and the resulting assistance was set to the minimum achievable by the system (a delay of 50 ms), on the basis of single-blinded pairwise preference tuning45 during pilot testing. Finally, the delayed joint moment estimates were lowpass filtered to better match the frequency content of human movement46 and increase user comfort.
The model was validated online with ten participants to assess its ability to accurately estimate human joint moments while providing assistance. No user-specific data were included in training to keep the tests user-independent. Furthermore, we developed a best-case baseline method based on current state-of-the-art exoskeleton control to compare against our joint moment estimator (details in the Supplementary Information); for cyclic activities, the baseline method estimated the user- and stride-averaged hip and knee moments from each activity (for example, for level walking, the baseline used the average level walking curve) and for 'impedance-like' activities (for example, jumping in place), the baseline method estimated the hip and knee moments by estimating zero moment when in swing or flight and by using a linear spring-damper model fit to each activity during stance (Fig. 3a). Unstructured activities were omitted from the baseline because of their lack of phase or impedance-like behaviour, which highlights the limitations of current exoskeleton control. We implemented the baseline method post hoc with perfect gait phase estimates and task classification (that is, a perfectly accurate classifier of 28 classes), thus representing the theoretical best possible performance achievable by this type of control architecture.
Our deep neural network estimated hip and
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knee moments significantly better than the baseline method for both cyclic (hip R2 0.79, knee R2 0.86) and impedance-like activities (hip R2 0.81, knee R2 0.87) without any participant-specific calibration (Fig. 3b,c). Representative time series are shown in Fig. 3d–f. Comparing within each activity, our estimator significantly outperformed the baseline method for 12 of the 19 total comparisons of R2 at the hip and 13 of the comparisons at the knee (Extended Data Fig. 4a,b), with similar results in root mean-square error (r.m.s.e.) (cyclic hip and knee r.m.s.e. 0.15 and 0.13 N m kg−1, impedance-like hip and knee r.m.s.e. 0.21 and 0.16 N m kg−1) and in normalized mean absolute error (MAE) (cyclic hip and knee normalized MAEs 7.3 and 5.5%; impedance-like hip and knee normalized MAEs 7.1 and 6.0%) (Extended Data Figs. 4c–f and 5a–d). The baseline method did not significantly outperform our approach on any individual activity in R2 , r.m.s.e. or normalized MAE. In reality, the high-level state estimators required for the baseline method (that is, a task classifier, gait phase estimator and pose estimator) also have non-zero error12,20–23,25, further detracting from this approach and highlighting the benefits of our regression-based method. We also found that during unstructured tasks that were not well-defined as cyclic or impedance-like, our approach maintained performance with an average hip R2 of 0.80 and knee R2 of 0.82 (Fig. 3b). Thus, our task-agnostic controller mimicked the natural behaviours of human movement, seamlessly modulating assistance throughout the transient motions common in daily life29.
Given the black box nature of our approach it is possible that the neural network could generate large, erroneous joint moments leading to undesirable exoskeleton assistance. To analyse model under- and overestimation, we computed the normalized hip and knee estimate error at each time instance as the difference between the absolute value of the joint moment estimate and the absolute value of the ground-truth label, normalized by the peak-to-peak range of the ground-truth label. Extended Data Fig. 5e depicts the distribution of the normalized hip and knee error from the online validation trials (representing roughly 10 million instances total), in which negative and positive values correspond to under- and overestimates, respectively. As shown in the figure, large under- and overestimates were uncommon with means close to zero (hip mean −2.7%; knee mean −1.3%) and standard deviations of 7.8 and 6.6% for the hip and knee, respectively. Furthermore, time series examples of the most severe instances of under- and overestimation from the joint moment estimator are shown in Extended Data Fig. 5f.
Of the 28 evaluated activities, nine were withheld from the training set (details in Methods). The average R2 of our estimator on these held-out tasks was 0.83 and 0.85 for the hip and knee, respectively, demonstrating the ability of the network to generalize to the hold-out tasks. To further investigate estimator generalization, three users also completed
Fig. 2 | Deep neural network training and deployment for joint moment estimation. a, Lower-limb joint moment labels were calculated in OpenSim using optical motion capture, force plate data and user-specific musculoskeletal models; a TCN was trained to predict these joint moment labels from timesynchronized exoskeleton sensor data. During deployment, to improve power delivery and user comfort, the estimates were transformed into commanded exoskeleton torque through a continuous function consisting of a scale, delay and a lowpass filter. est., estimate. b, Users wore the exoskeleton while performing a wide range of cyclic, impedance-like and unstructured tasks.
