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[MATH] at time [MATH] are used. The first aspect of the intention decoder is to decipher discrete gestures [MATH] from EMG signals |
[MATH] . Then it deciphers the state of the arm [MATH] consisting of planar arm position [MATH] and planar arm velocity [MATH] from IMU signals [MATH] . The gestures [MATH] and arm state [MATH] are translated to mouse movement and mouse clicks, which provide feedback of the decoded intended gesture [MATH] to the user. ... |
[MATH] from the IMU of the Myo armband and maps it to arm state [MATH] . The next few paragraphs give an insight about our proposed intention decoder, however the complete details of this pipeline are omitted due to space constraints. |
4.1.1 Gesture decoding using HMM We use HMM, see Rabiner ( 1989 , a common probabilistic machine learning technique to decode gestures from the EMG signals. Our HMM implementation uses discrete states which are the gestures |
[MATH] and continuous observations related to EMG signals which are modeled as a multivariate Gaussian distribution. The Myo Armband produces a [MATH] -dimensional spatial EMG signal [MATH] . We use the mean |
[MATH] and standard deviation [MATH] of the signals over [MATH] window and [MATH] frame shift as input observations. The final feature observed by the HMM is is given by [MATH] . We collect the training data [MATH] for 1 minute, during which the user performs all [MATH] gestures. The gestures are implemented in a fixed... |
4.1.2 Arm movement decoding using a Kalman filter We use a standard discrete-time Kalman filter Thrun et al. ( 2005 to decode the arm state [MATH] from the IMU signals |
[MATH] . We consider only planar motions of the arm as we will be using a planar environment for the GUI and the formation controller. The arm state is transformed into mouse position [MATH] and velocity [MATH] by an appropriate scaling and sent to the GUI (Section 4.2 ). We use a discrete, linear time-invariant model ... |
[EQUATION] where [MATH] is the input acceleration given by the planar angular orientation of the arm which is under our control, [MATH] is the update time constant and [MATH] is the Gaussian process noise. In this way, the acceleration of the mouse pointer is controlled by changing the arm orientation, which is a more ... |
[MATH] signals to observe the states is given by [EQUATION] where [MATH] is the distance between the MYO armband to the tip of the user’s finger, which can be measured or fixed approximately and [MATH] is the Gaussian measurement noise present in the gyroscope and magnetometer signals. Equations ( and ( ) are in the st... |
4.2 Problem 5: User Interface Design We developed a GUI in MATLAB which takes in the input from the human through the computer mouse and performs the desired behavior with simulated robots. The user interacts with the GUI using arm movements and gestures which are mapped to mouse movements and mouse clicks according to... |
[MATH] on the [MATH] to right side of the screen using mouse scroll or the “wave up” and “wave down” gestures to increase or decrease the angle [MATH] respectively. On the top right corner scaling [MATH] is chosen again by the “wave up” and “wave down” gestures in a similar manner as the desired angle. The larger area ... |
4.3 Problem 4: Swarm Controller Our swarm controller is designed to achieve the interpreter’s intention [MATH] at time [MATH] . Having second-order integrator dynamics for the agents, and the need of controlling the swarm centroid motivates our controller which extends Cortés ( 2009 (for first-order agents) with the dy... |
With [MATH] being the position and velocity of the [MATH] agent, our second-order distributed swarm controller takes the form: [EQUATION] |
where [MATH] are control gains and [MATH] is the rotation matrix corresponding to [MATH] . The variable [MATH] is the estimated center of the swarm by the [MATH] agent. Note that the [MATH] are the Metropolis weights defined in Section 2.2 . This algorithm, which applies to second-order systems, cancels out the drift o... |
[MATH] . The FODAC algorithm in Zhu and Martínez ( 2010 in equation ( 4b ) is used to distributively estimate the mean of time varying reference signal [MATH] which would give us the estimate of the swarm’s centroid [MATH] |
Using ( ) the swarm achieves the desired interpreter’s intention [MATH] . After some calculations, with [MATH] [MATH] as the combined state of the swarm, the state space form of our swarm controller is represented as: |
[EQUATION] Here [MATH] is a dummy state introduced to obtain a linear system in standard form. It is interesting to note that the swarm controller ( ) consists of an autonomous component |
[MATH] and a controlled component [MATH] housing the desired interpreter’s intention [MATH] . So [MATH] can be communicated once at the beginning of the [MATH] iteration and the agents just need to adjust their positions and communicate locally with their neighbors to achieve the intermediate goal. Letting |
