diff --git "a/app/src/content/article.mdx" "b/app/src/content/article.mdx"
--- "a/app/src/content/article.mdx"
+++ "b/app/src/content/article.mdx"
@@ -27,6 +27,7 @@ import ch2_so100_to_planar_manipulator from './assets/image/figures/ch2/ch2-so10
import ch2_planar_manipulator_free from './assets/image/figures/ch2/ch2-planar-manipulator-free.png';
import ch2_planar_manipulator_floor from './assets/image/figures/ch2/ch2-planar-manipulator-floor.png';
import ch2_planar_manipulator_floor_shelf from './assets/image/figures/ch2/ch2-planar-manipulator-floor-shelf.png';
+import ch2_planar_manipulator_floor_box from './assets/image/figures/ch2/ch2-planar-manipulator-floor-box.png';
import ch2_classical_limitations from './assets/image/figures/ch2/ch2-classical-limitations.png';
import ch3_learning_benefits from './assets/image/figures/ch3/ch3-learning-benefits.png';
import ch3_learning_atlas from './assets/image/figures/ch3/ch3-learning-atlas.png';
@@ -50,15 +51,14 @@ import ch4_act from './assets/image/figures/ch4/ch4-act.png';
import ch4_act_encoder from './assets/image/figures/ch4/ch4-act-encoder.png';
import ch4_act_decoder from './assets/image/figures/ch4/ch4-act-decoder.png';
import ch4_diffusion_policy from './assets/image/figures/ch4/ch4-diffusion-policy.png';
+import ch4_async_inference from './assets/image/figures/ch4/ch4-async-inference.png';
+import ch4_queues from './assets/image/figures/ch4/ch4-queues.png';
import ch5_ml_vs_robotics_foundation from './assets/image/figures/ch5/ch5-ml-vs-robotics-foundation.png';
import ch5_generalist_policies_timeline from './assets/image/figures/ch5/ch5-generalist-policies-timeline.png';
import ch5_trends from './assets/image/figures/ch5/ch5-trends.png';
import ch5_pi0 from './assets/image/figures/ch5/ch5-pi0.png';
-import ch5_smolvla from './assets/image/figures/ch5/ch5-smolvla.png';
-import ch2_planar_manipulator_floor_box from './assets/image/figures/ch2/ch2-planar-manipulator-floor-box.png';
-import ch4_async_inference from './assets/image/figures/ch4/ch4-async-inference.png';
-import ch4_queues from './assets/image/figures/ch4/ch4-queues.png';
import ch5_pi0_sampling_timesteps from './assets/image/figures/ch5/ch5-pi0-sampling-timesteps.png';
+import ch5_smolvla from './assets/image/figures/ch5/ch5-smolvla.png';
## Foreword
@@ -81,15 +81,17 @@ We sincerely hope this tutorial serves as a valuable starting point for your jou
## Introduction
+
+
+lerobot is the open-source library for end-to-end robotics developed by Hugging Face. The library is vertically integrated on the entire robotics stack, supporting low-level control of real-world robot devices, advanced data and inference optimizations, as well as SOTA robot learning methods with simple implementations in pure Pytorch.
+
Autonomous robotics holds the premise of relieving humans from repetitive, tiring or dangerous manual tasks. Consequently, the field of robotics has been widely studied since its first inception in the 1950s. Lately, advancements in Machine Learning (ML) have sparked the development of a relatively new class of methods used to tackle robotics problems, leveraging large amounts of data and computation rather than human expertise and modeling skills to develop autonomous systems.
@@ -97,17 +99,17 @@ The frontier of robotics research is indeed increasingly moving away from classi
Moreover, since end-to-end learning on ever-growing collections of text and image data has historically been at the core of the development of *foundation models* capable of semantic reasoning across multiple modalities (images, text, audio, etc.), deriving robotics methods grounded in learning appears particularly consequential, especially as the number of openly available datasets continues to grow.
-Robotics is, at its core, an inherently multidisciplinary field, requiring a wide range of expertise in both *software* and *hardware*. The integration of learning-based techniques further broadens this spectrum of skills, raising the bar for both research and practical applications. `lerobot` is an open-source library designed to integrate end-to-end with the entire robotics stack. With a strong focus on accessible, real-world robots (1) `lerobot` supports many, openly available, robotic platforms for manipulation, locomotion and even whole-body control. `lerobot`also implements a (2) unified, low-level approach to reading/writing robot configurations to extend support for other robot platforms with relatively low effort. The library introduces `LeRobotDataset`, (3) a native robotics dataset’s format currently being used by the community to efficiently record and share datasets. `lerobot` also supports many state-of-the-art (SOTA) algorithms in robot learning--mainly based on Reinforcement Learning (RL) and Behavioral Cloning (BC) techniques--with efficient implementations in Pytorch, and extended support to experimentation and experiments tracking. Lastly, `lerobot` defines a custom, optimized inference stack for robotic policies decoupling action planning from action execution, proving effective in guaranteeing more adaptability at runtime.
+Robotics is, at its core, an inherently multidisciplinary field, requiring a wide range of expertise in both *software* and *hardware*. The integration of learning-based techniques further broadens this spectrum of skills, raising the bar for both research and practical applications. `lerobot` is an open-source library designed to integrate end-to-end with the entire robotics stack. With a strong focus on accessible, real-world robots `lerobot` supports many, openly available, robotic platforms for manipulation, locomotion and even whole-body control. `lerobot`also implements a unified, low-level approach to reading/writing robot configurations to extend support for other robot platforms with relatively low effort. The library introduces `LeRobotDataset`, a native robotics dataset’s format currently being used by the community to efficiently record and share datasets. `lerobot` also supports many state-of-the-art (SOTA) algorithms in robot learning--mainly based on Reinforcement Learning (RL) and Behavioral Cloning (BC) techniques--with efficient implementations in Pytorch, and extended support to experimentation and experiments tracking. Lastly, `lerobot` defines a custom, optimized inference stack for robotic policies decoupling action planning from action execution, proving effective in guaranteeing more adaptability at runtime.
This tutorial serves the double purpose of providing useful references for the Science behind--and practical use of--common robot learning techniques. To this aim, we strike to provide a rigorous yet concise overview of the core concepts behind the techniques presented, paired with practical examples of how to use such techniques concretely, with code examples in `lerobot`, for researchers and practitioners interested in the field of robot learning. This tutorial is structured as follows:
-- Section 2 reviews classical robotics foundations, introducing the limitations of dynamics-based approaches to robotics.
+- Section [classical] reviews classical robotics foundations, introducing the limitations of dynamics-based approaches to robotics.
-- Section 3 elaborates on the limitations of dynamics-based methods, and introduce RL as a practical approach to solve robotics problems, considering its upsides and potential limitations.
+- Section [learning-rl] elaborates on the limitations of dynamics-based methods, and introduce RL as a practical approach to solve robotics problems, considering its upsides and potential limitations.
-- Section 4 further describes robot learning techniques that aim at solving single-tasks learning, leveraging BC techniques to autonomously reproduce specific expert demonstrations.
+- Section [robot-imitation-learning] further describes robot learning techniques that aim at solving single-tasks learning, leveraging BC techniques to autonomously reproduce specific expert demonstrations.
-- Section 5 presents recent contributions on developing generalist models for robotics applications, by learning from large corpora of multi-task multi-robot data (*robotics foundation models*).
+- Section [learning-foundation] presents recent contributions on developing generalist models for robotics applications, by learning from large corpora of multi-task multi-robot data (*robotics foundation models*).
Our goal with this tutorial is to provide an intuitive explanation of the reasons various disparate ideas from Machine Learning (ML) have converged and are powering the current evolution of Robotics, driving the unprecedented progress we see today. We complement our presentation of the most common and recent approaches in robot learning with practical code implementations using `lerobot`, and start here by presenting the dataset format introduced with `lerobot`.
@@ -207,6 +209,7 @@ for epoch in range(num_epochs):
## Classical Robotics
+
*Know your enemy* \[...\]
@@ -222,33 +225,37 @@ TL;DR Learning-based approaches to robotics are motivated by the need to (1) gen
### Explicit and Implicit Models
+
+
+Overview of methods to generate motion (clearly non-exhausitve, see @bekrisStateRobotMotion2024). The different methods can be grouped based on whether they explicitly (dynamics-based) or implicitly (learning-based) model robot-environment interactions.
+
-Robotics is concerned with producing artificial motion in the physical world in useful, reliable and safe fashion. Thus, robotics is an inherently multi-disciplinar domain: producing autonomous motion in the physical world requires, to the very least, interfacing different software (motion planners) and hardware (motion executioners) components. Further, knowledge of mechanical, electrical, and software engineering, as well as rigid-body mechanics and control theory have therefore proven quintessential in robotics since the field first developed in the 1950s. More recently, Machine Learning (ML) has also proved effective in robotics, complementing these more traditional disciplines @connellRobotLearning1993. As a direct consequence of its multi-disciplinar nature, robotics has developed as a rather wide array of methods, all concerned with the main purpose of producing artificial motion in the physical world.
+Robotics is concerned with producing artificial motion in the physical world in useful, reliable and safe fashion. Thus, robotics is an inherently multi-disciplinar domain: producing autonomous motion in the physical world requires, to the very least, interfacing different software (motion planners) and hardware (motion executioners) components. Further, knowledge of mechanical, electrical, and software engineering, as well as rigid-body mechanics and control theory have therefore proven quintessential in robotics since the field first developed in the 1950s. More recently, Machine Learning (ML) has also proved effective in robotics, complementing these more traditional disciplines @connellRobotLearning1993. As a direct consequence of its multi-disciplinar nature, robotics has developed as a rather wide array of methods, all concerned with the main purpose of producing artificial motion in the physical world.
-Methods to produce robotics motion range from traditional *explicit* models--dynamics-based[^1] methods, leveraging precise descriptions of the mechanics of robots’ rigid bodies and their interactions with eventual obstacles in the environment--to *implicit* models--learning-based methods, treating artificial motion as a statistical pattern to learn given multiple sensorimotor readings @agrawalComputationalSensorimotorLearning, @bekrisStateRobotMotion2024. A variety of methods have been developed between these two extrema. For instance, @hansenTemporalDifferenceLearning2022 show how learning-based systems can benefit from information on the physics of problems, complementing a traditional learning method such as Temporal Difference (TD)-learning @suttonReinforcementLearningIntroduction2018 with Model-Predictive Control (MPC). Conversely, as explicit models may be relying on assumptions proving overly simplistic--or even unrealistic--in practice, learning can prove effective to improve modeling of complex phenomena or complement perception @mccormacSemanticFusionDense3D2016. Such examples aim at demonstrating the richness of approaches to robotics, and Figure 2 graphically illustrates some of the most relevant techniques. Such a list is clearly far from being exhaustive, and we refer to @bekrisStateRobotMotion2024 for a more comprehensive overview of both general and application-specific methods for motion generation. In this section, we wish to introduce the inherent benefits of learning-based approaches to robotics--the core focus on this tutorial.
+Methods to produce robotics motion range from traditional *explicit* models--dynamics-based[^1] methods, leveraging precise descriptions of the mechanics of robots’ rigid bodies and their interactions with eventual obstacles in the environment--to *implicit* models--learning-based methods, treating artificial motion as a statistical pattern to learn given multiple sensorimotor readings @agrawalComputationalSensorimotorLearning, @bekrisStateRobotMotion2024. A variety of methods have been developed between these two extrema. For instance, @hansenTemporalDifferenceLearning2022 show how learning-based systems can benefit from information on the physics of problems, complementing a traditional learning method such as Temporal Difference (TD)-learning @suttonReinforcementLearningIntroduction2018 with Model-Predictive Control (MPC). Conversely, as explicit models may be relying on assumptions proving overly simplistic--or even unrealistic--in practice, learning can prove effective to improve modeling of complex phenomena or complement perception @mccormacSemanticFusionDense3D2016. Such examples aim at demonstrating the richness of approaches to robotics, and Figure [generating-motion-atlas] graphically illustrates some of the most relevant techniques. Such a list is clearly far from being exhaustive, and we refer to @bekrisStateRobotMotion2024 for a more comprehensive overview of both general and application-specific methods for motion generation. In this section, we wish to introduce the inherent benefits of learning-based approaches to robotics--the core focus on this tutorial.
### Different Types of Motion
+
+
+Different kinds of motions are achieved with potentially very different robotic platforms. From left to right, top to bottom: ViperX, SO-100, Boston Dynamics’ Spot, Open-Duck, 1X’s NEO, Boston Dynamics’ Atlas. This is an example list of robotic platforms and is (very) far from being exhaustive.
+
-In the vast majority of instances, robotics deals with producing motion via actuating joints connecting nearly entirely-rigid links. A key distinction between focus areas in robotics is based on whether the generated motion modifies (1) the absolute state of the environment (via dexterity), (2) the relative state of the robot with respect to its environment (exercising mobility skills), or (3) a combination of the two (Figure 3).
+In the vast majority of instances, robotics deals with producing motion via actuating joints connecting nearly entirely-rigid links. A key distinction between focus areas in robotics is based on whether the generated motion modifies (1) the absolute state of the environment (via dexterity), (2) the relative state of the robot with respect to its environment (exercising mobility skills), or (3) a combination of the two (Figure [robotics-platforms-atlas]).
Effects such as (1) are typically achieved *through* the robot, i.e. generating motion to perform an action inducing a desirable modification, effectively *manipulating* the environment (manipulation). Motions like (2) may result in changes in the robot’s physical location within its environment. Generally, modifications to a robot’s location within its environment may be considered instances of the general *locomotion* problem, further specified as *wheeled* or *legged* locomotion based on whenever a robot makes use of wheels or leg(s) to move in the environment. Lastly, an increased level of dynamism in the robot-environment interactions can be obtained combining (1) and (2), thus designing systems capable to interact with *and* move within their environment. This category is problems is typically termed *mobile manipulation*, and is characterized by a typically much larger set of control variables compared to either locomotion or manipulation alone.
@@ -258,68 +265,78 @@ The traditional body of work developed since the very inception of robotics is i
Robot manipulators typically consist of a series of links and joints, articulated in a chain finally connected to an *end-effector*. Actuated joints are considered responsible for generating motion of the links, while the end effector is instead used to perform specific actions at the target location (e.g., grasping/releasing objects via closing/opening a gripper end-effector, using a specialized tool like a screwdriver, etc.).
-Recently, the development of low-cost manipulators like the ALOHA @zhaoLearningFineGrainedBimanual2023 ALOHA-2 @aldacoALOHA2Enhanced and SO-100/SO-101 @knightStandardOpenSO100 platforms significantly lowered the barrier to entry to robotics, considering the increased accessibility of these robots compared to more traditional platforms like the Franka Emika Panda arm (Figure 4).
+Recently, the development of low-cost manipulators like the ALOHA @zhaoLearningFineGrainedBimanual2023 ALOHA-2 @aldacoALOHA2Enhanced and SO-100/SO-101 @knightStandardOpenSO100 platforms significantly lowered the barrier to entry to robotics, considering the increased accessibility of these robots compared to more traditional platforms like the Franka Emika Panda arm (Figure [robotic-platforms-costs]).
+
+
+Cheaper, more accessible robots are starting to rival traditional platforms like the Panda arm platforms in adoption in resource-constrained scenarios. The SO-100, in particular, has a cost in the 100s of Euros, and can be entirely 3D-printed in hours, while the industrially-manufactured Panda arm costs tens of thousands of Euros and is not openly available.
+
Deriving an intuition as per why learning-based approaches are gaining popularity in the robotics community requires briefly analyzing traditional approaches for manipulation, leveraging tools like forward and inverse kinematics (FK, IK) and control theory. Providing a detailed overview of these methods falls (well) out of the scope of this tutorial, and we refer the reader to works including @sicilianoSpringerHandbookRobotics2016, @lynchModernRoboticsMechanics2017, @tedrakeRoboticManipulationPerception, @tedrakeUnderactuatedRoboticsAlgorithms for a much more comprehensive description of these techniques. Here, we mostly wish to highlight the benefits of ML over these traditional techniques
+
+
+The SO-100 arm is a 6-dof manipulator arm. Preventing some of its joints (shoulder pane, wrist flex and wrist roll) from actuating, it can be represented as a traditional 2-dof planar manipulator (the gripper joint in the end-effector is not considered towards the count of the degrees of freedom used to produce motion).
