CACTO-SL: Using Sobolev Learning to improve Continuous Actor-Critic with Trajectory Optimization

Trajectory Optimization (TO) and Reinforcement Learning (RL) are powerful and complementary tools to solve optimal control problems. On the one hand, TO can efficiently compute locally-optimal solutions, but it tends to get stuck in local minima if the problem is not convex. On the other hand, RL is typically less sensitive to non-convexity, but it requires a much higher computational effort. Recently, we have proposed CACTO (Continuous Actor-Critic with Trajectory Optimization), an algorithm that uses TO to guide the exploration of an actor-critic RL algorithm. In turns, the policy encoded by the actor is used to warm-start TO, closing the loop between TO and RL. In this work, we present an extension of CACTO exploiting the idea of Sobolev learning. To make the training of the critic network faster and more data efficient, we enrich it with the gradient of the Value function, computed via a backward pass of the differential dynamic programming algorithm. Our results show that the new algorithm is more efficient than the original CACTO, reducing the number of TO episodes by a factor ranging from 3 to 10, and consequently the computation time. Moreover, we show that CACTO-SL helps TO to find better minima and to produce more consistent results.

Risk-Sensitive Extended Kalman Filter

In robotics, designing robust algorithms in the face of estimation uncertainty is a challenging task. Indeed, controllers often do not consider the estimation uncertainty and only rely on the most likely estimated state. Consequently, sudden changes in the environment or the robot's dynamics can lead to catastrophic behaviors. In this work, we present a risk-sensitive Extended Kalman Filter that allows doing output-feedback Model Predictive Control (MPC) safely. This filter adapts its estimation to the control objective. By taking a pessimistic estimate concerning the value function resulting from the MPC controller, the filter provides increased robustness to the controller in phases of uncertainty as compared to a standard Extended Kalman Filter (EKF). Moreover, the filter has the same complexity as an EKF, so that it can be used for real-time model-predictive control. The paper evaluates the risk-sensitive behavior of the proposed filter when used in a nonlinear model-predictive control loop on a planar drone and industrial manipulator in simulation, as well as on an external force estimation task on a real quadruped robot. These experiments demonstrate the abilities of the approach to improve performance in the face of uncertainties significantly.

Contact Models in Robotics: a Comparative Analysis

Physics simulation is ubiquitous in robotics. Whether in model-based approaches (e.g., trajectory optimization), or model-free algorithms (e.g., reinforcement learning), physics simulators are a central component of modern control pipelines in robotics. Over the past decades, several robotic simulators have been developed, each with dedicated contact modeling assumptions and algorithmic solutions. In this article, we survey the main contact models and the associated numerical methods commonly used in robotics for simulating advanced robot motions involving contact interactions. In particular, we recall the physical laws underlying contacts and friction (i.e., Signorini condition, Coulomb's law, and the maximum dissipation principle), and how they are transcribed in current simulators. For each physics engine, we expose their inherent physical relaxations along with their limitations due to the numerical techniques employed. Based on our study, we propose theoretically grounded quantitative criteria on which we build benchmarks assessing both the physical and computational aspects of simulation. We support our work with an open-source and efficient C++ implementation of the existing algorithmic variations. Our results demonstrate that some approximations or algorithms commonly used in robotics can severely widen the reality gap and impact target applications. We hope this work will help motivate the development of new contact models, contact solvers, and robotic simulators in general, at the root of recent progress in motion generation in robotics.

MegaPose: 6D Pose Estimation of Novel Objects via Render & Compare

We introduce MegaPose, a method to estimate the 6D pose of novel objects, that is, objects unseen during training. At inference time, the method only assumes knowledge of (i) a region of interest displaying the object in the image and (ii) a CAD model of the observed object. The contributions of this work are threefold. First, we present a 6D pose refiner based on a render&compare strategy which can be applied to novel objects. The shape and coordinate system of the novel object are provided as inputs to the network by rendering multiple synthetic views of the object's CAD model. Second, we introduce a novel approach for coarse pose estimation which leverages a network trained to classify whether the pose error between a synthetic rendering and an observed image of the same object can be corrected by the refiner. Third, we introduce a large-scale synthetic dataset of photorealistic images of thousands of objects with diverse visual and shape properties and show that this diversity is crucial to obtain good generalization performance on novel objects. We train our approach on this large synthetic dataset and apply it without retraining to hundreds of novel objects in real images from several pose estimation benchmarks. Our approach achieves state-of-the-art performance on the ModelNet and YCB-Video datasets. An extensive evaluation on the 7 core datasets of the BOP challenge demonstrates that our approach achieves performance competitive with existing approaches that require access to the target objects during training. Code, dataset and trained models are available on the project page: https://megapose6d.github.io/.