[MATH] , the desired intention [MATH] in this state space is given by [MATH] Now we will theoretically analyze the performance of the proposed swarm controller in the next section. |
4.4 Swarm Controller Analysis In this section we will analyze our proposed controller ) to determine stability and convergence. We will look at the case when [MATH] remains constant for |
[MATH] So this makes our system time-invariant in that interval. In this work, we will make use of the following assumptions on [MATH] |
Assumption 1 (Connectivity) The communication graph [MATH] has at least one globally reachable vertex at every time [MATH] Assumption 2 |
(Constant graphs). The communication graph [MATH] remains constant for [MATH] System ( ) represents [MATH] copies of the same dynamics corresponding to [MATH] different dimensions. To simplify notation, we will analyze only one of the dimensions. After fixing [MATH] and omitting it for simplicity, our swarm controller ... |
[EQUATION] where [MATH] . System ( ) is an interconnected system whose stability depends on the chosen gains [MATH] and [MATH] . We will use the discrete analogue of composite Lyapunov functions Khalil ( 2002 to design the gains that guarantee the stability of the interconnected system. With [MATH] we can state the fol... |
Theorem 1 (Stability of Swarm Controller). Under Assumption 1 (connectivity) and Assumption 2 (constant interconnection graph), with the control gains satisfying [MATH] , the swarm globally uniformly asymptotically stabilizes to the desired state [MATH] under the swarm controller dynamics ( ) from any initial condition... |
The proof of Theorem is presented in the Appendix. Next we will use the results of Theorem to get an intuition of the role of graph connectivity ( [MATH] and [MATH] ) in the convergence of our swarm controller ( ). |
Corollary 1 The convergence rate of ( ) is directly proportional to [MATH] and [MATH] of the communication graph. The proof of Corollary can be found in the Appendix. Using these results we will design a planning algorithm, which optimally determines the intermediate subgoals which will be described in Section 4.5.2 |
4.5 The interpreter In this section we describe the role of the interpreter in the framework. For ease of illustration, we consider the formulation in |
[MATH] D space. The interpreter mainly consists of two parts: the behavior specifier and the planner, which are illustrated in the following paragraphs. |
4.5.1 Problem 2: Behavior Specifier The Behavior specifier converts the desired human intention into parameters that can be comprehended by the swarm. The human user specifies the desired shape [MATH] which takes the form of an arbitrary polygon, the desired centroid [MATH] , scaling [MATH] and rotation [MATH] . The in... |
[MATH] is calculated, where [MATH] is the area of polygon [MATH] . We assume the density is large enough to fit [MATH] robots in the shape [MATH] . Note that, since the shape [MATH] is bounded, there exists a large enough box [MATH] such that [MATH] and [MATH] is equal to a perfect square |
[MATH] , for some [MATH] and [MATH] Using this density, robots are distributed uniformly in the bounding box [MATH] of the polygon [MATH] by creating a meshgrid. Finally, we discard the generated points not in the polygon and we arrive at the desired formation [MATH] of [MATH] points shown in the right half of Figure 5... |
4.5.2 Problem 3: Planner The Planner receives the decoded human intention in the form of desired formation [MATH] (or, equivalently, [MATH] ), scaling |
[MATH] , rotation [MATH] , and centroid [MATH] . The planner then constructs a set of intermediate way points [MATH] where [MATH] denotes the number of intermediate steps in the plan to reach the final goal. |
To do this, we employ an [MATH] -Horizon Discrete Switched Linear Quadratic Regulator (DSLQR) formulation. A particular DSLQR problem with a dynamical variable [MATH] and time horizon [MATH] can be formulated as follows: |
[EQUATION] where [MATH] . Here, the running cost consist of a switching LQ cost function, with parameterized matrices [MATH] and [MATH] , depending on a mode [MATH] The function will be designed to enhance swarm performance while the linear constraint will be used to enforce an easy-to-interpret behavior by a human, wh... |
Details and methodology of DSLQR systems can be found in Zhang et al. ( 2009 . We show next how we apply this approach in our particular setup and describe the matrices that we choose for our framework. |
(i) Human-Interpretable Dynamics: We introduce the notion of Human Interpretable Dynamics (HID) to denote a dynamical system that can be easily understood by a human. Since the interpreter needs to provide feedback to the user, the planner needs to provide an abstraction of the complicated swarm dynamics in an [MATH] -... |
Here, we propose a simple linear dynamical system approach to model these dynamics, which takes into account the desired human intention |
[MATH] . We suppose that fully actuated linear dynamical systems are more easily understandable by humans, as opposed to other nonlinear system models. We let |