+
-Consider the (simple) case where a SO-100 is restrained from actuating (1) the shoulder pane and (2) the wrist flex and roll motors. This effectively reduces the degrees of freedom of the SO-100 from the original 5+1 (5 joints + 1 gripper) to 2+1 (shoulder lift, elbow flex + gripper). As the end-effector does not impact motion in this model, the SO-100 is effectively reduced to the planar manipulator robot presented in Figure 5, where spheres represent actuators, and solid lines indicate length-$l$ links from the base of the SO-100 to the end-effector (*ee*).
+Consider the (simple) case where a SO-100 is restrained from actuating (1) the shoulder pane and (2) the wrist flex and roll motors. This effectively reduces the degrees of freedom of the SO-100 from the original 5+1 (5 joints + 1 gripper) to 2+1 (shoulder lift, elbow flex + gripper). As the end-effector does not impact motion in this model, the SO-100 is effectively reduced to the planar manipulator robot presented in Figure [make-so100-planar-manipulator], where spheres represent actuators, and solid lines indicate length-$l$ links from the base of the SO-100 to the end-effector (*ee*).
Further, let us make the simplifying assumption that actuators can produce rotations up to $2 \pi$ radians. In practice, this is seldom the case due to movement obstructions caused by the robot body itself (for instance, the shoulder lift cannot produce counter-clockwise movement due to the presence of the robot’s base used to secure the SO-100 to its support and host the robot bus), but we will introduce movement obstruction at a later stage.
-All these simplifying assumptions leave us with the planar manipulator of Figure 6, free of moving its end-effector by controlling the angles $\theta_1$ and $\theta_2$, jointly referred to as the robot’s *configuration*, and indicated with $q = [\theta_1, \theta_2 ] \in [-\pi, +\pi]^2$. The axis attached to the joints indicate the associated reference frame, whereas circular arrows indicate the maximal feasible rotation allowed at each joint. In this tutorial, we do not cover topics related to spatial algebra, and we instead refer the reader to and for excellent explanations of the mechanics and theoretical foundations of producing motion on rigid bodies.
+All these simplifying assumptions leave us with the planar manipulator of Figure [planar-manipulation-simple], free of moving its end-effector by controlling the angles $\theta_1$ and $\theta_2$, jointly referred to as the robot’s *configuration*, and indicated with $q = [\theta_1, \theta_2 ] \in [-\pi, +\pi]^2$. The axis attached to the joints indicate the associated reference frame, whereas circular arrows indicate the maximal feasible rotation allowed at each joint. In this tutorial, we do not cover topics related to spatial algebra, and we instead refer the reader to and for excellent explanations of the mechanics and theoretical foundations of producing motion on rigid bodies.
-
+
+
+
+Constrained by surface and (fixed) obstacle
+Planar, 2-dof schematic representation of the SO-100 manipulator under diverse deployment settings. From left to right: completely free of moving; constrained by the presence of the surface; constrained by the surface and presence of obstacles. Circular arrows around each joint indicate the maximal rotation feasible at that joint.
-Considering the (toy) example presented in Figure 6, then we can analytically write the end-effector’s position $p \in \mathbb R^2$ as a function of the robot’s configuration, $p = p(q), p: \mathcal Q \mapsto \mathbb R^2$. In particular, we have:
+Considering the (toy) example presented in Figure [planar-manipulation-simple], then we can analytically write the end-effector’s position $p \in \mathbb R^2$ as a function of the robot’s configuration, $p = p(q), p: \mathcal Q \mapsto \mathbb R^2$. In particular, we have:
$$
`p(q) = \begin{pmatrix} p_x(\theta_1, \theta_2)\\ p_y(\theta_1, \theta_2) \end{pmatrix} = \begin{pmatrix} l \cos(\theta_1) + l \cos(\theta_1 + \theta_2)\\ l \sin(\theta_1) + l \sin(\theta_1 + \theta_2) \end{pmatrix} \in S^{n=2}_{l_1+l_2} = \{ p(q) \in \mathbb R^2: \Vert p(q) \Vert_2^2 \leq (2l)^2, \ \forall q \in \mathcal Q \}`
@@ -335,7 +352,7 @@ $\htmlId{ik_problem}{\min_{q \in \mathcal Q} \Vert p(q) - p^* \Vert_2^2 \, .}$
Exact analytical solutions to IK are even less appealing when one considers the presence of obstacles in the robot’s workspace, resulting in constraints on the possible values of $q \in \mathcal Q \subseteq [-\pi, +\pi]^n \subset \mathbb R^n$ in the general case of $n$-links robots.
-For instance, the robot in Figure 7 is (very naturally) obstacled by the presence of the surface upon which it rests: $\theta_1$ can now exclusively vary within $[0, \pi]$, while possible variations in $\theta_2$ depend on $\theta_1$ (when $\theta_1 \to 0$ or $\theta_1 \to \pi$, further downwards movements are restricted). Even for a simplified kinematic model, developing techniques to solve eq. [ik_problem] is in general non-trivial in the presence of constraints, particularly considering that the feasible set of solutions $\mathcal Q$ may change across problems. Figure 9 provides an example of how the environment influences the feasible set considered, with a new set of constraints deriving from the position of a new obstacle.
+For instance, the robot in Figure [planar-manipulator-floor] is (very naturally) obstacled by the presence of the surface upon which it rests: $\theta_1$ can now exclusively vary within $[0, \pi]$, while possible variations in $\theta_2$ depend on $\theta_1$ (when $\theta_1 \to 0$ or $\theta_1 \to \pi$, further downwards movements are restricted). Even for a simplified kinematic model, developing techniques to solve eq. [ik_problem] is in general non-trivial in the presence of constraints, particularly considering that the feasible set of solutions $\mathcal Q$ may change across problems. Figure [planar-manipulator-floor-shelf] provides an example of how the environment influences the feasible set considered, with a new set of constraints deriving from the position of a new obstacle.
However, IK--solving eq. [ik_problem] for a feasible $q$--only proves useful in determining information regarding the robot’s configuration in the goal pose, and crucially does not provide information on the *trajectory* to follow over time to reach a target pose. Expert-defined trajectories obviate to this problem providing a length-$K$ succession of goal poses $\tau_K = [p^*_0, p^*_1, \dots p^*_K]$ for tracking. In practice, trajectories can also be obtained automatically through *motion planning* algorithms, thus avoiding expensive trajectory definition from human experts. However, tracking $\tau_K$ via IK can prove prohibitively expensive, as tracking would require $K$ resolutions of eq. [ik_problem] (one for each target pose). *Differential* inverse kinematics (diff-IK) complements IK via closed-form solution of a variant of eq. [ik_problem]. Let $J(q)$ denote the Jacobian matrix of (partial) derivatives of the FK-function $f_\text{FK}- \mathcal Q \mapsto \mathcal P$, such that $J(q) = \frac{\partial f_{FK}(q)}{\partial q }$. Then, one can apply the chain rule to any $p(q) = f_{\text{FK}}(q)$, deriving $\dot p = J(q) \dot q$, and thus finally relating variations in the robot configurations to variations in pose, thereby providing a platform for control.
@@ -358,6 +375,8 @@ r0.3
+
+
One such case is presented in Figure [planar-manipulator-box-velocity], where another rigid body other than the manipulator is moving in the environment along the horizontal axis, with velocity $\dot x_B$. Accounting analytically for the presence of this disturbance--for instance, to prevent the midpoint of the link from ever colliding with the object--requires access to $\dot x_B$ at least, to derive the equation characterizing the motion of the environment.
@@ -374,28 +393,31 @@ We point the interested reader to , , and for extended coverage of FK, IK, di
Despite the last 60+ years of robotics research, autonomous robots are still largely incapable of performing tasks at human-level performance in the physical world generalizing across (1) robot embodiments (different manipulators, different locomotion platforms, etc.) and (2) tasks (tying shoe-laces, manipulating a diverse set of objects). While essential in the early development of robotics, the aforementioned methods require significant human expertise to be used in practice, and are typically specific to a particular applicative problem.
+
+
+Dynamics-based approaches to robotics suffer from several limitations: (1) orchestrating multiple components poses integration challenges; (2) the need to develop custom processing pipelines for the sensing modalities and tasks considered hinders scalability; (3) simplified analytical models of physical phenomena (here friction at the gripper; credits to @antonovaReinforcementLearningPivoting2017) limit real-world performance. Lastly, (4) dynamics-based methods overlook trends in the availability and growth of robotics data.
+
-Dynamics-based robotics pipelines have historically been developed sequentially, engineering the different blocks now within most architectures for specific purposes. That is, sensing, state estimation, mapping, planning, (diff-)IK, and low-level control have been traditionally developed as distinct modules with fixed interfaces. Pipelining these specific modules proved error-prone, and brittleness emerges--alongside compounding errors--whenever changes incur (e.g., changes in lighting for sensing, occlusion/failure of sensors, control failures). Adapting such a stack to new tasks or robotic platforms often entails re-specifying objectives, constraints, and heuristics at multiple stages, incurring significant engineering overhead.
+Dynamics-based robotics pipelines have historically been developed sequentially, engineering the different blocks now within most architectures for specific purposes. That is, sensing, state estimation, mapping, planning, (diff-)IK, and low-level control have been traditionally developed as distinct modules with fixed interfaces. Pipelining these specific modules proved error-prone, and brittleness emerges--alongside compounding errors--whenever changes incur (e.g., changes in lighting for sensing, occlusion/failure of sensors, control failures). Adapting such a stack to new tasks or robotic platforms often entails re-specifying objectives, constraints, and heuristics at multiple stages, incurring significant engineering overhead.
-Moreover, classical planners operate on compact, assumed-sufficient state representations; extending them to reason directly over raw, heterogeneous and noisy data streams is non-trivial. This results in a limited scalability to multimodal data and multitask settings, as incorporating high-dimensional perceptual inputs (RGB, depth, tactile, audio) traditionally required extensive engineering efforts to extract meaningful features for control. Also, the large number of tasks, coupled with the adoption of *per-task* planners, goal parameterizations, and safety constraints, results in an explosion in design and validation options, with little opportunity to reuse solutions across tasks.
+Moreover, classical planners operate on compact, assumed-sufficient state representations; extending them to reason directly over raw, heterogeneous and noisy data streams is non-trivial. This results in a limited scalability to multimodal data and multitask settings, as incorporating high-dimensional perceptual inputs (RGB, depth, tactile, audio) traditionally required extensive engineering efforts to extract meaningful features for control. Also, the large number of tasks, coupled with the adoption of *per-task* planners, goal parameterizations, and safety constraints, results in an explosion in design and validation options, with little opportunity to reuse solutions across tasks.
-Setting aside integration and scalability challenges: developing accurate modeling of contact, friction, and compliance for complicated systems remains difficult. Rigid-body approximations are often insufficient in the presence of deformable objects, and relying on approximated models hinders real-world applicability of the methods developed. In the case of complex, time-dependent and/or non-linear dynamics, even moderate mismatches in parameters, unmodeled evolutions, or grasp-induced couplings can qualitatively affect the observed dynamics.
+Setting aside integration and scalability challenges: developing accurate modeling of contact, friction, and compliance for complicated systems remains difficult. Rigid-body approximations are often insufficient in the presence of deformable objects, and relying on approximated models hinders real-world applicability of the methods developed. In the case of complex, time-dependent and/or non-linear dynamics, even moderate mismatches in parameters, unmodeled evolutions, or grasp-induced couplings can qualitatively affect the observed dynamics.
-Lastly, dynamics-based methods (naturally) overlook the rather recent increase in availability of openly-available robotics datasets. The curation of academic datasets by large centralized groups of human experts in robotics @collaborationOpenXEmbodimentRobotic2025, @khazatskyDROIDLargeScaleInTheWild2025 is now increasingly complemented by a growing number of robotics datasets contributed in a decentralized fashion by individuals with varied expertise. If not tangentially, dynamics-based approaches are not posed to maximally benefit from this trend, which holds the premise of allowing generalization in the space of tasks and embodiments, like data was the cornerstone for advancements in vision @alayracFlamingoVisualLanguage2022 and natural-language understanding @brownLanguageModelsAre2020.
+Lastly, dynamics-based methods (naturally) overlook the rather recent increase in availability of openly-available robotics datasets. The curation of academic datasets by large centralized groups of human experts in robotics @collaborationOpenXEmbodimentRobotic2025, @khazatskyDROIDLargeScaleInTheWild2025 is now increasingly complemented by a growing number of robotics datasets contributed in a decentralized fashion by individuals with varied expertise. If not tangentially, dynamics-based approaches are not posed to maximally benefit from this trend, which holds the premise of allowing generalization in the space of tasks and embodiments, like data was the cornerstone for advancements in vision @alayracFlamingoVisualLanguage2022 and natural-language understanding @brownLanguageModelsAre2020.
-Taken together, these limitations (Figure 10) motivate the exploration of learning-based approaches that can (1) integrate perception and control more tightly, (2) adapt across tasks and embodiments with reduced expert modeling interventions and (3) scale gracefully in performance as more robotics data becomes available.
+Taken together, these limitations (Figure [classical-limitations]) motivate the exploration of learning-based approaches that can (1) integrate perception and control more tightly, (2) adapt across tasks and embodiments with reduced expert modeling interventions and (3) scale gracefully in performance as more robotics data becomes available.
## Robot (Reinforcement) Learning
+
*Approximate the solution, not the problem* \[...\]
@@ -408,59 +430,67 @@ Richard Sutton
TL;DR The need for expensive high-fidelity simulators can be obviated by learning from real-world data, using sample-efficient algorithms that can safely train directly on hardware.
+Learning-based robotics streamlines perception-to-action by learning a (1) unified high-level controller capable to take (2) high-dimensional, unstructured sensorimotor information. Learning (3) does not require a dynamics model and instead focuses on interaction data, and (4) empirically correlates with the scale of the data used.
+
-Learning-based techniques for robotics naturally address the limitations presented in 2 (Figure 11). Learning-based techniques typically rely on prediction-to-action (*visuomotor policies*), thereby directly mapping sensorimotor inputs to predicted actions, streamlining control policies by removing the need to interface multiple components. Mapping sensorimotor inputs to actions directly also allows to add diverse input modalities, leveraging the automatic feature extraction characteristic of most modern learning systems. Further, learning-based approaches can in principle entirely bypass modeling efforts and instead rely exclusively on interactions data, proving transformative when dynamics are challenging to model or even entirely unknown. Lastly, learning for robotics (*robot learning*) is naturally well posed to leverage the growing amount of robotics data openly available, just as computer vision first and natural language processing later did historically benefit from large scale corpora of (possibly non curated) data, in great part overlooked by dynamics-based approaches.
+Learning-based techniques for robotics naturally address the limitations presented in [classical] (Figure [robot-learning-upsides]). Learning-based techniques typically rely on prediction-to-action (*visuomotor policies*), thereby directly mapping sensorimotor inputs to predicted actions, streamlining control policies by removing the need to interface multiple components. Mapping sensorimotor inputs to actions directly also allows to add diverse input modalities, leveraging the automatic feature extraction characteristic of most modern learning systems. Further, learning-based approaches can in principle entirely bypass modeling efforts and instead rely exclusively on interactions data, proving transformative when dynamics are challenging to model or even entirely unknown. Lastly, learning for robotics (*robot learning*) is naturally well posed to leverage the growing amount of robotics data openly available, just as computer vision first and natural language processing later did historically benefit from large scale corpora of (possibly non curated) data, in great part overlooked by dynamics-based approaches.
-Being a field at its relative nascent stages, no prevalent technique(s) proved distinctly better better in robot learning. Still, two major classes of methods gained prominence: reinforcement learning (RL) and Behavioral Cloning (BC) (Figure 12). In this section, we provide a conceptual overview of applications of the former to robotics, as well as introduce practical examples of how to use RL within `lerobot`. We then introduce the major limitations RL suffers from, to introduce BC techniques in the next sections ([learning-bc-single-sec-learning-bc-generalist]).