c, Training activities for the moment estimator were selected using a forward selection algorithm to maximize the relative improvement in model generalization across tasks. Validation r.m.s.e. decreased as the training set grew, with the first 19 tasks reducing r.m.s.e. to 0.133 N m kg−1, which was within 5% of the best model accuracy with all the tasks included. This task set was used to train the real-time models used in the rest of this study. For reference, peak-topeak hip and knee moments ranged from 2 to 4 N m kg−1 for most activities in the dataset. Results were computed from leave-one-participant-out cross-fold validation using a 12-participant dataset (error bars omitted for clarity).
eight completely new tasks,
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described in Extended Data Table 2, that had not been previously tested or analysed (Supplementary Fig. 1 and Supplementary Video 5). These tasks were intentionally designed to be highly unique from the original dataset to push the limits of our approach, including burpees, mimicking a basketball layup and walking on a split belt treadmill with differing belt speeds. Our approach generalized well to the tasks reflective of typical human movement, and when pushed to extremely dynamic behaviours outside of the training set, our approach provided directionally correct assistance, but the magnitude and shape lost accuracy (R2 ranged from 0.24 to 0.92 at the hip and from 0.32 to 0.91 at the knee for the eight new tasks; Supplementary Fig. 1c,d). These results demonstrate the ability of the estimator to generalize to never-before-seen activities but highlights that task-specific training data is beneficial for activities with highly different dynamics (for example, when offloading bodyweight through the hands on the ground). Extra details and discussion comparing our joint moment estimator relative to previous methods and regarding its performance during new tasks are provided in the Supplementary Information.
Augmenting user energetics across tasks
To quantify the impact of our task-agnostic controller on the user, we measured user metabolic cost during four activities under three assistance conditions: wearing the exoskeleton with our task-agnostic controller (exo on), without wearing the exoskeleton (no exo) and wearing
Fig. 3 | Online joint moment estimation performance. a, We compared our neural network-based joint moment estimator (deployed online) to a best-case baseline method (computed offline) that relied on perfect task classification and gait phase. b, Our approach significantly improved $R^2$ at the hip by $0.13 \pm 0.04$ (19 $\pm$ 6%, P = 2 $\times$ 10 $^{-7}$ ) and at the knee by $0.25 \pm 0.04$ (40 $\pm$ 7%, P < 10 $^{-16}$ ) compared to the baseline method during cyclic activities. For impedance-like tasks, our approach improved $R^2$ by $0.31 \pm 0.05$ (63 $\pm 10\%$ , $P = 4 \times 10^{-16}$ ) at the hip and by $0.32 \pm 0.02$ (57 $\pm 3\%$ , $P < 10^{-16}$ ) at the knee compared to the baseline method. Black squares depict inter-participant mean, coloured boxes depict interquartile range, horizontal lines within boxes depict inter-participant median and error bars depict inter-participant minimum and maximum (n=10). c, Estimator $R^2$ is shown per task for our approach and the baseline method. Each marker corresponds to the inter-participant average per single
task (n = 10, except for the run condition where n = 9). d, Representative strides from various cyclic tasks are shown. The baseline method required a different task classification for each depicted ambulation mode, whereas our approach did not require any discrete switching. e, Representative trials are shown when squatting to the left, right and symmetrically. The impedance control-based approach failed to capture changes in joint moments by relying solely on kinematics. Instead, our approach accurately modified joint moments with the change in weight distribution across the user's legs. $\mathbf{f}$ , A representative trial during leftward cutting is shown, depicting the ability of our approach to seamlessly modulate assistance during highly unstructured behaviours. As it is unclear how to extend the baseline method to these types of activity, it was omitted. Estimator $R^2$ relative to ground truth is shown for our approach (ours) and the baseline method (base) above each representative trial.
the exoskeleton without assistance (zero torque). The task-agnostic controller significantly reduced metabolic cost for all four tasks compared to zero torque (P < 0.05) with relative reductions ranging from 8.0% during the lift weight task to 19.7% during 5° inclined walking (Fig. 4a). Relative to no exo, our approach significantly reduced user metabolic cost during the weight lifting task and during running (P < 0.05); however, our approach increased metabolic cost during level-ground walking (P < 0.05). Given the similarity in level walking estimator accuracy and metabolic cost reduction relative to zero torque in our previous work, which did reduce metabolic cost relative to no exo using a lighter weight hip-only exoskeleton14, it is likely that the increase in metabolic cost in this study was due to the added mass penalty of the hip-knee exoskeleton, not the controller itself47. Nevertheless
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