Differentiable Collision Detection: a Randomized Smoothing Approach

Understand

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.