[MATH] denote the state of the HID system with [MATH] , where [MATH] . Then, the HID takes the form: [EQUATION] where matrices [MATH] and control input [MATH] . In this paper, we choose [MATH] and [MATH] to be identity matrices. This seems to be the most intuitive dynamics as the control input applies directly on the s... |
We use the [MATH] horizon Discrete LQR control technique to drive the HID towards [MATH] starting from some initial configuration [MATH] . By considering a change of variable [MATH] , we define a first term contributing to the problem cost functional as follows: |
[EQUATION] where the matrices [MATH] are positive definite and [MATH] is a step change applied during the [MATH] time. So [MATH] is chosen such that the cost [MATH] is minimized. This is solved using the standard LQR approach, and the results are shown in Figure 5(a) for a [MATH] horizon problem. Intuitively, one can c... |
(ii) Swarm performance costs. We just discussed how to generate intermediate shapes taking into account the HID. Now we consider the swarm performance and communication cost to choose the operating mode [MATH] in the general setup. The operating modes [MATH] correspond to a subset of [MATH] -disk graphs defined over th... |
[MATH] by choosing appropriate communication radii. Operating costs involved: To increase the speed of convergence and to facilitate quicker interpretation by a human, we need to maximize the notion of connectivity involving the second smallest eigenvalue [MATH] or [MATH] of the respective Laplacian matrices [MATH] and... |
[MATH] increases iff the determinant of [MATH] increases. So the connectivity cost [MATH] being in formation [MATH] and operation mode [MATH] at time [MATH] is given by: |
[EQUATION] To ensure [MATH] remains well scaled and positive we introduce positive constants [MATH] and [MATH] respectively. Having a [MATH] corresponding to a higher communication radius implies that we will be using more energy to communicate and maintain communication links. This is encoded as a communication cost [... |
[EQUATION] where [MATH] is the communication range at time [MATH] and [MATH] is a positive constant used for scaling. Adding these costs together defines the total cost used by the planner as: |
[EQUATION] where [MATH] [MATH] [MATH] and [MATH] Observe that a solution to the above problem requires the evaluation of all possible graph combinations for different chosen controls [MATH] . By choosing the graphs based on the communication radii, and considering a class of formations, we reduce significantly the numb... |
and [MATH] , then, given this, we optimize in the [MATH] variable using the DSLQR approach from Zhang et al. ( 2009 . This is further illustrated and discussed in Section 5.3 |
Implementation Results 5.1 System Setup The user has the choice to use either the MYO armband or the mouse to interact with a GUI to control the formation of a simulated swarm in a two dimensional environment. The swarm controller developed in Section 4.3 essentially generates waypoints for the swarm to follow, we assu... |
5.2 Intention Decoding We performed tests to gauge the accuracy and speed of the proposed HMM and Kalman Filter models. For the HMM model, some of our previous tests had given an accuracy levels of over 90% on an average Suresh ( 2016 for similar gestures and framework. On preliminary tests we observed similar results ... |
describes the error involved in each of the trials. It can be seen that the errors involved are about the same with both interfaces, however the speed of using the mouse is higher than the other. This is also due to the fact that users are accustomed to using the mouse for years and need time to adapt to the new interf... |
5.3 DSLQR Formulation Now we will validate the proposed framework by running simulations of a swarm of 50 agents to reach the desired human intention. Below, we illustrate a particular execution of our framework. |
Figure (a)-(d) indicate the desired human intention communicated by the human. Using [MATH] [MATH] [MATH] [MATH] [MATH] [MATH] the planner was implemented for a |
[MATH] horizon problem with [MATH] subsystems. The communication ranges are [MATH] , corresponding to the three operating modes. Figure 7(e) illustrates the intermediate shapes resulting from the [MATH] horizon planner, starting from the current intention(triangle on the left), to the desired intention(larger rotated q... |
[MATH] mode during the [MATH] timestep. During the [MATH] timestep another switching occurs to the [MATH] operating mode to maintain minimum cost. This is coherent with the intuition of using larger communication radii for more sparse swarms. As the scaling increases with every timestep the agents are forced further ap... |
Conclusions and Future Work In this work we have proposed and successfully implemented a novel HSI framework for formation control, where the user draws the desired shape using intuitive gestures, and the swarm successfully depicts the drawn shape. We have combined diverse tools from control theory, network science, ma... |
