DiffPills: Differentiable Collision Detection for Capsules and Padded Polygons

TL;DR

This paper introduces DiffPills, a set of differentiable collision detection algorithms for capsules and padded polygons, enabling gradient-based optimization in robotics and simulation.

Contribution

It formulates collision detection as differentiable convex quadratic programs, allowing for seamless integration with gradient-based methods.

Findings

Provides differentiable proximity and closest points computation

Enables use in trajectory optimization and reinforcement learning

Achieves reliable gradient-based collision detection

Abstract

Collision detection plays an important role in simulation, control, and learning for robotic systems. However, no existing method is differentiable with respect to the configurations of the objects, greatly limiting the sort of algorithms that can be built on top of collision detection. In this work, we propose a set of differentiable collision detection algorithms between capsules and padded polygons by formulating these problems as differentiable convex quadratic programs. The resulting algorithms are able to return a proximity value indicating if a collision has taken place, as well as the closest points between objects, all of which are differentiable. As a result, they can be used reliably within other gradient-based optimization methods, including trajectory optimization, state estimation, and reinforcement learning methods.