+Being a field at its relative nascent stages, no prevalent technique(s) proved distinctly better better in robot learning. Still, two major classes of methods gained prominence- reinforcement learning (RL) and Behavioral Cloning (BC) (Figure [robot-learning-atlas]). In this section, we provide a conceptual overview of applications of the former to robotics, as well as introduce practical examples of how to use RL within `lerobot`. We then introduce the major limitations RL suffers from, to introduce BC techniques in the next sections ([learning-bc-single-sec-learning-bc-generalist]).
+
+
+Overview of the robot learning methods implemented in lerobot.
+
-In Figure 12 we decided to include generalist robot models @blackp0VisionLanguageActionFlow2024, @shukorSmolVLAVisionLanguageActionModel2025 alongside task-specific BC methods. While significant different in spirit--*generalist* models are language-conditioned and use instructions to generate motion valid across many tasks, while *task-specific* models are typically not language-conditioned and used to perform a single task--foundation models are largely trained to reproduce trajectories contained in a large training set of input demonstrations. Thus, we argue generalist policies can indeed be grouped alongside other task-specific BC methods, as they both leverage similar training data and schemas.
+In Figure [robot-learning-atlas] we decided to include generalist robot models @blackp0VisionLanguageActionFlow2024, @shukorSmolVLAVisionLanguageActionModel2025 alongside task-specific BC methods. While significant different in spirit--*generalist* models are language-conditioned and use instructions to generate motion valid across many tasks, while *task-specific* models are typically not language-conditioned and used to perform a single task--foundation models are largely trained to reproduce trajectories contained in a large training set of input demonstrations. Thus, we argue generalist policies can indeed be grouped alongside other task-specific BC methods, as they both leverage similar training data and schemas.
-Figure 12 illustrates this categorization graphically, explicitly listing all the robot learning policies currently available in `lerobot`: Action Chunking with Transformers (ACT) @zhaoLearningFineGrainedBimanual2023, Diffusion Policy @chiDiffusionPolicyVisuomotor2024, Vector-Quantized Behavior Transformer (VQ-BeT) @leeBehaviorGenerationLatent2024, $\pi_0$ @blackp0VisionLanguageActionFlow2024, SmolVLA @shukorSmolVLAVisionLanguageActionModel2025, Human-in-the-loop Sample-efficient RL (HIL-SERL) @luoPreciseDexterousRobotic2024 and TD-MPC @hansenTemporalDifferenceLearning2022.
+Figure [robot-learning-atlas] illustrates this categorization graphically, explicitly listing all the robot learning policies currently available in `lerobot`- Action Chunking with Transformers (ACT) @zhaoLearningFineGrainedBimanual2023, Diffusion Policy @chiDiffusionPolicyVisuomotor2024, Vector-Quantized Behavior Transformer (VQ-BeT) @leeBehaviorGenerationLatent2024, $\pi_0$ @blackp0VisionLanguageActionFlow2024, SmolVLA @shukorSmolVLAVisionLanguageActionModel2025, Human-in-the-loop Sample-efficient RL (HIL-SERL) @luoPreciseDexterousRobotic2024 and TD-MPC @hansenTemporalDifferenceLearning2022.
+
+
+Examples of two different robotics tasks performed using RL. In the manipulation task (A) an agent learns to reach for a yellow plastic block in its environment, and to put it inside of a box. In the locomotion task (B) an agent learns to move its center of mass sideways without falling.
+
-Applications of RL to robotics have been long studied, to the point the relationship between these two disciplines has been compared to that between physics and matematics @koberReinforcementLearningRobotics. Indeed, due to their interactive and sequential nature, many robotics problems can be directly mapped to RL problems. Figure 13 depicts two of such cases. Reaching for an object to move somewhere else in the scene is an indeed sequential problem where at each cycle the controller needs to adjust the position of the robotic arm based on their current configuration and the (possibly varying) position of the object. Figure 13 also shows an example of a locomotion problem, where sequentiality is inherent in the problem formulation. While sliding to the side, the controller has to constantly keep adjusting to the robot’s propioperception to avoid failure (falling).
+Applications of RL to robotics have been long studied, to the point the relationship between these two disciplines has been compared to that between physics and matematics @koberReinforcementLearningRobotics. Indeed, due to their interactive and sequential nature, many robotics problems can be directly mapped to RL problems. Figure [robotics-with-rl-examples] depicts two of such cases. Reaching for an object to move somewhere else in the scene is an indeed sequential problem where at each cycle the controller needs to adjust the position of the robotic arm based on their current configuration and the (possibly varying) position of the object. Figure [robotics-with-rl-examples] also shows an example of a locomotion problem, where sequentiality is inherent in the problem formulation. While sliding to the side, the controller has to constantly keep adjusting to the robot’s propioperception to avoid failure (falling).
### A (Concise) Introduction to RL
-The RL framework @suttonReinforcementLearningIntroduction2018, which we briefly introduce here, has often been used to model robotics problems @koberReinforcementLearningRobotics. RL is a subfield within ML fundamentally concerned with the development of autonomous systems (*agents*) learning how to *continuously behave* in an evolving environment, developing (ideally, well-performing) control strategies (*policies*). Crucially for robotics, RL agents can improve via trial-and-error only, thus entirely bypassing the need to develop explicit models of the problem dynamics, and rather exploiting interaction data only. In RL, this feedback loop (Figure 14) between actions and outcomes is established through the agent sensing a scalar quantity (*reward*).
+The RL framework @suttonReinforcementLearningIntroduction2018, which we briefly introduce here, has often been used to model robotics problems @koberReinforcementLearningRobotics. RL is a subfield within ML fundamentally concerned with the development of autonomous systems (*agents*) learning how to *continuously behave* in an evolving environment, developing (ideally, well-performing) control strategies (*policies*). Crucially for robotics, RL agents can improve via trial-and-error only, thus entirely bypassing the need to develop explicit models of the problem dynamics, and rather exploiting interaction data only. In RL, this feedback loop (Figure [rl-most-famous-pic]) between actions and outcomes is established through the agent sensing a scalar quantity (*reward*).
+
+
+Agent-Environment interaction diagram (image credits to @suttonReinforcementLearningIntroduction2018).
+
Formally, interactions between an agent and its environment are typically modeled via a Markov Decision Process (MDP) @bellmanMarkovianDecisionProcess1957. Representing robotics problems via MDPs offers several advantages, including (1) incorporating uncertainty through MDP’s inherently stochastic formulation and (2) providing a theoretically sound framework for learning *without* an explicit dynamic model. While accommodating also a continuous time formulation, MDPs are typically considered in discrete time in RL, thus assuming interactions to atomically take place over the course of discrete *timestep* $t=0,1,2,3, \dots, T$. MDPs allowing for an unbounded number of interactions ( $T \to + \infty$ ) are typically termed *infinite-horizon*, and opposed to *finite-horizon* MDPs in which $T$ cannot grow unbounded. Unless diversely specified, we will only be referring to discrete-time finite-horizon (*episodic*) MDPs here.
@@ -470,9 +500,9 @@ Formally, a lenght-$T$ Markov Decision Process (MDP) is a tuple $\mathcal M = \l
- $\mathcal A$ is the *action space*; $a_t\in \mathcal A$ may represent joint torques, joint velocities, or even end-effector commands. In general, actions correspond to commands intervenings on the configuration of the robot.
-- $\mathcal D$ represents the (possibly non-deterministic) environment dynamics, with $\mathcal D: \mathcal S\times \mathcal A\times \mathcal S\mapsto [0, 1]$ corresponding to $\mathcal D\, (s_t, a_t, s_{t+1})= \mathbb P (s_{t+1}\vert s_t, a_t)$. For instance, for a planar manipulator dynamics could be considered deterministic when the environment is fully described (Figure 6), and stochastic when unmodeled disturbances depending on non-observable parameters intervene (Figure [planar-manipulator-box-velocity]).
+- $\mathcal D$ represents the (possibly non-deterministic) environment dynamics, with $\mathcal D: \mathcal S\times \mathcal A\times \mathcal S\mapsto [0, 1]$ corresponding to $\mathcal D\, (s_t, a_t, s_{t+1})= \mathbb P (s_{t+1}\vert s_t, a_t)$. For instance, for a planar manipulator dynamics could be considered deterministic when the environment is fully described (Figure [planar-manipulation-simple]), and stochastic when unmodeled disturbances depending on non-observable parameters intervene (Figure [planar-manipulator-box-velocity]).
-- $r: \mathcal S\times \mathcal A\times \mathcal S\to \mathbb R$ is the *reward function*, weighing the transition $(s_t, a_t, s_{t+1})$ in the context of the achievement of an arbitrary goal. For instance, a simple reward function for quickly moving the along the $x$ axis in 3D-space (Figure 13) could be based on the absolute position of the robot along the $x$ axis ($p_x$), present negative penalties for falling over (measured from $p_z$) and a introduce bonuses $\dot p_x$ for speed, $r (s_t, a_t, s_{t+1})\equiv r(s_t) = p_{x_t} \cdot \dot p_{x_t} - \tfrac{1}{p_{z_t}}$.
+- $r- \mathcal S\times \mathcal A\times \mathcal S\to \mathbb R$ is the *reward function*, weighing the transition $(s_t, a_t, s_{t+1})$ in the context of the achievement of an arbitrary goal. For instance, a simple reward function for quickly moving the along the $x$ axis in 3D-space (Figure [robotics-with-rl-examples]) could be based on the absolute position of the robot along the $x$ axis ($p_x$), present negative penalties for falling over (measured from $p_z$) and a introduce bonuses $\dot p_x$ for speed, $r (s_t, a_t, s_{t+1})\equiv r(s_t) = p_{x_t} \cdot \dot p_{x_t} - \tfrac{1}{p_{z_t}}$.
Lastly, $\gamma \in [0,1]$ represent the discount factor regulating preference for immediate versus long-term reward (with an effective horizon equal to $\tfrac{1}{1-\gamma}$), and $\rho$ is the distribution, defined over $\mathcal S$, the MDP’s *initial* state is sampled from, $s_0 \sim \rho$.
@@ -517,17 +547,19 @@ $$
`\htmlId{q-as-v}{Q_\pi(s_t, a_t) = \mathbb{E}_{s_{t+1}\sim \mathbb P(\bullet \vert s_t, a_t)} [r_t + \gamma V_\pi(s_{t+1})]\\ V_\pi(s_t) = \mathbb E_{a_t\sim \pi(\bullet \vert s_t)} [Q_\pi (s_t, a_t)]}`
$$
- Inducing an ordering over states and state-action pairs under $\pi$, value functions are central to most RL algorithms. A variety of methods have been developed in RL as standalone attemps to find (approximate) solutions to the problem of maximizing cumulative reward (Figure 15).
+ Inducing an ordering over states and state-action pairs under $\pi$, value functions are central to most RL algorithms. A variety of methods have been developed in RL as standalone attemps to find (approximate) solutions to the problem of maximizing cumulative reward (Figure [rl-algos-atlas]).
+
+
+Popular RL algorithms. See @SpinningUp2018 for a complete list of citations.
+
Popular approaches to continuous state and action space--such as those studied within robotics--include @schulmanTrustRegionPolicy2017, @schulmanProximalPolicyOptimization2017, @haarnojaSoftActorCriticOffPolicy2018. Across manipulation @akkayaSolvingRubiksCube2019 and locomotion @leeLearningQuadrupedalLocomotion2020 problems, RL proved extremely effective in providing a platform to (1) adopt a unified, streamlined perception-to-action pipeline, (2) natively integrate propioperception with multi-modal high-dimensional sensor streams (3) disregard a description of the environment dynamics, by focusing on observed interaction data rather than modeling, and (4) anchor policies in the experience collected and stored in datasets. For a more complete survey of applications of RL to robotics, we refer the reader to @koberReinforcementLearningRobotics, @tangDeepReinforcementLearning2024.
@@ -535,37 +567,41 @@ Popular approaches to continuous state and action space--such as those studied w
Streamlined end-to-end control pipelines, data-driven feature extraction and a disregard for explicit modeling in favor of interaction data are all features of RL for robotics. However, particularly in the context of real-world robotics, RL still suffers from limitations concerning machine safety and learning efficiency.
-First, especially early in training, actions are typically explorative, and thus erractic. On physical systems, untrained policies may command high velocities, self-collisiding configurations, or torques exceeding joint limits, leading to wear and potential hardware damage. Mitigating these risks requires external safeguards (e.g., watchdogs, safety monitors, emergency stops), often incuring in a high degree of human supervision. Further, in the typical episodic setting considered in most robotics problems, experimentation is substantially slowed down by the need to manually reset the environment over the course of training, a time-consuming and brittle process.
+First, especially early in training, actions are typically explorative, and thus erractic. On physical systems, untrained policies may command high velocities, self-collisiding configurations, or torques exceeding joint limits, leading to wear and potential hardware damage. Mitigating these risks requires external safeguards (e.g., watchdogs, safety monitors, emergency stops), often incuring in a high degree of human supervision. Further, in the typical episodic setting considered in most robotics problems, experimentation is substantially slowed down by the need to manually reset the environment over the course of training, a time-consuming and brittle process.
-Second, learning with a limited number of samples remains problematic in RL, limiting the applicability of RL in real-world robotics due to consequently prohibitive timescales of training. Even strong algorithms such as SAC @haarnojaSoftActorCriticOffPolicy2018 typically require a large numbers of transitions $\{ (s_t, a_t, r_t, s_{t+1})\}_{t=1}^N$. On hardware, generating these data is time-consuming and can even be prohibitive.
+Second, learning with a limited number of samples remains problematic in RL, limiting the applicability of RL in real-world robotics due to consequently prohibitive timescales of training. Even strong algorithms such as SAC @haarnojaSoftActorCriticOffPolicy2018 typically require a large numbers of transitions $\{ (s_t, a_t, r_t, s_{t+1})\}_{t=1}^N$. On hardware, generating these data is time-consuming and can even be prohibitive.
+
+
+Simulated (left) vs. real-world (right) OpenDuck. Discrepancies in the simulation dynamics (reality gap) pose risks to policy transfer.
+
-Training RL policies in simulation @tobinDomainRandomizationTransferring2017 addresses both issues: it eliminates physical risk and dramatically increases throughput. Yet, simulators require significant modeling effort, and rely on assumptions (simplified physical modeling, instantaneous actuation, static environmental conditions, etc.) limiting transferring policies learned in simulation due the discrepancy between real and simulated environments (*reality gap*, Figure 16). *Domain randomization* (DR) is a popular technique to overcome the reality gap, consisting in randomizing parameters of the simulated environment during training, to induce robustness to specific disturbances. In turn, DR is employed to increase the diversity of scenarios over the course of training, improving on the chances sim-to-real transfer @akkayaSolvingRubiksCube2019, @antonovaReinforcementLearningPivoting2017, @jiDribbleBotDynamicLegged2023. In practice, DR is performed further parametrizing the *simulator*’s dynamics $\mathcal D \equiv \mathcal D_\xi$ with a *dynamics* (random) vector $\xi$ drawn an arbitrary distribution, $\xi \sim \Xi$. Over the course of training--typically at each episode’s reset--a new $\xi$ is drawn, and used to specify the environment’s dynamics for that episode. For instance, one could decide to randomize the friction coefficient of the surface in a locomotion task (Figure 17), or the center of mass of an object for a manipulation task.
+Training RL policies in simulation @tobinDomainRandomizationTransferring2017 addresses both issues: it eliminates physical risk and dramatically increases throughput. Yet, simulators require significant modeling effort, and rely on assumptions (simplified physical modeling, instantaneous actuation, static environmental conditions, etc.) limiting transferring policies learned in simulation due the discrepancy between real and simulated environments (*reality gap*, Figure [synthetic-vs-real-duck]). *Domain randomization* (DR) is a popular technique to overcome the reality gap, consisting in randomizing parameters of the simulated environment during training, to induce robustness to specific disturbances. In turn, DR is employed to increase the diversity of scenarios over the course of training, improving on the chances sim-to-real transfer @akkayaSolvingRubiksCube2019, @antonovaReinforcementLearningPivoting2017, @jiDribbleBotDynamicLegged2023. In practice, DR is performed further parametrizing the *simulator*’s dynamics $\mathcal D \equiv \mathcal D_\xi$ with a *dynamics* (random) vector $\xi$ drawn an arbitrary distribution, $\xi \sim \Xi$. Over the course of training--typically at each episode’s reset--a new $\xi$ is drawn, and used to specify the environment’s dynamics for that episode. For instance, one could decide to randomize the friction coefficient of the surface in a locomotion task (Figure [ducks-on-terrains]), or the center of mass of an object for a manipulation task.