[MATH] space. Lastly, we have integrated the framework by developing a GUI environment which interacts with user by means of gestures, and rest of the framework is encapsulated in the GUI using matlab simulations. |
Future work will involve validation of the proposed framework with robustness towards noise and uncertainties. We also wish to learn the Human Interpret-able dynamics from existing human behavior models and data. |
{ack} We thank Mac Schwager for useful discussions regarding the HMM formulation used in this work. We also thank Chidi Ewenike, Ramon Duran and Tomaz Torres for their help in developing the Myo armband setup used in this work. |
Appendix Preliminaries for proof of Theorm Let us first define the following quantities : [MATH] [MATH] [MATH] [MATH] ; and [MATH] |
With these definitions System ( ) can be represented as : [EQUATION] where [MATH] is the system dynamics of the [MATH] system, [MATH] is the interconnection to the [MATH] system and |
[MATH] is the drift of the [MATH] system. Now [MATH] resembles the shape stabilizing JOR algorithm in Cortés ( 2009 with some additional centroid drift |
[MATH] . From Cortés ( 2009 we know this system converges to the desired shape with some centroid translation. Henceforth, we will ignore the drift [MATH] while analyzing the overall system stability. As we see next, stability is established by first analyzing the convergence rates of each of the subsystems defined by ... |
Lemma 1 The subsystem [MATH] is globally uniformly asymptotically stable at [MATH] {pf} Considering [MATH] , we have that the eigenvalues |
[MATH] and [MATH] is a simple eigenvalue with right eigenvector [MATH] , which shows [MATH] is globally stable. We can perform a similarity transformation on [MATH] to get |
[MATH] where [MATH] is the symmetric normalized Laplacian of the graph. It holds that the eigenvalues of [MATH] are the same as [MATH] and the eigenvectors are those of [MATH] scaled by a factor of [MATH] . We perform a Hotelling deflation Saad ( 2003 on [MATH] using the largest eigenvalue to get [MATH] . In this way, ... |
[MATH] where [MATH] is the second smallest eigenvalue of the normalized Laplacian [MATH] . We will proceed by analyzing the stability properties of [MATH] which is similar to analyzing the stability of [MATH] since the eigenvalues and their related properties are the same. |
With [MATH] and [MATH] we have [EQUATION] The above observation follows from the fact that [MATH] is symmetric and [MATH] hence the eigenvalues [MATH] , which makes [MATH] negative definite. From Lyapunov theory we have that [MATH] is globally uniformly asymptotically stable about the origin. From the theory of symmetr... |
[EQUATION] which gives us a convergence rate for the [MATH] dynamics. [MATH] Now we will analyze the second subsystem. The Matrix [MATH] has 1 as the simple eigenvalue with eigenvector |
[MATH] . The matrix [MATH] is Schur stable and [MATH] , where [MATH] is the second smallest eigenvalue associated with the weighted graph |
[MATH] . Hence we will analyze the convergence of the system [MATH] , which will give us the convergence rate for system [MATH] Lemma 2 |
The system [MATH] is globally uniformly asymptotically stable to the origin, and the convergence rate of system [MATH] is proportional to [MATH] |
{pf} With [MATH] and [MATH] we have [EQUATION] This follows from the fact that the eigenvalues [MATH] , which makes [MATH] negative definite. Hence according to Lyapunov theory |
[MATH] is globally uniformly asymptotically stable to the origin. In addition, [EQUATION] which finally gives us the convergence rate for the [MATH] |
dynamics. [MATH] The analysis of the third subsystem, [MATH] , is trivial. Now, let us define the following constants: [MATH] [MATH] |
[MATH] [MATH] and [MATH] Now we are ready to state the stability of System ( ). Proof of Theorm {pf} The system ( ) can be equivalently represented in the form ( ). Now let us first consider driftless system ( ). The positive definite Lyapunov functions [MATH] and the interconnection functions |
[MATH] satisfy the conditions of ( 16 ) for all [MATH] From Lemma and Lemma for each subsystem [MATH] we have: [EQUATION] Now if we consider a diagonal matrix [MATH] with diagonal entries [MATH] , a column vector |
[MATH] and a matrix [MATH] , we can define a Matrix [MATH] as follows [EQUATION] [EQUATION] The Matrix [MATH] is an M-matrix, which is characterized by non-positive off diagonal entries and positive leading principal minors. The former property is satisfied by inspecting [MATH] . The first leading principal minor is po... |
Now, we choose [MATH] accordingly such that [MATH] defined according to 17 ) is an M matrix. Now from Khalil ( 2002 (cf. Theorem 9.2) we can conclude that the interconnected system ( ) is globally stable. |
