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