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.

Collision detection is a fundamental problem in various domains, such as robotics, computational physics, and computer graphics. In general, collision detection is tackled as a computational geometry problem, with the so-called Gilbert, Johnson, and Keerthi (GJK) algorithm being the most adopted solution nowadays. While introduced in 1988, GJK remains the most effective solution to compute the distance or the collision between two 3D convex geometries. Over the years, it was shown to be efficient, scalable, and generic, operating on a broad class of convex shapes, ranging from simple primitives (sphere, ellipsoid, box, cone, capsule, etc.) to complex meshes involving thousands of vertices. In this article, we introduce several contributions to accelerate collision detection and distance computation between convex geometries by leveraging the fact that these two problems are fundamentally optimization problems. Notably, we establish that the GJK algorithm is a specific sub-case of the well-established Frank-Wolfe (FW) algorithm in convex optimization. By adapting recent works linking Polyak and Nesterov accelerations to Frank-Wolfe methods, we also propose two accelerated extensions of the classic GJK algorithm. Through an extensive benchmark over millions of collision pairs involving objects of daily life, we show that these two accelerated GJK extensions significantly reduce the overall computational burden of collision detection, leading to computation times that are up to two times faster. Finally, we hope this work will significantly reduce the computational cost of modern robotic simulators, allowing the speed-up of modern robotic applications that heavily rely on simulation, such as reinforcement learning or trajectory optimization.

Collision detection is an important component of many 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.