+
+
+(A) HIL-SERL allows for real-world training of high performance RL agents by building on top advancements presented by of SAC, RLPD and SERL. (B) Example of human intervention during a HIL-SERL training process on a SO-100.
+
-Building on off-policy deep Q-learning with replay buffers, entropy regularization for better exploration and performance, expert demonstrations to guide learning, and a series of tools and recommendations for real-world training using reward classifiers (Figure 18), @luoPreciseDexterousRobotic2024 introduce human interactions during training, learning near-optimal policies in challenging real-world manipulation tasks in 1-2 hours.
+Building on off-policy deep Q-learning with replay buffers, entropy regularization for better exploration and performance, expert demonstrations to guide learning, and a series of tools and recommendations for real-world training using reward classifiers (Figure [hil-serl-blocks]), @luoPreciseDexterousRobotic2024 introduce human interactions during training, learning near-optimal policies in challenging real-world manipulation tasks in 1-2 hours.
Human in the Loop Sample Efficient Robot reinforcement Learning (HIL-SERL) @luoPreciseDexterousRobotic2024 augments offline-to-online RL with targeted human corrections during training, and employs prior data to (1) train a reward classifier and (2) bootstrap RL training on expert trajectories. While demonstrations provide the initial dataset seeding learning and constraining early exploration, interactive corrections allow a human supervisor to intervene on failure modes and supply targeted interventions to aid the learning process. Crucially, human interventions are stored in both the offline and online replay buffers, differently from the autonomous transitions generated at training time and stored in the online buffer only. Consequently, given an intervention timestep $k \in (0, T)$, length-$K$ human intervention data $\{ s^{\text{human}}_k, a^{\text{human}}_k, r^{\text{human}}_k, s^{\text{human}}_{k+1},\}_{k=1}^K$ is more likely to be sampled for off-policy learning than the data generated online during training, providing stronger supervision to the agent while still allowing for autonomous learning. Empirically, HIL-SERL attains near-perfect success rates on diverse manipulation tasks within 1-2 hours of training @luoPreciseDexterousRobotic2024, underscoring how offline datasets with online RL can markedly improve stability and data efficiency, and ultimately even allow real-world RL-training.
-#### Code Example: Real-world RL
+#### Code Example- Real-world RL
**TODO(fracapuano): work out rl training example**
@@ -662,6 +700,7 @@ Advances in Behavioral Cloning (BC) from corpora of human demonstrations address
## Robot (Imitation) Learning
+
*The best material model for a cat is another, or preferably the same cat*
@@ -674,29 +713,33 @@ Norbert Wiener
TL;DR Behavioral Cloning provides a natural platform to learn from real-world interactions without the need to design any reward function, and generative models prove more effective than point-wise policies at dealing with multimodal demonstration datasets.
+(A) Average (with standard deviation) evolution of the actuation levels over the first 5 recorded episodes in lerobot/svla_so101_pickplace. Proprioperceptive state provide invaluable to determine the robot’s state during an episode. (B) Camera frames are also recorded alongside measurements on the robot’s state, capturing information about the robot’s interaction with its environment.
+
-Learning from human demonstrations provides a pragmatic alternative to the reinforcement-learning pipeline discussed in Section 3. Indeed, in real-world robotics online exploration is typically costly and potentially unsafe, and designing (dense) reward signals is a brittle and task-specific process. In general, success detection itself may often require bespoke instrumentation, while episodic training demands reliable resets--all factors complicating training RL algorithms on hardware at scale. Behavioral Cloning (BC) sidesteps these constraints by casting control an imitation learning problem, leveraging previously collected expert demonstrations. Most notably, by learning to imitate autonomous systems naturally adhere to the objectives, preferences, and success criteria implicitly encoded in the data, which obviates reduces early-stage exploratory failures and obviates hand-crafted reward shaping altogether.
+Learning from human demonstrations provides a pragmatic alternative to the reinforcement-learning pipeline discussed in Section [learning-rl]. Indeed, in real-world robotics online exploration is typically costly and potentially unsafe, and designing (dense) reward signals is a brittle and task-specific process. In general, success detection itself may often require bespoke instrumentation, while episodic training demands reliable resets--all factors complicating training RL algorithms on hardware at scale. Behavioral Cloning (BC) sidesteps these constraints by casting control an imitation learning problem, leveraging previously collected expert demonstrations. Most notably, by learning to imitate autonomous systems naturally adhere to the objectives, preferences, and success criteria implicitly encoded in the data, which obviates reduces early-stage exploratory failures and obviates hand-crafted reward shaping altogether.
-Formally, let $\mathcal D = \{ \tau^{(i)} \}_{i=1}^N$ be a set of expert trajectories, with $\tau^{(i)} = \{(o_t^{(i)}, a_t^{(i)})\}_{t=0}^{T_i}$ representing the $i$-th trajectory in $\mathcal D$, $o_t \in \mathcal O$ denoting observations (e.g., images and proprioception altogether), and $a_t \in \mathcal A$ the expert actions. Typically, observations $o \in \mathcal O$ consist of both image and proprioperceptive information, while actions $a \in \mathcal A$ represent control specifications for the robot to execute, e.g. a joint configuration. Note that differently from Section 3, in the imitation learning context $\mathcal D$ denotes an offline dataset collecting $N$ length-$T_i$ reward-free (expert) human trajectories $\tau^{(i)}$, and *not* the environment dynamics. Similarily, in this section $\tau^{(i)}$ represent a length-$T_i$ trajectory of observation-action pairs, which crucially *omits entirely any reward* information. Figure 19 graphically shows trajectories in terms of the average evolution of the actuation on the 6 joints over a group of teleoperated episodes for the SO-100 manipulator. Notice how proprioperceptive states are captured jointly with camera frames over the course of the recorded episodes, providing a unified high-frame rate collection of teleoperation data. Figure 20 shows $(o_t, a_t)$-pairs for the same dataset, with the actions performed by the human expert illustrated just alongside the corresponding observation. In principle, (expert) trajectories $\tau^{(i)}$ can have different lengths since demonstrations might exhibit multi-modal strategies to attain the same goal, resulting in possibly multiple, different behaviors.
+Formally, let $\mathcal D = \{ \tau^{(i)} \}_{i=1}^N$ be a set of expert trajectories, with $\tau^{(i)} = \{(o_t^{(i)}, a_t^{(i)})\}_{t=0}^{T_i}$ representing the $i$-th trajectory in $\mathcal D$, $o_t \in \mathcal O$ denoting observations (e.g., images and proprioception altogether), and $a_t \in \mathcal A$ the expert actions. Typically, observations $o \in \mathcal O$ consist of both image and proprioperceptive information, while actions $a \in \mathcal A$ represent control specifications for the robot to execute, e.g. a joint configuration. Note that differently from Section [learning-rl], in the imitation learning context $\mathcal D$ denotes an offline dataset collecting $N$ length-$T_i$ reward-free (expert) human trajectories $\tau^{(i)}$, and *not* the environment dynamics. Similarily, in this section $\tau^{(i)}$ represent a length-$T_i$ trajectory of observation-action pairs, which crucially *omits entirely any reward* information. Figure [ch4-bc-trajectories] graphically shows trajectories in terms of the average evolution of the actuation on the 6 joints over a group of teleoperated episodes for the SO-100 manipulator. Notice how proprioperceptive states are captured jointly with camera frames over the course of the recorded episodes, providing a unified high-frame rate collection of teleoperation data. Figure [ch4-observation-action-mapping] shows $(o_t, a_t)$-pairs for the same dataset, with the actions performed by the human expert illustrated just alongside the corresponding observation. In principle, (expert) trajectories $\tau^{(i)}$ can have different lengths since demonstrations might exhibit multi-modal strategies to attain the same goal, resulting in possibly multiple, different behaviors.
+
+
+Sample observations and action pairs over the course of a given trajectory recorded in lerobot/svla_so101_pickplace. Observations, comprising of both proprioperceptive and visual information, are recorded alongside the configuration of a second, leader robot controlled by a human expert, providing complete information for regressing actions given observation.
+
Behavioral Cloning (BC) @pomerleauALVINNAutonomousLand1988a aims at synthetizing synthetic behaviors by learning the mapping from observations to actions, and in its most natural formulation can be effectively tackled as a *supevised* learning problem, consisting of learning the (deterministic) mapping $f: \mathcal O\mapsto \mathcal A, \ a_t = f(o_t)$ by solving
``` math
@@ -708,17 +751,19 @@ Typically, the expert’s joint observation-action distribution $p: \mathcal O\t
Despite the inherent challenges of learning on non-i.i.d. data, the BC formulation affords several operational advantages in robotics. First, training happens offline and typically uses expert human demonstration data, hereby severily limiting exploration risks by preventing the robot from performing dangerous actions altogether. Second, reward design is entirely unnecessary in BC, as demonstrations already reflect human intent and task completion. This also mitigates the risk of misalignment and specification gaming (*reward hacking*), otherwise inherent in purely reward-based RL @heessEmergenceLocomotionBehaviours2017. Third, because expert trajectories encode terminal conditions, success detection and resets are implicit in the dataset. Finally, BC scales naturally with growing corpora of demonstrations collected across tasks, embodiments, and environments. However, BC can in principle only learn behaviors that are, at most, as good as the one exhibited by the demonstrator, and thus critically provides no mitigation for the suboptimal decision making that might be enaced by humans. Still, while problematic in sequential-decision making problems for which expert demonstrations are not generally available--data migth be expensive to collect, or human performance may be inherently suboptimal--many robotics applications benefit from relative cheap pipelines to acquire high-quality trajectories generated by humans, thus justifying BC approaches.
+
+
+Point-wise policies suffer from limitations due to (A) covariate shifts and poor approximation of (B) multimodal demonstrations. (A) Initially small errors may drive the policy out of distribution, incuring in a vicious circle ultimately resulting in failure. (B) Both modes of reaching for a target object in a scene, either left or right-first, are equally as good and thus equally as likely to be present in a dataset of human demonstrations, ultimately resulting in multimodal demonstrations.
+
-While conceptually elegant, point-estimate policies $f : \mathcal O\mapsto \mathcal A$ learned by solving [loss-minimization-SL] have been observed to suffer from (1) compounding errors @rossReductionImitationLearning2011 and (2) poor fit to multimodal distributions @florenceImplicitBehavioralCloning2022, @keGraspingChopsticksCombating2020. Figure 21 illustrates these two key issues related to learning *explicit policies* @florenceImplicitBehavioralCloning2022. Besides sequentiality in $\mathcal D$, compounding errors due to *covariate shift* may also prove catastrophic, as even small $\epsilon$-prediction errors $0 < \Vert \mu(o_t) - a_t \Vert \leq \epsilon$ can quickly drive the policy into out-of-distribution states, incuring in less confident generations and thus errors compounding (Figure 21, left).Moreover, point-estimate policies typically fail to learn *multimodal* targets, which are very common in human demonstrations solving robotics problems, since multiple trajectories can be equally as good towards the accomplishment of a goal (e.g., symmetric grasps, Figure 21, right). In particular, unimodal regressors tend to average across modes, yielding indecisive or even unsafe commands @florenceImplicitBehavioralCloning2022. To address poor multimodal fitting, @florenceImplicitBehavioralCloning2022 propose learning the generative model $p(o, a)$ underlying the samples in $\mathcal D$, rather than an explicitly learning a prediction function $f(o) = a$.
+While conceptually elegant, point-estimate policies $f : \mathcal O\mapsto \mathcal A$ learned by solving [loss-minimization-SL] have been observed to suffer from (1) compounding errors @rossReductionImitationLearning2011 and (2) poor fit to multimodal distributions @florenceImplicitBehavioralCloning2022, @keGraspingChopsticksCombating2020. Figure [ch4-issues-with-bc] illustrates these two key issues related to learning *explicit policies* @florenceImplicitBehavioralCloning2022. Besides sequentiality in $\mathcal D$, compounding errors due to *covariate shift* may also prove catastrophic, as even small $\epsilon$-prediction errors $0 < \Vert \mu(o_t) - a_t \Vert \leq \epsilon$ can quickly drive the policy into out-of-distribution states, incuring in less confident generations and thus errors compounding (Figure [ch4-issues-with-bc], left).Moreover, point-estimate policies typically fail to learn *multimodal* targets, which are very common in human demonstrations solving robotics problems, since multiple trajectories can be equally as good towards the accomplishment of a goal (e.g., symmetric grasps, Figure [ch4-issues-with-bc], right). In particular, unimodal regressors tend to average across modes, yielding indecisive or even unsafe commands @florenceImplicitBehavioralCloning2022. To address poor multimodal fitting, @florenceImplicitBehavioralCloning2022 propose learning the generative model $p(o, a)$ underlying the samples in $\mathcal D$, rather than an explicitly learning a prediction function $f(o) = a$.
### A (Concise) Introduction to Generative Models
@@ -726,31 +771,35 @@ Generative Models (GMs) aim to learn the stochastic process underlying the very
#### Variational Auto-Encoders
+
+
+Intuitively, latent variable in a single latent model may contain information regarding the task being performed, which directly results in the likelihood of the same observation-action pair being different for two different tasks. When (A) picking a block the likelihood of a wide gripper’s opening should be higher than narrower one, while it should be the opposite when (B) pushing the block.
+
A common inductive bias used in GM posits samples $(o,a)$ are influenced from an unobservable latent variable $z \in Z$, resulting in
``` math
\htmlId{BC-latent-variable}{p (o,a) = \int_{\text{supp}({Z})} p(o,a \vert z) p(z)}
```
-Intuitively, in the case of observation-action pairs $(o, a)$ for a robotics application, $z$ could be some high level representation of the underlying task being performed by the human demonstrator. In such case, treating $p(o,a)$ as a marginalization over $\text{supp}({Z})$ of the complete joint distribution $p(o,a,z)$ natively captures the effect different tasks have on the likelihood of observation-action pairs. Figure 22 graphically illustrates this concept in the case of a (A) picking and (B) pushing task, for which, nearing the target object, the likelihood of actions resulting in opening the gripper--the higher $q_6$, the wider the gripper’s opening--should intuitively be (A) high or (B) low, depending on the task performed. While the latent space $Z$ typically has a much richer structure than the set of all actual tasks performed, [BC-latent-variable] still provides a solid framework to learn joint distribution conditioned on unobservable yet relevant factors. Figure 23 represents this framework of latent-variable for a robotics application: the true, $z$-conditioned generative process on assigns *likelihood* $p((o,a) \vert z)$ to the single $(o,a)$-pair. Using Bayes’ theorem, one can reconstruct the *posterior* distribution on $\text{supp}({Z})$, $q_\theta(z \vert o,a)$ from the likelihood $p_\theta(o,a \vert z)$, *prior* $p_\theta(z)$ and *evidence* $p_\theta(o,a)$. VAEs approximate the latent variable model presented in [BC-latent-variable]) using an *approximate posterior* $q_\phi(z \vert o,a)$ while regressing parameters for a parametric likelihood, $p_\theta(o,a \vert z)$ (Figure 23).