As the interconnections are asymptically stable we can infer the following. Firstly, the subsystem ( 6a ) denoting the position of the agents stabilizes to the desired shape, orientation and scaling according to Cortés ( 2009 and also reach the desired centroid due to the shifting term [MATH] . Additionally, assumption... |
[MATH] . Thus, the overall system converges to the desired state [MATH] [MATH] Proof of Corollary {pf} For connected graphs we know that [MATH] and [MATH] . From Equations ( 14 ) and ( 15 ) we can see that the convergence of the swarm dynamics is faster with higher values of [MATH] and [MATH] We know that the convergen... |
[MATH] . However from Theorm we need to satisfy: [EQUATION] Equation ( 18 ) reveals that, given a fixed [MATH] the upperbound on [MATH] can be increased with an increase in [MATH] and [MATH] .Hence, we have faster convergence of system ( ) with higher graph connectivity. [MATH] |
# Source: arxiv 1805.02493 # Title: GeneVis - An interactive visualization tool for combining cross-discipline datasets within genetics # Sections: all # Downloaded: 2026-03-02T08:41:59.833996+00:00 |
GeneVis An interactive visualization tool for combining cross-discipline datasets within genetics Abstract Summary: GeneVis is a web-based tool to visualize complementary data sets of different disciplines within the field of genetics. It overlays gene-cluster information, gene-interaction data and gene-disease associa... |
Availability: The source of GeneVis is available at Contact: casper.vanleeuwen@surfsara.nl Introduction The continuous technological advancement in the fields of genetics, genomics and bioinformatics has led to large data sets on gene clusters, gene-gene interactions and the association of genes with diseases. One of t... |
GeneVis uses force-directed graphs as a basis to visualize relations between gene clusters, between clusters and individual genes and between individual genes (figure ). Force-directed graphs are a general way to visualize relational data (Eades et al .,, 1984 (Tollis et al .,, 1999 (Fruchterman and Reingold,, 1991 , a... |
Method 2.1 Datasets GeneVis allows a simultaneous visualization of three complementary types of datasets: a gene cluster dataset, a gene-gene interaction dataset and a gene-disease association dataset. All datasets must be provided in either tab or comma-separated tabular file formats. For example file formats see Appe... |
2.1.1 Gene cluster dataset To visualize gene clusters with GeneVis, the gene cluster dataset should contain a list of gene names with the associated gene cluster. The cluster data can either be based on a hard (0 or 1) or soft probability clustering (between 0 and 1), which both will be handled appropriately by GeneVis... |
2.1.2 Gene-gene interaction dataset GeneVis can visualize any form of gene-gene interaction that can be scored as an interaction strength between 0 and 1. To visualize gene-gene interactions, GeneVis requires a tabular dataset of genes containing 3 columns, the source gene Entrez ID (SourceGeneId), the target gene Entr... |
2.1.3 Gene-disease association dataset The gene-disease association dataset is a tabular dataset containing diseases and its associated genes and scores. Each row in this dataset is a study about a certain disease and it’s associated gene(s) and that studies [MATH] -value (see table ). This dataset must contain at leas... |
2.2 Cluster View GeneVis offers two levels of visualization. In Cluster View (left panel, figure ) all gene clusters present in the gene cluster dataset and their overlap are shown. The layout of the graph of clusters is determined by means of a force-directed graph layout algorithm (Tollis et al .,, 1999 . Each gene c... |
An edge between two cluster nodes describes the gene overlap between the clusters. The size and the color intensity of the edge both scale with the amount of overlap between the clusters, meaning the wider and brighter the edge, the more overlap there is between the connected clusters, in terms of numbers of genes. |
Clusters can be inspected by highlighting the cluster, which will reveal the underlying genes associated with the cluster in GeneView. |
2.3 Gene View The Gene View (right panel, figure ) visualizes the individual gene interactions within a selected cluster. Each gene is represented as a node and each edge is an interaction between the genes. The gene nodes are represented as pie charts, where the size represents that gene’s association with the selecte... |
1) ”Level of connectedness highlighting” which highlights all the gene interactions connected to the highlighted gene through different levels of connectivity, e.g. a level of connectedness of 2 reveals all the connected genes to the highlighted gene as level 1 and all the genes connected to the genes in level 1 as lev... |
2) ”Link threshold highlighting” progresses through all the connected gene interactions and highlights those interactions whose interaction score is above the given threshold. |
3) ”Top-n link highlighting” highlights the top n highest interaction links and its genes starting from the highlighted gene. 2.4 Disease Mode |
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