28 research outputs found
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
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.Comment: 7 pages, 6 figures, 2 table
Décret, motivé par la motion de Maribon-Montaut, supprimant le cautionnement pour les receveurs, lors de la séance du 7 floréal an II (26 avril 1794)
Montaut Louis Maribon de. Décret, motivé par la motion de Maribon-Montaut, supprimant le cautionnement pour les receveurs, lors de la séance du 7 floréal an II (26 avril 1794). In: Tome LXXXIX - Du 29 germinal au 13 floréal an II (18 avril au 2 mai 1794) p. 384
Remarques sur la pétition du club Electoral qui demande la garantie illimitée des opinions et de la liberté de la presse et que le peuple rentre dans la plénitude de ses droits en nommant ses fonctionnaires publics, lors de la séance du 20 fructidor an II (6 septembre 1794)
Montaut Bernard-Louis-Célestin, Billaud-Varenne. Remarques sur la pétition du club Electoral qui demande la garantie illimitée des opinions et de la liberté de la presse et que le peuple rentre dans la plénitude de ses droits en nommant ses fonctionnaires publics, lors de la séance du 20 fructidor an II (6 septembre 1794). In: Archives Parlementaires de 1787 à 1860 - Première série (1787-1799) Tome XCVI - Du 10 fructidor au 22 fructidor an II (27 août au 8 septembre 1794) Paris : CNRS éditions, 1990. p. 318
Remarques sur la pétition du club Electoral qui demande la garantie illimitée des opinions et de la liberté de la presse et que le peuple rentre dans la plénitude de ses droits en nommant ses fonctionnaires publics, lors de la séance du 20 fructidor an II (6 septembre 1794)
Montaut Bernard-Louis-Célestin, Billaud-Varenne. Remarques sur la pétition du club Electoral qui demande la garantie illimitée des opinions et de la liberté de la presse et que le peuple rentre dans la plénitude de ses droits en nommant ses fonctionnaires publics, lors de la séance du 20 fructidor an II (6 septembre 1794). In: Archives Parlementaires de 1787 à 1860 - Première série (1787-1799) Tome XCVI - Du 10 fructidor au 22 fructidor an II (27 août au 8 septembre 1794) Paris : CNRS éditions, 1990. p. 318
Collision Detection Accelerated: An Optimization Perspective
International audienceCollision 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
Augmenting differentiable physics with randomized smoothing
International audienceIn 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
Leveraging Randomized Smoothing for Optimal Control of Nonsmooth Dynamical Systems
Optimal Control (OC) algorithms such as Differential Dynamic Programming (DDP) take advantage of the derivatives of the dynamics to efficiently control physical systems. Yet, in the presence of nonsmooth dynamical systems, such class of algorithms are likely to fail due, for instance, to the presence of discontinuities in the dynamics derivatives or because of non-informative gradient during the solving. On the contrary, Reinforcement Learning (RL) algorithms have shown better empirical results in scenarios exhibiting nonsmooth effects (contacts, frictions, etc). Our approach leverages recent works on Randomized Smoothing (RS) to tackle nonsmoothness issues commonly encountered in Optimal Control, and provides key insights on the interplay between RL and OC through the prism of RS methods. This naturally leads us to introduce the Randomized Differential Dynamic Programming (R-DDP) algorithm accounting for deterministic but non-smooth dynamics in a very sample-efficient way. The experiments demonstrate that our method is able to solve classic robotic problems with dry friction and frictional contacts, where classical OC algorithms are likely to fail and RL algorithms require in practice a prohibitive number of samples to find an optimal solution