+Intuitively, in the case of observation-action pairs $(o, a)$ for a robotics application, $z$ could be some high level representation of the underlying task being performed by the human demonstrator. In such case, treating $p(o,a)$ as a marginalization over $\text{supp}({Z})$ of the complete joint distribution $p(o,a,z)$ natively captures the effect different tasks have on the likelihood of observation-action pairs. Figure [ch4-task-effect-on-pairs] graphically illustrates this concept in the case of a (A) picking and (B) pushing task, for which, nearing the target object, the likelihood of actions resulting in opening the gripper--the higher $q_6$, the wider the gripper’s opening--should intuitively be (A) high or (B) low, depending on the task performed. While the latent space $Z$ typically has a much richer structure than the set of all actual tasks performed, [BC-latent-variable] still provides a solid framework to learn joint distribution conditioned on unobservable yet relevant factors. Figure [ch4-latent-variable-model] represents this framework of latent-variable for a robotics application- the true, $z$-conditioned generative process on assigns *likelihood* $p((o,a) \vert z)$ to the single $(o,a)$-pair. Using Bayes’ theorem, one can reconstruct the *posterior* distribution on $\text{supp}({Z})$, $q_\theta(z \vert o,a)$ from the likelihood $p_\theta(o,a \vert z)$, *prior* $p_\theta(z)$ and *evidence* $p_\theta(o,a)$. VAEs approximate the latent variable model presented in [BC-latent-variable]) using an *approximate posterior* $q_\phi(z \vert o,a)$ while regressing parameters for a parametric likelihood, $p_\theta(o,a \vert z)$ (Figure [ch4-latent-variable-model]).
+
+
+(A) The latent variable model in a robotics application regulates influence between observed (o, a) variables and an unobservable latent variable. (B) VAEs approximate exact latent variable models by means of variational inference.
+
Given a dataset $\mathcal D$ consisting of $N$ i.i.d. observation-action pairs, the log-likelihood of all datapoints under $\theta$ (in Bayesian terms, the *evidence* $p_\theta(\mathcal D)$) can thus be written as:
@@ -794,7 +843,7 @@ Indeed, it is very common in practice to approximate from the learned likelihood
#### Diffusion Models
-VAEs approximate probability distributions via a *single* latent variable model, assuming the underlying unknown distribution can be factored according to [BC-latent-variable], and solve the variational inference problem of jointly learning the likelihood $p_\theta$ and (approximate) posterior $q_\phi$ for such model. In that, the unknown data distribution $p(o,a)$ is effectively approximated via $\int_Z p(z) p_\theta(o,a \vert z)$, and the underlying generative process reproduced by (1) sampling a latent variable and (2) learning to decode it into a (ideally) high-likelihood sample under the (unknown) $p(o,a)$. Diffusion Models (DMs) @hoDenoisingDiffusionProbabilistic2020 are another class of GMs which treat the similar problem of approximating an underlying unknown data distribution--*variational inference*--by *partially* extending VAEs to the case where *multiple* latent variables influence each other and the generative process underlying $o,a$ itself. In particular, DMs posit the generative process can be decomposed to a series of piece-wise (Markovian) interactions between (latent) variables (Figure 24), resulting in
+VAEs approximate probability distributions via a *single* latent variable model, assuming the underlying unknown distribution can be factored according to [BC-latent-variable], and solve the variational inference problem of jointly learning the likelihood $p_\theta$ and (approximate) posterior $q_\phi$ for such model. In that, the unknown data distribution $p(o,a)$ is effectively approximated via $\int_Z p(z) p_\theta(o,a \vert z)$, and the underlying generative process reproduced by (1) sampling a latent variable and (2) learning to decode it into a (ideally) high-likelihood sample under the (unknown) $p(o,a)$. Diffusion Models (DMs) @hoDenoisingDiffusionProbabilistic2020 are another class of GMs which treat the similar problem of approximating an underlying unknown data distribution--*variational inference*--by *partially* extending VAEs to the case where *multiple* latent variables influence each other and the generative process underlying $o,a$ itself. In particular, DMs posit the generative process can be decomposed to a series of piece-wise (Markovian) interactions between (latent) variables (Figure [ch4-many-latents]), resulting in
$$
`\htmlId{BC-multi-latent-model-1}{p(\underbrace{o,a}_{= z_0}) = \int_{\text{supp}({Z_0})} \int_{\text{supp}({Z_1})} \ldots \int_{\text{supp}({Z_T})} p(z_0, z_1, \dots z_T)\\ p(z_0, z_1, \dots z_T) = p(z_T) \prod_{t=0}^{T} p(z_{t-1} \vert z_t),}`
@@ -802,15 +851,17 @@ $$
where we explicitly showed the marginalization over the multiple latents in [BC-multi-latent-model-1], and used the law of conditional probability and Markov property in [BC-multi-latent-model-2].
+
+
+HMLV models posit the data generation process is influenced by a stack of Markov-dependent latent variables, with samples from the posterior distribution being progressively higher up in the hierarchy.
+
Similarily to VAEs, providing an exact interpretation for the latent variables is typically not possible. Still, one fairly reasonable application-driven intuition is that, by providing a model of the hierarchical, decoupled interaction of latent variables, Hierarchical Markov Latent Variable (HMLV) models attempt to capture the different resolutions at which different conditioning factors intervene, so that in a robotics application for instance, one could naturally distinguish between early-stage trajectory planning ($t \to T$) and fine-grained adjustments ($t \to 0$). In that, HMLV models thus provide a framework to perform variational inference via multiple, sequential sampling steps from different higher level distributions instead of approximating the generative process with a single-latent variable model. DMs are a particular instantiation of HMLV models for which the posterior $q( z_t \vert z_{t-1}) = \mathcal N(z_t \sqrt{1-\beta_t}, \beta_t \mathbf{I})$ for a given $\beta_t \in \mathbb R^+$, thereby iteratively reducing the signal-to-noise ratio as $\beta_t$ increases along the latents hierarchy.
@@ -826,29 +877,33 @@ $$
In their seminal work on using DMs for variational inference, @hoDenoisingDiffusionProbabilistic2020 introduce major contributions regarding solving $\min_\theta -\log p_\theta(o,a)$. In particular, @hoDenoisingDiffusionProbabilistic2020 exclusively adopt a fixed *Gaussian* posterior in the form of $q(z_t \vert z_{t-1}) = \mathcal{N}(\sqrt{1-\beta_t}z_{t-1}, \beta_t \mathbf I)$. The choice of adopting Gaussians has profound implications on the generative process modeled. Indeed, under the (mild) assumption that the variance is sufficiently small $\beta_t \leq \eta, \eta \in \mathbb R^+$, @sohl-dicksteinDeepUnsupervisedLearning2015 proved that the likelihood $p(z_{t-1} \vert z_t)$ is Gaussian as well, which allows for the particularly convenient parametrization of the approximate likelihood $p_\theta (x_{t-1} \vert x_t) = \mathcal N(\mu_\theta(x_t, t), \Sigma_\theta(x_t,t)), \ t \in [1,T]$, as well as for closed-form tractability of the KL-divergence terms in [diffusion-likelihood]. Further, the posterior’s structure also enables an analytical description for the distribution of the $t$-th latent variable, $q(z_t \vert z_0) = \mathcal N (\sqrt{\bar{\alpha}_t}z_0, (1-\bar{\alpha}_t) \mathbf{I})$, with $\alpha_t = 1-\beta_t, \ \bar \alpha_t = \prod_{k=1}^t \alpha_k$, which conveniently prevents iterative posterior sampling.
+
+
+DMs iteratively corrupt samples (left) from an unknown distribution into a quasi-standard Gaussian (center), learning the displacement field (right) that permits to reconstruct samples from the unknown target distribution by iteratively denoising samples of a tractable, easy-to-sample distribution.
+
-Finally, adopting Gaussian posteriors permits a particularly pleasing interpretation of the dynamics of training DMs @permenterInterpretingImprovingDiffusion2024. By using Gaussian posteriors, the hierarchical latent variables effectively lose increasingly more information circa the original (unknown) distribution’s sample, $z_0$, increasingly distributing according to a standard Gaussian and thus containing no information at all (Figure 25). Figure 25 illustrates this procedure on a simplified, bidimensional observation-action distribution, where we considered $o=q_2$ and $a=q^h_2$, with $q_2$ representing the robot’s *elbow flex* actuation and $q^h_2$ the human teleoperator’s robot elbow flex.
+Finally, adopting Gaussian posteriors permits a particularly pleasing interpretation of the dynamics of training DMs @permenterInterpretingImprovingDiffusion2024. By using Gaussian posteriors, the hierarchical latent variables effectively lose increasingly more information circa the original (unknown) distribution’s sample, $z_0$, increasingly distributing according to a standard Gaussian and thus containing no information at all (Figure [diffusion-robot-actions]). Figure [diffusion-robot-actions] illustrates this procedure on a simplified, bidimensional observation-action distribution, where we considered $o=q_2$ and $a=q^h_2$, with $q_2$ representing the robot’s *elbow flex* actuation and $q^h_2$ the human teleoperator’s robot elbow flex.
+
+
+A joint action-observation distribution, in the simplified case where the observation is the elbow-flex actuation in a SO-100, and the action is the recorded position for the same joint in the teleoperator arm. The motion recorded being teleoperated, the points distribute along a the diagonal.
+
-Because the recorded behavior is teleoperated, measurements mostly distribute along the line $a = o + \eta, \eta \sim N(0,1)$, with $\eta$-variability accouting for minor control inconsistencies (Figure 26). Using Gaussian posteriors--i.e., adding Gaussian noise--effectively simulates a *Brownian motion* for the elements in the distribution’s support (in Figure 25, $\mathcal O\times \mathcal A$), whereby information *diffuses away* from the samples, and comparing the diffused samples to the original data points one can derive an estimate of the total displacement induced by diffusion. Under the only assumption that the likelihood of the diffused samples is low under the original unknown data distribution, then one can effectively approximate the unkwown distribution by learning to *reverse* such displacement. This key intuition allows to write a simplified training objective: $\htmlId{diffusion-simplified-loss}{\mathcal L(\theta) = \mathbb{E}_{t, z_0, \epsilon} \big[ \Vert \epsilon - \epsilon_\theta(\sqrt{\bar \alpha_t} z_0 + \epsilon \sqrt{1 - \bar \alpha_t}, t) \Vert^2 \big], \quad t \sim \mathcal{U}(\{1,\dots,T\}), \quad z_0 \sim \mathcal{D}, \quad \epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I}).}$
+Because the recorded behavior is teleoperated, measurements mostly distribute along the line $a = o + \eta, \eta \sim N(0,1)$, with $\eta$-variability accouting for minor control inconsistencies (Figure [ch4-action-vs-observation-distribution]). Using Gaussian posteriors--i.e., adding Gaussian noise--effectively simulates a *Brownian motion* for the elements in the distribution’s support (in Figure [diffusion-robot-actions], $\mathcal O\times \mathcal A$), whereby information *diffuses away* from the samples, and comparing the diffused samples to the original data points one can derive an estimate of the total displacement induced by diffusion. Under the only assumption that the likelihood of the diffused samples is low under the original unknown data distribution, then one can effectively approximate the unkwown distribution by learning to *reverse* such displacement. This key intuition allows to write a simplified training objective: $\htmlId{diffusion-simplified-loss}{\mathcal L(\theta) = \mathbb{E}_{t, z_0, \epsilon} \big[ \Vert \epsilon - \epsilon_\theta(\sqrt{\bar \alpha_t} z_0 + \epsilon \sqrt{1 - \bar \alpha_t}, t) \Vert^2 \big], \quad t \sim \mathcal{U}(\{1,\dots,T\}), \quad z_0 \sim \mathcal{D}, \quad \epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I}).}$
In this simplified (minimization) objective, the optimization process differs from [diffusion-likelihood] in that, rather than maxizing $p_\theta$ directly, the parameters $\theta$ of the pairwise likelihood $p_\theta(z_{t-1} \vert z_t)$ are adjusted to *predict the total displacement* $\epsilon$ for a randomly long ($t \sim \mathcal{U}(\{1,\dots,T\}$ )) diffusion process starting from a sample of the target distribution.
@@ -856,6 +911,8 @@ By learning the total displacement from a generally, uninformative corrupted sam
#### Flow Matching
+
+
The posterior parametrization adopted by DMs proved traditionally effective, yet it raised concerns circa its efficiency at inference time, where a possibly large of compute-expensive denoising steps are needed in order to recover a sample from the target distribution. Flow Matching (FM) @lipmanFlowMatchingGenerative2023 extends DMs to the general case of arbitrary, parametrized likelihood and posteriors, and in this defines a superseding class of GMs providing a unified framework for learning *continuous transformations* between distributions, encompassing and generalizing DMs. Instead of a *stochastic, discrete, multi-step* denoising process, FM aims to learn a *deterministic, continuous, differentiable flow* $\psi [0,1] \times Z \mapsto Z$, formalized starting from possibly time-dependent vector field $v: [0,1] \times Z \mapsto Z$ transporting samples from a simple prior distribution $p_0$--e.g., a standard Gaussian--to a more complex, potentially unknown data distribution $p_1$ over time. Note how FM models time $t \in [0,1]$ to be varying continuously while moving away *from* an easy-to-sample distribution $p_0$ *towards* the unknown data-distribution, $p_1$. This results in a continuous and deterministic trajectory for each sample, which can be more efficient to generate compared to the stochastic paths of DMs. Formally, FM can be fully characterized by an ordinary differential equation (ODE) relating instantaneous variations of flows with the underlying vector field, and hence providing complete trajectories over the distributions’ support when integrating over time,
$$
@@ -870,27 +927,31 @@ FM proved very effective in a variety of applications, ranging from image @esse
```
Note that the traditional discrete-time noise-scheduler ${\beta_t}_{t=0}^T$ is now generalized to a continuous map $\beta : [0,1] \mapsto \mathbb R^+$. Crucially, @lipmanFlowMatchingGenerative2023 prove that by exclusively optimizing the vector field for individual data points $z_0 \in \mathcal D$ individually, one also retrieves the optimal flow to morph the entire support of the initial distribution $p_0$ into $p_1 \ \text{s.t.} \mathcal D \sim p_1$.
+
+
+Probability distributions can be modified applying vector fields resulting in a flow of mass in the support. When acting over time, vector fields can effectively change the distribution’s structure.
+
-While the noising schedule of DMs results in a stochastic process that resembles a random walk, FM allows for more general--potentially, deterministic--likelihood and posterior parametrization. In the FM literature the likelihood and posterior probabilty densities defined along a HMLV model are typically jointly referred to as a *probability path*, where the distributions for successive adjacent transitions in the HMLV model are related by the (normalized) flow between them (Figure 27). The inherent flexibility of FM is one of their key advantages over DMs, as it opens up the possibility of *learning* more efficient paths. For instance, one can design probability paths inspired by Optimal Transport (OT)--a subdiscipline studying the problem of finding the most efficient way to morph one probability distribution into another. Probability paths obtained through OT paths tend to be *straighter* than diffusion paths (Figure 28), which can lead to faster and more stable training, as well as higher-quality sample generation with fewer steps at inference time. By avoiding unnecessary backtracking associated with the inherent stochastic nature of both the noising and denoising process in DMs, test-time compute is typically significantly reduced, while retaining comparable results @lipmanFlowMatchingGenerative2023.
+While the noising schedule of DMs results in a stochastic process that resembles a random walk, FM allows for more general--potentially, deterministic--likelihood and posterior parametrization. In the FM literature the likelihood and posterior probabilty densities defined along a HMLV model are typically jointly referred to as a *probability path*, where the distributions for successive adjacent transitions in the HMLV model are related by the (normalized) flow between them (Figure [ch4-normalizing-flows]). The inherent flexibility of FM is one of their key advantages over DMs, as it opens up the possibility of *learning* more efficient paths. For instance, one can design probability paths inspired by Optimal Transport (OT)--a subdiscipline studying the problem of finding the most efficient way to morph one probability distribution into another. Probability paths obtained through OT paths tend to be *straighter* than diffusion paths (Figure [ch4-diffusion-paths-versus-fm]), which can lead to faster and more stable training, as well as higher-quality sample generation with fewer steps at inference time. By avoiding unnecessary backtracking associated with the inherent stochastic nature of both the noising and denoising process in DMs, test-time compute is typically significantly reduced, while retaining comparable results @lipmanFlowMatchingGenerative2023.
+
+
+Compared to diffusion, flow matching distorts distribution along a less randomic pattern, resulting in a clearer interpolation between source and target distribution. The visualization shows an example comparison between these two methods on joint distribution of robot observations and actions over T = 50 steps.