Constrained Differential Dynamic Programming: A primal-dual augmented Lagrangian approach

Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver to iteratively compute its solution. On one hand, differential dynamic programming (DDP) provides an efficient approach to transcribe the optimal control problem into a finite-dimensional problem while optimally exploiting the sparsity induced by time. On the other hand, augmented Lagrangian methods make it possible to formulate efficient algorithms with advanced constraint-satisfaction strategies. In this paper, we propose to combine these two approaches into an efficient optimal control algorithm accepting both equality and inequality constraints. Based on the augmented Lagrangian literature, we first derive a generic primal-dual augmented Lagrangian strategy for nonlinear problems with equality and inequality constraints. We then apply it to the dynamic programming principle to solve the value-greedy optimization problems inherent to the backward pass of DDP, which we combine with a dedicated globalization strategy, resulting in a Newton-like algorithm for solving constrained trajectory optimization problems. Contrary to previous attempts of formulating an augmented Lagrangian version of DDP, our approach exhibits adequate convergence properties without any switch in strategies. We empirically demonstrate its interest with several case-studies from the robotics literature.

ProxNLP: a primal-dual augmented Lagrangian solver for nonlinear programming in Robotics and beyond

Mathematical optimization is the workhorse behind several aspects of modern robotics and control. In these applications, the focus is on constrained optimization, and the ability to work on manifolds (such as the classical matrix Lie groups), along with a specific requirement for robustness and speed. In recent years, augmented Lagrangian methods have seen a resurgence due to their robustness and flexibility, their connections to (inexact) proximal-point methods, and their interoperability with Newton or semismooth Newton methods. In the sequel, we present primal-dual augmented Lagrangian method for inequality-constrained problems on manifolds, which we introduced in our recent work, as well as an efficient C++ implementation suitable for use in robotics applications and beyond.

Differentiable Collision Detection: a Randomized Smoothing Approach

Collision detection appears as a canonical operation in a large range of robotics applications from robot control to simulation, including motion planning and estimation. While the seminal works on the topic date back to the 80s, it is only recently that the question of properly differentiating collision detection has emerged as a central issue, thanks notably to the ongoing and various efforts made by the scientific community around the topic of differentiable physics. Yet, very few solutions have been suggested so far, and only with a strong assumption on the nature of the shapes involved. In this work, we introduce a generic and efficient approach to compute the derivatives of collision detection for any pair of convex shapes, by notably leveraging randomized smoothing techniques which have shown to be particularly adapted to capture the derivatives of non-smooth problems. This approach is implemented in the HPP-FCL and Pinocchio ecosystems, and evaluated on classic datasets and problems of the robotics literature, demonstrating few micro-second timings to compute informative derivatives directly exploitable by many real robotic applications including differentiable simulation.

Enforcing the consensus between Trajectory Optimization and Policy Learning for precise robot control

Reinforcement learning (RL) and trajectory optimization (TO) present strong complementary advantages. On one hand, RL approaches are able to learn global control policies directly from data, but generally require large sample sizes to properly converge towards feasible policies. On the other hand, TO methods are able to exploit gradient-based information extracted from simulators to quickly converge towards a locally optimal control trajectory which is only valid within the vicinity of the solution. Over the past decade, several approaches have aimed to adequately combine the two classes of methods in order to obtain the best of both worlds. Following on from this line of research, we propose several improvements on top of these approaches to learn global control policies quicker, notably by leveraging sensitivity information stemming from TO methods via Sobolev learning, and augmented Lagrangian techniques to enforce the consensus between TO and policy learning. We evaluate the benefits of these improvements on various classical tasks in robotics through comparison with existing approaches in the literature.

Augmenting differentiable physics with randomized smoothing

In the past few years, following the differentiable programming paradigm, there has been a growing interest in computing the gradient information of physical processes (e.g., physical simulation, image rendering). However, such processes may be non-differentiable or yield uninformative gradients (i.d., null almost everywhere). When faced with the former pitfalls, gradients estimated via analytical expression or numerical techniques such as automatic differentiation and finite differences, make classical optimization schemes converge towards poor quality solutions. Thus, relying only on the local information provided by these gradients is often not sufficient to solve advanced optimization problems involving such physical processes, notably when they are subject to non-smoothness and non-convexity issues.In this work, inspired by the field of zero-th order optimization, we leverage randomized smoothing to augment differentiable physics by estimating gradients in a neighborhood. Our experiments suggest that integrating this approach inside optimization algorithms may be fruitful for tasks as varied as mesh reconstruction from images or optimal control of robotic systems subject to contact and friction issues.

Collision Detection Accelerated: An Optimization Perspective

Collision detection between two convex shapes is an essential feature of any physics engine or robot motion planner. It has often been tackled as a computational geometry problem, with the Gilbert, Johnson and Keerthi (GJK) algorithm being the most common approach today. In this work we leverage the fact that collision detection is fundamentally a convex optimization problem. In particular, we establish that the GJK algorithm is a specific sub-case of the well-established Frank-Wolfe (FW) algorithm in convex optimization. We introduce a new collision detection algorithm by adapting recent works linking Nesterov acceleration and Frank-Wolfe methods. We benchmark the proposed accelerated collision detection method on two datasets composed of strictly convex and non-strictly convex shapes. Our results show that our approach significantly reduces the number of iterations to solve collision detection problems compared to the state-of-the-art GJK algorithm, leading to up to two times faster computation times.