+
In practice, FM can be applied to generative modeling by learning a vector field regressor $v_\theta(z, t)$ to approximate a given target vector field $u(t, z)$. In the particular case of DMs, $u(t, z)$ is defined as in [fm-diffusion-vector-field], while in priciple the target vector field can be learned to induce a particular transportation, or fixed according to OT. Given a sample from the data distribution $z_1 \sim p_1$ and a sample from an easy-to-sample prior $z_0 \sim p_0$, CFM defines a simple path between them using *linear interpolation* between samples $z_t = (1-t)z_0 + t z_1$, resulting in the target vector field $u(t, z_t) = z_1 - z_0$. Then, a FM model can be trained with the simple regression objective defined as $\htmlId{flow-matching-objective}{\mathcal L(\theta) = \mathbb{E}_{t, z_0, z_1} \big[ \Vert v_\theta((1-t)z_0 + t z_1, t) - (z_1 - z_0) \Vert^2 \big], \quad t \sim \mathcal{U}([0,1]),}$ where $z_0 \sim p_0(\bullet)$ and $z_1 \sim p_1(\bullet)$. Note how in [flow-matching-objective]--differently from [diffusion-simplified-loss]--time is assumed to be varying continuously $t \sim \mathcal U([0,1])$ rather than discretely $t \sim \mathcal U(\{0,1\})$, a key property of flow-based models. The objective in [flow-matching-objective] directly regresses the learned vector field onto the simple, straight path connecting a point from the prior and a point from the data, providing a simulation-free training procedure that is both stable and efficient. At inference time, samples are generated by starting with $z_0 \sim p_0$ and iteratively refined according to $\frac{dz}{dt} = v_\theta(z_t, t)$ for $t \in [0,1]$--an operation that can be numerically carried out with standard ODE solvers.
@@ -904,39 +965,45 @@ In practice, when learning from demonstrations adopting CVAEs results in a sligh
In their work, @zhaoLearningFineGrainedBimanual2023 ablated using a GM to learn from human demonstrations compared to a simpler, supervised objective, $\mathcal L_1(a,a^\prime) = \Vert a - a^\prime \Vert_1$. Interestingly, they found the performance of these two approaches to be comparable when learning from *scripted* demonstrations. That is, when learning from data collected rolling out a predetermined set of commands $[q^c_0, q^c_1, \dots]$, GM did *not* prove competitive compared to standard supervised learning. However, when learning from human demonstrations--i.e., from data collected executing commands coming from a human controller $[q^h_0, q^h_1, \dots]$--they found performance (success rate on a downstream task) to be severily (-33.3%) hindered from adopting a standard supervised learning objective compared to a richer, potentially more complex to learn variational objective, in keeping with the multimodal nature of human demonstrations data and findings presented in @florenceImplicitBehavioralCloning2022. The authors also ablate the action chunking paradigm, reporting significant performance gains for performing action chunking (1% vs. 44% success rate). To avoid acting openloop, @zhaoLearningFineGrainedBimanual2023 design an inference process consisting in performing inference at every timestep $t$ and then aggregate overlapping chunks using chunks’ exponential moving average.
+
+
+Action Chunking with Transformer (ACT), as in @zhaoLearningFineGrainedBimanual2023. ACT introduces an action chunking paradigm to cope with high-dimensional multi-modal demonstration data, and a transformer-based CVAE architecture.
+
-In ACT (Figure 29), inference for a given observation $o \in \mathcal O$ could be performed by (1) computing a prior $p_\omega(z \vert o)$ for the latent and (2) decoding an action chunk from a sampled latent $z \sim p_\omega(\bullet \vert o)$, similarily to how standard VAEs generate samples, with the exception that vanilla VAEs typically pose $p(z\vert o) \equiv p(z) \sim N(\mathbf{0}, \mathbf{I})$ and thus skip (1).
+In ACT (Figure [ch4-act]), inference for a given observation $o \in \mathcal O$ could be performed by (1) computing a prior $p_\omega(z \vert o)$ for the latent and (2) decoding an action chunk from a sampled latent $z \sim p_\omega(\bullet \vert o)$, similarily to how standard VAEs generate samples, with the exception that vanilla VAEs typically pose $p(z\vert o) \equiv p(z) \sim N(\mathbf{0}, \mathbf{I})$ and thus skip (1).
+
+
+The CVAE encoder used in ACT. Input action chunks are first embedded and aggregated with positional embeddings, before being processed alongside embedded proprioperceptive information, and a learned [CLS] token used to aggregate input level information, and predict the style variable z. The encoder is entirely disregarded at inference time.
+
However, the authors claim using a deterministic procedure to derive $z$ may benefit policy evaluation, and thus avoid sampling from the conditional prior at all. At test time, instead, they simply use $z = \mathbf{0}$, as the conditional prior on $z$ used in training is set to be the unit Gaussian. At test time, conditioning on the observation $o$ is instead achieved through explicitly feeding proprioperceptive and visual observations to the decoder, $p_\theta(a \vert z, o)$, while during training $z$ is indeed sampled from the approximate posterior distribution $p_\phi(z \vert o, a)$, which, however, disregards image observations and exclusively uses proprioperceptive states to form $o$ for efficiency reasons (as the posterior $q_\phi$ is completely disregarded at test time).
+
+
+The CVAE decoder used in ACT, comprising of a full encoder-decoder Transformer architecture. Camera observations from all n camera views are first embedded using pre-trained visual encoders, and then concatenated to the corresponding positional embeddings. Then, alongside embeddings for the proprioperceptive information available and the style variable z retrieved from the CVAE encoder, the Transformer encoder shares the matrices K, Q with the Transformer decoder, trained to decode fixed position embeddings into action valid chunks.
+
#### Code Example: Learning ACT
@@ -952,33 +1019,37 @@ $$
Notice how in [diffusion-policy-objective] the noise regressor is conditioned both on the latent variable rank $t$ *and* on a stack of previous observations $o_{t-T_o-t}$. @chiDiffusionPolicyVisuomotor2024 claim the combination of (1) conditioning on a horizon of previous observations and (2) predicting multiple actions into the future allows DP to *commit to specific modes* in the data at inference time, which proves essential for good performance and avoiding undecisiveness.
+
+
+The Diffusion Policy archicture, as in @chiDiffusionPolicyVisuomotor2024. A stack of Ho previous observations is used as external conditioning to denoise a group of Ha actions. Conditioning is used at every layer of a U-Net block, and in practice allows to obtain fully-formed action chunks with as little as T = 10 denoising steps.
+
-Figure 32 shows the convolution-based version of the architecture proposed by @chiDiffusionPolicyVisuomotor2024, illustrating inference on a single sample from $\mathcal D$ for simplicity. An arbitrarily noisy chunk of $H_a$ actions $\tilde a_{t:t+H_a}$ is mapped to a learned high-dimensional space. Similarily, both image observations and poses are embedded before being aggregated to the action embeddings. Then, a U-Net @ronnebergerUNetConvolutionalNetworks2015 is trained to regress the noise added into $\tilde a_{t:t+H_a}$, using observation conditioning information at every layer and seeking to optimize [diffusion-policy-objective]. At inference time, the noise predictor is used to predict the quantity of noise at every $t \in [T, \dots, 0 ]$ and iteratively subtract it from $\tilde a_{t:t+T_a}$, reversing the diffusion process simulated in training conditioned on $o_{t-T_o:t}$ to predict $a_{t:t+T_a}$.
+Figure [diffusion-policy-architecture] shows the convolution-based version of the architecture proposed by @chiDiffusionPolicyVisuomotor2024, illustrating inference on a single sample from $\mathcal D$ for simplicity. An arbitrarily noisy chunk of $H_a$ actions $\tilde a_{t:t+H_a}$ is mapped to a learned high-dimensional space. Similarily, both image observations and poses are embedded before being aggregated to the action embeddings. Then, a U-Net @ronnebergerUNetConvolutionalNetworks2015 is trained to regress the noise added into $\tilde a_{t:t+H_a}$, using observation conditioning information at every layer and seeking to optimize [diffusion-policy-objective]. At inference time, the noise predictor is used to predict the quantity of noise at every $t \in [T, \dots, 0 ]$ and iteratively subtract it from $\tilde a_{t-t+T_a}$, reversing the diffusion process simulated in training conditioned on $o_{t-T_o:t}$ to predict $a_{t:t+T_a}$.
-Training using 50-150 demos (15-60 minutes of teleoperation data) DP achieves strong performance on a variety of simulated and real-world tasks, including dexterous and deformable manipulation tasks such as sauce pouring and mat unrolling. Notably, the authors ablated the relevance of using RGB camera streams as input to their policy, and observed how high frame-rate visual observations can be used to attain performance (measured as success rate) comparable to that of state-based policies, typically trained in simulation with priviledged information not directly available in real-world deployments. As high-frame rate RGB inputs naturally accomodate for dynamic, fast changing environments, @chiDiffusionPolicyVisuomotor2024’s conclusion offers significant evidence for learning streamlined control policies directly from pixels. In their work, @chiDiffusionPolicyVisuomotor2024 also ablate the performance of DP against their baseline against the size of the dataset collected, showing that DP outperforms the considered baseline for every benchmark size considered. Further, to accelerate inference, @chiDiffusionPolicyVisuomotor2024 employ Denoising Diffusion Implicit Models @songDenoisingDiffusionImplicit2022, a variant of Denoising Diffusion Probabilistic Models @hoDenoisingDiffusionProbabilistic2020 (DDPM) adopting a strictly deterministic denoising paradigm (differently from DDPM’s natively stochastic one) inducing the same final distribution’s as DDPM’s, and yet resulting in 10 times less denoising steps at inference time @chiDiffusionPolicyVisuomotor2024. Across a range of simulated and real-world tasks, @chiDiffusionPolicyVisuomotor2024 find DPs particularly performant when implementing a transformer-based network as $\epsilon_\theta$, although the authors note the increased sensitivity of transformer networks to hyperparameters and thus explicitly recommend starting out with a simpler, convolution-based architecture for diffusion (Figure 32), which are however reported to be biased towards learning low-frequency components @tancikFourierFeaturesLet2020 and thus may prove more challenging to train with non-smooth action sequences.
+Training using 50-150 demos (15-60 minutes of teleoperation data) DP achieves strong performance on a variety of simulated and real-world tasks, including dexterous and deformable manipulation tasks such as sauce pouring and mat unrolling. Notably, the authors ablated the relevance of using RGB camera streams as input to their policy, and observed how high frame-rate visual observations can be used to attain performance (measured as success rate) comparable to that of state-based policies, typically trained in simulation with priviledged information not directly available in real-world deployments. As high-frame rate RGB inputs naturally accomodate for dynamic, fast changing environments, @chiDiffusionPolicyVisuomotor2024’s conclusion offers significant evidence for learning streamlined control policies directly from pixels. In their work, @chiDiffusionPolicyVisuomotor2024 also ablate the performance of DP against their baseline against the size of the dataset collected, showing that DP outperforms the considered baseline for every benchmark size considered. Further, to accelerate inference, @chiDiffusionPolicyVisuomotor2024 employ Denoising Diffusion Implicit Models @songDenoisingDiffusionImplicit2022, a variant of Denoising Diffusion Probabilistic Models @hoDenoisingDiffusionProbabilistic2020 (DDPM) adopting a strictly deterministic denoising paradigm (differently from DDPM’s natively stochastic one) inducing the same final distribution’s as DDPM’s, and yet resulting in 10 times less denoising steps at inference time @chiDiffusionPolicyVisuomotor2024. Across a range of simulated and real-world tasks, @chiDiffusionPolicyVisuomotor2024 find DPs particularly performant when implementing a transformer-based network as $\epsilon_\theta$, although the authors note the increased sensitivity of transformer networks to hyperparameters and thus explicitly recommend starting out with a simpler, convolution-based architecture for diffusion (Figure [diffusion-policy-architecture]), which are however reported to be biased towards learning low-frequency components @tancikFourierFeaturesLet2020 and thus may prove more challenging to train with non-smooth action sequences.
#### Code Example: Learning Diffusion Policies
### Optimized Inference
+
+
Modern visuomotor policies output *action chunks*-sequences $\pi(o_t) = \mathbf{A}_t$ with $\mathbf{A}_t = \bigl(a_t,a_{t+1},\dots,a_{t+H_a}\bigr)$ being a sequence of $H_a \gg 1$ low-level commands enqueued in an action queue, originating from an environment observation, $o_t$. Predicting series of actions instead of single commands proved essential in learning complex, multi-modal behavior @zhaoLearningFineGrainedBimanual2023, @chiDiffusionPolicyVisuomotor2024.
Typically, the robot executes the entire action chunk $\mathbf{A}_t$, before a new observation $o_{t+H_a}$ is passed to the policy $\pi$ to predict the next chunk. This results in open-loop inference in between observations captured every $H_a$ timesteps. @zhaoLearningFineGrainedBimanual2023 adopts a different strategy whereby the robot controller interleaves chunk prediction $\mathbf{A}_t \gets \pi(o_t)$ and chunk consumption $a_t \gets \text{PopFront(MATHEXPR)}$, computing a new chunk of actions at every timestep $t$ and aggregating the predicted chunks on overlapping sections. While adaptive--every observation at every timestep $o_t$ is processed--such approaches rely on running inference continuously, which can be prohibitive in resource-constrained scenarios, such as edge deployments.
A less resource-intensive approach is to entirely exhaust the chunk $\mathbf{A}$ before predicting a new chunk of actions, a strategy we refer to as *synchronous* (sync) inference. Sync inference efficiently allocates computation every $H_a$ timesteps, resulting in a reduced average computational burden at control time. In contrast, it inherently hinders the responsiveness of robot systems, introducing blind lags due to the robot being *idle* while computing $\mathbf{A}$.
-We directly assess the lack of adaptiveness of robot systems due to acting open-loop, and the presence of lags at runtime by decoupling action chunk prediction $\mathbf{A}$ from action execution $a_t \gets \text{PopFront}(\mathbf{A}_t)$, developing an *asynchronous* (async) inference stack ([alg-async-inference]), whereby a $\text{RobotClient}$ sends an observation $o_t$ to a $\text{PolicyServer}$, receiving an action chunk $\mathbf{A}_t$ once inference is complete (33). In this, we avoid execution lags by triggering chunk prediction while the control loop is still consuming a previously available queue, aggregating it with the newly incoming queue whenever available. In turn, async-inference tightens the loop between action prediction and action execution, by increasing the frequency at which observations are processed for chunk prediction. Crucially, decoupling action prediction from action execution also directly allows to allocate more computational resources on a remote policy server sending actions to the robot client over networks, something which may prove very effective in resource-constrained scenarios such as low-power robots.
+We directly assess the lack of adaptiveness of robot systems due to acting open-loop, and the presence of lags at runtime by decoupling action chunk prediction $\mathbf{A}$ from action execution $a_t \gets \text{PopFront}(\mathbf{A}_t)$, developing an *asynchronous* (async) inference stack ([alg-async-inference]), whereby a $\text{RobotClient}$ sends an observation $o_t$ to a $\text{PolicyServer}$, receiving an action chunk $\mathbf{A}_t$ once inference is complete ([ch4-async-inference]). In this, we avoid execution lags by triggering chunk prediction while the control loop is still consuming a previously available queue, aggregating it with the newly incoming queue whenever available. In turn, async-inference tightens the loop between action prediction and action execution, by increasing the frequency at which observations are processed for chunk prediction. Crucially, decoupling action prediction from action execution also directly allows to allocate more computational resources on a remote policy server sending actions to the robot client over networks, something which may prove very effective in resource-constrained scenarios such as low-power robots.
-
+
Asynchronous inference. Illustration of the asynchronous inference stack. Note that the policy can be run on a remote server, possibly with GPUs.
+
+
**Input:** horizon $T$, chunk size $H_a$, threshold $g\in[0,1]$ **Init:** capture $o_0$; send $o_0$ to ; receive $\mathbf{A}_0 \gets \pi(o_0)$ $a_t \gets \text{PopFront}(\mathbf{A}_t)$ ($a_t$) capture new observation, $o_{t+1}$ `async_handle` $\gets \text{AsyncInfer}(o_{t+1})$ $\tilde{\mathbf{A}}_{t+1} \gets \pi(o_{t+1})$ $\mathbf{A}_{t+1} \gets f(\mathbf{A}_t,\tilde{\mathbf{A}}_{t+1})$
@@ -998,8 +1072,8 @@ We directly assess the lack of adaptiveness of robot systems due to acting open-
$\mathbf{A}_{t+1} \gets \mathbf{A}_t$
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+
##### Implementation details
@@ -1010,7 +1084,7 @@ Algorithmically, we attain (1) on the -side by consuming actions from a readily
Interestingly, the behavior of async inference can be studied analytically. First, let $\ell$ be a random variable modeling the time needed to receive an action chunk $\mathbf{A}$ after sending an observation $o$, i.e. the sum of (1) the time to send across the observation $o$ between the and , $t_{C \to S}$ (2) the inference latency on the , $\ell_S$ and (3) the time to send $\mathbf{A}$ between the and , $t_{S \to C}$. Assuming independence, $\mathbb E [\ell] = \mathbb E[t_{C \to S}] + \mathbb E[\ell_S] + \mathbb E[t_{S \to C}]$ which can be further simplified to $\mathbb E[\ell] \simeq \mathbb E[\ell_S]$, assuming communication time is (1) equal in both directions and (2) negligible with respect to the inference latency. Second, let $\Delta t$ be the environment’s control cycle. With a real-world frame-rate of 30 frames per second, $\Delta t=33\text{ms}$. Consequently, exhausted queues at runtime-i.e. being idle awaiting for a new chunk-are avoided for $g \geq \frac{\mathbb E[\ell_S] / \Delta t}{H_a}$. In this, the queue threshold $g$ plays a major role relatively to the availability of actions to the .
-34 illustrates how the size of the action chunk $\lvert \mathbf{A}_t \rvert$ evolves over time for three representative values of $g$, detailing the following key scenarios:
+[ch4-queues] illustrates how the size of the action chunk $\lvert \mathbf{A}_t \rvert$ evolves over time for three representative values of $g$, detailing the following key scenarios:
- **Sequential limit $(g=0)$.** The client drains the entire chunk before forwarding a new observation to the server. During the round-trip latency needed to compute the next chunk, the queue is empty, leaving the robot *incapable of acting*. This reproduces the behavior of a fully sequential deployment and results in an average of $\mathbb E[\ell_S]$ idle seconds.
@@ -1018,7 +1092,7 @@ Interestingly, the behavior of async inference can be studied analytically. Firs
- **Compute-intensive limit $(g=1)$.** As an extreme case, and in keeping with @zhaoLearningFineGrainedBimanual2023, an observation is sent at *every* timestep. The queue is therefore almost always filled, with only a minor saw-tooth due to$\Delta t/\mathbb E[\ell_s] < 1$. While maximally reactive, this setting incurs one forward pass per control tick and can prove prohibitively expensive on limited hardware. Importantly, because the client is consuming actions while the server computes the next chunk, the available queue never gets filled again.
-
+
Action queue size evolution at runtime for various levels of g when (A) not filtering out observation based on joint-space similarity and (B) filtering out near-duplicates observation, measuring their similarity in joint-space.
-34 emphasizes the trade-off governed by $g$: small values place result in idle periods, whereas $g\approx 1$ assumes a highly accurate model and pays a significant compute price. In practice, choosing $g\in(0,1)$ allows to strike a balance between reactivity against resource budgets. If not for the aforementioned similarity filter, the would send observations for processing every $(1 - g) H_a \cdot \Delta t$ seconds, receiving a new chunk of actions every $(1 - g) H_a \cdot \Delta t + \mathbb E[\ell_S]$, on average. The presence of the observation similarity filter dilates this processing time, and serves the scope of avoiding the robot stalling due to the queue being constantly integrated with an incoming, nearly identical, action chunk. In particular, 34 results in a queue which is filled with incoming actions *unless* near-duplicate observations are filtered out from the processing pipeline. For clarity, the red arrow in 34 highlights a timestep where the observation similarity mechanism is bypassed, forcing a (nearly identical) observation to be processed as the queue results empty.
+[ch4-queues] emphasizes the trade-off governed by $g$: small values place result in idle periods, whereas $g\approx 1$ assumes a highly accurate model and pays a significant compute price. In practice, choosing $g\in(0,1)$ allows to strike a balance between reactivity against resource budgets. If not for the aforementioned similarity filter, the would send observations for processing every $(1 - g) H_a \cdot \Delta t$ seconds, receiving a new chunk of actions every $(1 - g) H_a \cdot \Delta t + \mathbb E[\ell_S]$, on average. The presence of the observation similarity filter dilates this processing time, and serves the scope of avoiding the robot stalling due to the queue being constantly integrated with an incoming, nearly identical, action chunk. In particular, [ch4-queues] results in a queue which is filled with incoming actions *unless* near-duplicate observations are filtered out from the processing pipeline. For clarity, the red arrow in [ch4-queues] highlights a timestep where the observation similarity mechanism is bypassed, forcing a (nearly identical) observation to be processed as the queue results empty.
-#### Code Example: Using Async Inference
+#### Code Example- Using Async Inference
## Generalist Robot Policies
+
*Specialization is for insects*
@@ -1051,31 +1127,35 @@ TL;DR Openly available large scale datasets and the development of stable, expre
The advent of large models trained on internet-scale datasets has drastically influenced fields like Computer Vision (CV) and Natural Language Processing (NLP), shifting the paradigm towards combining (1) an initial, task-agnostic large-scale pre-training stage and a (2) task-specific, adjustment phase. The pre-training/adaptation paradigm has now largely replaced more classic approaches consisting of task-specific data collection, curation and model training in many subdomains within CV and NLP, motivated by the main drawback of limited scalability for *task-specific approaches*, traditionally labor intensive. Factors including (1) the advancements in generalist models learned with self-supervision for perception @oquabDINOv2LearningRobust2024 or semantic understanding @devlinBERTPretrainingDeep2019 and (2) the popularization collective efforts to aggregate large-scale openly available datasets @collaborationOpenXEmbodimentRobotic2025, @khazatskyDROIDLargeScaleInTheWild2025 are increasingly pushing the field of robot learning towards the pre-train-and-adapt paradigm. This shift taps into the long-standing challenge of developing generalist robot policies, and holds the premise to surpass traditionally siloed approaches to robotics problems and develop a *foundation robotics model*. While Section [learning-bc-single] introduced methods for learning *single-task policies* such as ACT or Diffusion Policy, in this section we present advancements in developing *generalist, multi-task, policies*, capable of performing a wide range of tasks across different environments and embodiments, and guided by unstructured instructions given via natural language.
+
+
+Fields within ML such as Computer Vision and NLP converged on the development of foundation models, trained on a variety of large scale models and capable to perform multiple downstream tasks (top). Conversely, robotics suffered from limited standardization in terms of the architectures used, and siloed, task specific datasets, incurring in a high degree of fragmentation which traditionally hindered the development of generalist models for robotics in favour of task-specific models (bottom).
+
### Preliminaries: Models and Data
-The remarkable success of foundation models in NLP and CV is predicated on two core principles: architectural innovation and joint data-compute scaling. The transformer architecture proved instrumental in capturing long-range dependencies in sequential data such as text, and its stability and expressivity made it the *de facto* standard for modern large-scale models trained on internet-scale amounts of data. In stark contrast with popular NLP @raffelExploringLimitsTransfer2023 and CV @ImageNet_VSS09 general-purpose datasets, the field of robotics has historically developed around task-specific datasets which hinders scalability across problems, resulting in a concrete data deficit for general-purpose robot learning. Unlike the wealth of relatively readily available text and images on the internet, robotics data is intrinsically embodied--datasets collected for a manipulation robot typically differ entirely from locomotion datasets. Further, datasets consisting of expert demonstrations are (1) intrinsically expensive to collect (2) and notoriously heterogeneous--different human experts may perform the same task optimally yet in very different ways. In particular, since each expert trajectory is tied to a specific robot platform and the operating conditions of its environment and task, data heterogeneity has long posed a *methodological* challenge for scaling robotics datasets via aggregation. Beyond this, heterogeneity also raises *conceptual* issues: naively mixing data across embodiments can induce negative transfer, as control strategies developed in isolation for different robot systems in different environments may even conflict when combined. Thus, the high degree of fragmentation of robotics datasets and tasks has traditionally led to the development of *specialist* policies, trained on small, task-specific datasets, and which excel at their designated task but fail to generalize to new situations (Figure 35).
+The remarkable success of foundation models in NLP and CV is predicated on two core principles: architectural innovation and joint data-compute scaling. The transformer architecture proved instrumental in capturing long-range dependencies in sequential data such as text, and its stability and expressivity made it the *de facto* standard for modern large-scale models trained on internet-scale amounts of data. In stark contrast with popular NLP @raffelExploringLimitsTransfer2023 and CV @ImageNet_VSS09 general-purpose datasets, the field of robotics has historically developed around task-specific datasets which hinders scalability across problems, resulting in a concrete data deficit for general-purpose robot learning. Unlike the wealth of relatively readily available text and images on the internet, robotics data is intrinsically embodied--datasets collected for a manipulation robot typically differ entirely from locomotion datasets. Further, datasets consisting of expert demonstrations are (1) intrinsically expensive to collect (2) and notoriously heterogeneous--different human experts may perform the same task optimally yet in very different ways. In particular, since each expert trajectory is tied to a specific robot platform and the operating conditions of its environment and task, data heterogeneity has long posed a *methodological* challenge for scaling robotics datasets via aggregation. Beyond this, heterogeneity also raises *conceptual* issues: naively mixing data across embodiments can induce negative transfer, as control strategies developed in isolation for different robot systems in different environments may even conflict when combined. Thus, the high degree of fragmentation of robotics datasets and tasks has traditionally led to the development of *specialist* policies, trained on small, task-specific datasets, and which excel at their designated task but fail to generalize to new situations (Figure [ch5-ml-vs-robotics-foundation]).
+
+
+Early efforts in the development of generalist models for robotics include BC-Zero @jangBCZZeroShotTask2022, RT-1 @brohanRT1RoboticsTransformer2023, and RT-2 @brohanRT2VisionLanguageActionModels2023: large scale models trained on thousands of demonstrations. The open release of the Open-X @collaborationOpenXEmbodimentRobotic2025 and DROID datasets @khazatskyDROIDLargeScaleInTheWild2025 fostered the development of open source models: OpenVLA @kimOpenVLAOpenSourceVisionLanguageAction2024, π0 @blackp0VisionLanguageActionFlow2024 and SmolVLA @shukorSmolVLAVisionLanguageActionModel2025.
+
-Motivated by the pursuit of generalist robot policies, the research community started investigating what and how to integrate from other domains within ML. Figure 36 shows a timeline of some of the most popular contributions attempting at developing generalist policies. Starting from BC-Zero, a latent variable model trained on 25K+ demonstrations, the field has now evolved into $\pi_0$, a transformer-based model trained on 10M+ demonstrations and exhibiting strong few-shot capabilities across tasks and embodiments. For starters, Robotics Transformer 1 (RT-1) @brohanRT1RoboticsTransformer2023 represented a significant step in the direction of developing a generalist robot policies over prior work including (1) BC-Zero @jangBCZZeroShotTask2022 and (2) Gato @reedGeneralistAgent2022, in that @brohanRT1RoboticsTransformer2023 uses a much larger and diverse set of training tasks compared to both BC-Zero and Gato. In particular, RT-1 uses a transformer architecture, and is trained on as many as 130k human-recorded trajectories collected over 13 robots in the span on 17 months. RT-1 learns to process a history of camera images and a natural language instruction, and feeds the resulting sequence of high-dimensional tokens to a transformer, trained using a *classification loss on a discretized actions space* consisting of 6 256 bins, each for each joint of a 6-dof robotic arm.
+Motivated by the pursuit of generalist robot policies, the research community started investigating what and how to integrate from other domains within ML. Figure [ch5-generalist-policies-timeline] shows a timeline of some of the most popular contributions attempting at developing generalist policies. Starting from BC-Zero, a latent variable model trained on 25K+ demonstrations, the field has now evolved into $\pi_0$, a transformer-based model trained on 10M+ demonstrations and exhibiting strong few-shot capabilities across tasks and embodiments. For starters, Robotics Transformer 1 (RT-1) @brohanRT1RoboticsTransformer2023 represented a significant step in the direction of developing a generalist robot policies over prior work including (1) BC-Zero @jangBCZZeroShotTask2022 and (2) Gato @reedGeneralistAgent2022, in that @brohanRT1RoboticsTransformer2023 uses a much larger and diverse set of training tasks compared to both BC-Zero and Gato. In particular, RT-1 uses a transformer architecture, and is trained on as many as 130k human-recorded trajectories collected over 13 robots in the span on 17 months. RT-1 learns to process a history of camera images and a natural language instruction, and feeds the resulting sequence of high-dimensional tokens to a transformer, trained using a *classification loss on a discretized actions space* consisting of 6 256 bins, each for each joint of a 6-dof robotic arm.
Perhaps motivated by the contemporary successes of the transformer architecture in both CV and NLP, the same group of authors investigated using a discrete output space to model--inherently continuous--quantities such as actions, leveraging a (1) more powerful architecture and (2) scaling up the dataset used . In RT-2, @brohanRT2VisionLanguageActionModels2023 propose inheriting internet-scale semantic knowledge from large-scale multi-modal datasets to learn a single, *unified model* for robotics control. Such a model, termed *Vision-Language-Action* (VLA) in the original RT-2 paper, effectively casts robot control as a language modeling problem, and in particular as a Visual Question-Answering (VQ) task, whereby the output token space used to represent *string* tokens is shared with the *8-bits tokens* used to represent the 256 actuation levels of a 6-dof robot joint. In their work, @brohanRT2VisionLanguageActionModels2023 propose co-fine-tuning then-leading large-scale VLMs such as PaLIX @chenPaLIXScalingMultilingual2023 or PaLM-E @driessPaLMEEmbodiedMultimodal2023 on a mix of web and robotics data, thus complementing VQtraining with robotics-specific signal, learning to directly output robot actions in a shared token space for visual and language inputs. Using large models trained on internet-scale data as backbones for VLAs allows models to tap into the rich semantic knowledge embedded in the VLM’s parameters, interpret new commands as well as recognize unseen objects by connecting them to concepts acquired while pre-training. For instance, @brohanRT2VisionLanguageActionModels2023 show that while RT-2 has never been explicitly trained to repurpose tools for a hammering task, it can still combine its semantic understanding of images, so that when asked which object between (1) a piece of paper, (2) a pair of headphones or (3) a rock may be used instead of a hammer, it answers correctly, (3).
@@ -1083,17 +1163,19 @@ Traditionally, research involved not only training the model but also collecting
The success of large, proprietary models like RT-1 and RT-2, highlighted a growing accessibility gap in robotics research, as training and deploying large-scale models requires computational resources simply unattainable for most research institutions. The OpenVLA project @kimOpenVLAOpenSourceVisionLanguageAction2024 emerged in direct contrast of closed-source counterparts, as a community-driven effort to create powerful, openly available VLAs. In particular, @kimOpenVLAOpenSourceVisionLanguageAction2024 trained OpenVLA by exclusively leveraging openly available data (970K+ from the Open-X dataset), and share training recipes alongside the model weights. Architecturally, OpenVLA integrates a pre-trained vision encoder to project visual tokens into the embedding space of Llama2-7B @touvronLlama2Open2023 language model backbone. The language model backbone is then used to predict *discrete action tokens* over 256 activation levels.
+
+
+Robot learning is undergoing a paradigmatic shift: centralized data collections (A, left) are increasingly larger, often comprising Ms of demonstrations, and (A, right) decentralized approaches to data collection are also rising as an alternative for large scale data collection. (B) Generalist models are also becoming increasingly smaller and easier to run on limited hardware.
+
-Figure 37 illustrates graphically the two most relevant trends in modern robot learning. As datasets collected via centralized, cross-institutions cooperation of increasing size are made available for the research community, decentralized datasets collected by individual researchers and practitioners have also gained traction recently, closing the gap with academic benchmarks thanks to community-contributed datasets. Further, models used across tasks and embodiments are also becoming much more compute-efficient, and as a result the models’ size has been consistently reducing over time, with consequent gains for autonomous robots in real-world, resource-constrained environments.
+Figure [ch5-trends] illustrates graphically the two most relevant trends in modern robot learning. As datasets collected via centralized, cross-institutions cooperation of increasing size are made available for the research community, decentralized datasets collected by individual researchers and practitioners have also gained traction recently, closing the gap with academic benchmarks thanks to community-contributed datasets. Further, models used across tasks and embodiments are also becoming much more compute-efficient, and as a result the models’ size has been consistently reducing over time, with consequent gains for autonomous robots in real-world, resource-constrained environments.
### Modern VLAs
@@ -1111,17 +1193,19 @@ Recently, compute efficiency has also become a central focus in VLM research. Se
$\pi_0$ @blackp0VisionLanguageActionFlow2024 introduce a VLA consisting of a MoE architecture consisting of (1) a pre-trained VLM backbone (Gemma 2.6B @teamGemma2Improving2024) and (2) a dedicated action expert used to generate continuous actions via flow matching. Images and language are embedded with a late-fusion VLM (PaliGemma), while proprioceptive state and actions chunks are routed to a smaller action expert, initialized from scratch. The two separate experts communicate via self-attention layers, but maintain disjoint weights to obtain query, key and values matrices at each layer, maintaining specialization while efficiently allocating computation.
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+The π0architecture, as in @blackp0VisionLanguageActionFlow2024. Vision and language tokens are routed to a VLM backbone which is prevented from attending robot proprioperceptive states and action tokens, which are instead routed to a smaller subset of weights within the architecture. The architecture is trained with Flow Matching on 10M+ trajectories from a mixture of closed and openly available datasets.
+
-Concretely, $\pi_0$ is a unified transformer with two disjoint sets of weights $\phi, \theta$. A larger VLM backbone $p_\phi$ initialized from Gemma 2.6B processes multiple image frames obtained from multiple cameras points $[\{ I_t \}_{t=1}^n]$, as well as a language instruction $[\ell_t]$ used to describe the task considered. Concurrently, a 300M-parameter *action expert* based on a similar transformer architecture is used processes the robot proprioperceptive state $q_t$ and an action chunk $a_{t:t+H_a}$ (Figure 38). The different expert networks operate separately in processing the respective inputs and turning them into query, key and value matrices, and only share information between each other via self-attention layers. The outputs from the VLM backbone are disregarded, while the vector field regressed by the action expert is used to iteratively refine the action process. In particular, $\pi_0$uses a *blockwise causal attention mask* over tokens belonging to three separate blocks: (1) image and language tokens $\mathcal T_i$ obtained from $[\{ I_t \}_{t=1}^n, \ell_t]$, (2) proprioperceptive tokens $\mathcal T_q$ obtained from $q_t$, and (3) the action tokens $\mathcal T_a$ for items in the chunk $a^{\tau}_{t:t+H_a}$ at time $\tau$ in the flow-matching process. Notably, *within* each block the attention operations are bidirectional, while across blocks, future blocks are masked out. Formally, this corresponds to using the attention mask $\mathbf{A} = \bordermatrix{ \mathcal{T}_i \mathcal{T}_q \mathcal{T}_a \cr \mathcal{T}_i \mathbf{1} \mathbf{0} \mathbf{0} \cr \mathcal{T}_q \mathbf{1} \mathbf{1} \mathbf{0} \cr \mathcal{T}_a \mathbf{1} \mathbf{1} \mathbf{1} \cr }, \quad \mathbf{1}: \text{Bidirectional Attention}, \ \mathbf{0}: \text{Masked Attention}$ Note how *intra*-block directional attention allows tokens to communicate freely, while *inter*-block communication is mediated by the attention mask $\mathbf{A}$. *Blockwise causal masking* effectively prevents the pre-trained perception-language tokens from attending to robotics-tokens, likely out of distribution for VLM backbones traditionally trained on large corpora of internet, non-robotics, data. Crucially, because communication is obstructed between image-language tokens, proprioperceptive and action tokens, one can cache keys and values across denoising steps at runtime time, incuring in a reduced computational footprint and faster inference.
+Concretely, $\pi_0$ is a unified transformer with two disjoint sets of weights $\phi, \theta$. A larger VLM backbone $p_\phi$ initialized from Gemma 2.6B processes multiple image frames obtained from multiple cameras points $[\{ I_t \}_{t=1}^n]$, as well as a language instruction $[\ell_t]$ used to describe the task considered. Concurrently, a 300M-parameter *action expert* based on a similar transformer architecture is used processes the robot proprioperceptive state $q_t$ and an action chunk $a_{t:t+H_a}$ (Figure [ch5-pi0]). The different expert networks operate separately in processing the respective inputs and turning them into query, key and value matrices, and only share information between each other via self-attention layers. The outputs from the VLM backbone are disregarded, while the vector field regressed by the action expert is used to iteratively refine the action process. In particular, $\pi_0$uses a *blockwise causal attention mask* over tokens belonging to three separate blocks: (1) image and language tokens $\mathcal T_i$ obtained from $[\{ I_t \}_{t=1}^n, \ell_t]$, (2) proprioperceptive tokens $\mathcal T_q$ obtained from $q_t$, and (3) the action tokens $\mathcal T_a$ for items in the chunk $a^{\tau}_{t:t+H_a}$ at time $\tau$ in the flow-matching process. Notably, *within* each block the attention operations are bidirectional, while across blocks, future blocks are masked out. Formally, this corresponds to using the attention mask $\mathbf{A} = \bordermatrix{ \mathcal{T}_i \mathcal{T}_q \mathcal{T}_a \cr \mathcal{T}_i \mathbf{1} \mathbf{0} \mathbf{0} \cr \mathcal{T}_q \mathbf{1} \mathbf{1} \mathbf{0} \cr \mathcal{T}_a \mathbf{1} \mathbf{1} \mathbf{1} \cr }, \quad \mathbf{1}: \text{Bidirectional Attention}, \ \mathbf{0}: \text{Masked Attention}$ Note how *intra*-block directional attention allows tokens to communicate freely, while *inter*-block communication is mediated by the attention mask $\mathbf{A}$. *Blockwise causal masking* effectively prevents the pre-trained perception-language tokens from attending to robotics-tokens, likely out of distribution for VLM backbones traditionally trained on large corpora of internet, non-robotics, data. Crucially, because communication is obstructed between image-language tokens, proprioperceptive and action tokens, one can cache keys and values across denoising steps at runtime time, incuring in a reduced computational footprint and faster inference.
In $\pi_0$, both the VLM backbone and action expert are update using a *flow matching* loss, and in particular are updated minimizing:
@@ -1147,6 +1231,8 @@ r0.4
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Using such Beta distribution emphasizes higher noise levels during training, a choice @blackp0VisionLanguageActionFlow2024 argue allows $\pi_0$to focus on learning the mean of the data distribution $\mathbb E[a_{t:t+H_a} \vert o_t]$ during training, in keeping with @esserScalingRectifiedFlow2024. To further optimize performance and reduce inference time, @blackp0VisionLanguageActionFlow2024 propose reducing the support of the timestep distribution to $[0,s], \ s < 1$, as for any forward-integration step size $\delta = 1-s$ timesteps above $s$ are never sampled at inference time.
@@ -1161,23 +1247,25 @@ Lastly, @blackp0VisionLanguageActionFlow2024 present cross-embodiment experimen
VLAs remain in an early stage of development and are not yet as mature or widely adopted as LLMs and VLMs. Further, much of the impactful VLA progress remains proprietary, with many models sharing only weights while withholding full training details and essential methodological components. SmolVLA @shukorSmolVLAVisionLanguageActionModel2025 is an entirely open-source research effort, aiming to democratize the developments of robotics foundation models by open sourcing model, training recipes and data used.
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+The SmolVLA architecture, as in @shukorSmolVLAVisionLanguageActionModel2025. SmolVLA is a compact MoE model trained with flow matching to denoise action chunks. Vision and language tokens are fed to a VLM backbone, and share information with the proprioperceptive and action tokens via the attention mechanism. The attention expert interleaves SA and CA layers for further conditioning on the visual features from the VLM backbone. SmolVLA skips computations and reduces the visual tokens, resulting in 6x less memory usage than π0.
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-While encouraging efforts like $\pi_0$ @blackp0VisionLanguageActionFlow2024 demonstrate the feasibility of open VLA systems, they remain (1) large and compute-intensive and (2) dependent on closed datasets collected via centralized efforts on costly robotic platforms, ultimately hindering accessibility. SmolVLA mitigates both these accessibility issues by (1) prioritizing a compact, compute-efficient VLA design and (2) targeting community-contributed datasets on accessible robotic platforms such as the SO-100 and SO-101 arms. Similarly to $\pi_0$, SmolVLA (Figure 39) employs a MoE architecture combining a pretrained VLM backbone with a dedicated action expert, and trains with flow matching. To ensure efficiency and accessibility, SmolVLA adopts SmolVLM-2 @marafiotiSmolVLMRedefiningSmall2025 as its VLM backbone, considering SmolVLM-2’s reduced size and capability to process multiple image inputs alongside text items. SmolVLM-2 uses SigLIP @zhaiSigmoidLossLanguage2023 as vision encoder, producing visual features for a SmolLM2 language decoder @allalSmolLM2WhenSmol2025. Further, SmolVLA adopts a smaller action expert consisting of $\sim$100M parameters and an interleaved stack of self and cross-attention layers. To improve efficiency, the action expert adopts a reduced embedding dimension compared to the VLM backbone, resulting in $d_{v_\theta} = 0.75 d_{\text{VLM}}$. @shukorSmolVLAVisionLanguageActionModel2025’s design choices thus result in a much smaller size model compared to $\pi_0$, consisting of around 450M parameters versus $\pi_0$’s 3.3B parameters.
+While encouraging efforts like $\pi_0$ @blackp0VisionLanguageActionFlow2024 demonstrate the feasibility of open VLA systems, they remain (1) large and compute-intensive and (2) dependent on closed datasets collected via centralized efforts on costly robotic platforms, ultimately hindering accessibility. SmolVLA mitigates both these accessibility issues by (1) prioritizing a compact, compute-efficient VLA design and (2) targeting community-contributed datasets on accessible robotic platforms such as the SO-100 and SO-101 arms. Similarly to $\pi_0$, SmolVLA (Figure [ch5-smolvla]) employs a MoE architecture combining a pretrained VLM backbone with a dedicated action expert, and trains with flow matching. To ensure efficiency and accessibility, SmolVLA adopts SmolVLM-2 @marafiotiSmolVLMRedefiningSmall2025 as its VLM backbone, considering SmolVLM-2’s reduced size and capability to process multiple image inputs alongside text items. SmolVLM-2 uses SigLIP @zhaiSigmoidLossLanguage2023 as vision encoder, producing visual features for a SmolLM2 language decoder @allalSmolLM2WhenSmol2025. Further, SmolVLA adopts a smaller action expert consisting of $\sim$100M parameters and an interleaved stack of self and cross-attention layers. To improve efficiency, the action expert adopts a reduced embedding dimension compared to the VLM backbone, resulting in $d_{v_\theta} = 0.75 d_{\text{VLM}}$. @shukorSmolVLAVisionLanguageActionModel2025’s design choices thus result in a much smaller size model compared to $\pi_0$, consisting of around 450M parameters versus $\pi_0$’s 3.3B parameters.
-Effectively, SmolVLA consumes multi-view RGB images, a natural-language instruction, and a projected sensorimotor state token as inputs, together with the noised *action chunk* $\tilde{a_{t:t+H_a}}$ the action expert $v_\theta$ is trained to denoise. In particular, robot proprioperceptive states are projected into a shared token space with the VLM to match $d_{\text{VLM}}$, and successively projected into the expert’s token space. Similarily to $\pi_0$, SmolVLA adopts separate experts communicating exclusively through self-attention layers, which do not employ the same blockwise causal masking in favour of a simple causal masking, resulting in a lower triangular attention mask.
+Effectively, SmolVLA consumes multi-view RGB images, a natural-language instruction, and a projected sensorimotor state token as inputs, together with the noised *action chunk* $\tilde{a_{t-t+H_a}}$ the action expert $v_\theta$ is trained to denoise. In particular, robot proprioperceptive states are projected into a shared token space with the VLM to match $d_{\text{VLM}}$, and successively projected into the expert’s token space. Similarily to $\pi_0$, SmolVLA adopts separate experts communicating exclusively through self-attention layers, which do not employ the same blockwise causal masking in favour of a simple causal masking, resulting in a lower triangular attention mask.
In contrast with $\pi_0$, the action expert interleaves *cross-attention* (CA) and *self-attention* (SA) layers, a choice shown to yield higher success and smoother action chunks in practice. While in the expert SA layers, tokens are used to obtain queries, keys and values, CA layers use action tokens only as queries, and instead project visual, language and proprioperceptive tokens in a shared action space to obtain keys and values. Notably, keys and values can be cached as well, resulting in performance gains at inference time.
-SmolVLA trims both token and layer compute. First, it *reduces visual tokens* via pixel shuffle to a fixed budget of 64 tokens per frame, foregoing tiling used during VLM pretraining for runtime efficiency. Second, it *skips upper VLM layers*: the action expert consumes features from the first $N$ decoder layers, with $N=L/2$ providing a good speed-performance trade-off and effectively halving downstream compute for the larger part of SmolVLA. Beyond model compactness, SmolVLA also contributes an inference stack that decouples action prediction from execution for responsiveness on modest hardware (Section 33).
+SmolVLA trims both token and layer compute. First, it *reduces visual tokens* via pixel shuffle to a fixed budget of 64 tokens per frame, foregoing tiling used during VLM pretraining for runtime efficiency. Second, it *skips upper VLM layers*: the action expert consumes features from the first $N$ decoder layers, with $N=L/2$ providing a good speed-performance trade-off and effectively halving downstream compute for the larger part of SmolVLA. Beyond model compactness, SmolVLA also contributes an inference stack that decouples action prediction from execution for responsiveness on modest hardware (Section [ch4-async-inference]).
Departing from reliance on proprietary datasets, SmolVLA pretrains exclusively on 450+ *community datasets*, totaling 20K+ trajectories. Because instructions in community contributed dataset can be noisy or missing, the authors re-annotate tasks with a small off-the-shelf VLM using frames sampled from the dataset, and standardize camera viewpoints by mapping sources to a consistent top/wrist/side ordering. At inference, similarily to $\pi_0$, SmolVLA integrates flow over 10 steps, resulting in fast inference. SmolVLA proves effective across a range of both real-world and simulated environments, rivaling $\pi_0$while being close to 40% faster and consuming 6x less memory.
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## Conclusions
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This tutorial has chronicled the paradigmatic shift transforming robotics, from the structured, model-based methods of its classical era to the dynamic, data-driven approaches that define modern robot learning. We began by examining the limitations of traditional dynamics-based control, highlighting the brittleness and the significant engineering overhead required by traditional approaches, which in turn motivates more flexible, less model-intensive learning approaches.
Our exploration of learning-based techniques revealed a clear trajectory of progress. We began with Reinforcement Learning, acknowledging its power to learn through interaction but also its real-world challenges, particularly sample inefficiency and the complexities of reward design. We saw how modern, data-driven approaches like HIL-SERL can make real-world RL feasible by incorporating human guidance and prior data. The inherent difficulties of RL, however, naturally motivated a deeper dive into imitation learning. This led us to single-task policies, where Behavioral Cloning, powered by advanced generative models like Action Chunking with Transformers and Diffusion Policy, demonstrated the ability to learn complex, multimodal behaviors directly from expert demonstrations. This laid the groundwork for the current frontier: the development of generalist, language-conditioned Vision-Language-Action models. Architectures like $\pi_0$ and SmolVLA--leveraging powerful pre-trained backbones and sophisticated generative modeling techniques like flow matching--represent a significant leap towards building foundational models for robotics that can generalize across varied tasks and embodiments.