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Collision detection between objects is critical for simulation, control, andlearning for robotic systems. However, existing collision detection routinesare inherently non-differentiable, limiting their applications ingradient-based optimization tools. In this work, we propose DCOL: a fast andfully differentiable collision-detection framework that reasons aboutcollisions between a set of composable and highly expressive convex primitiveshapes. This is achieved by formulating the collision detection problem as aconvex optimization problem that solves for the minimum uniform scaling appliedto each primitive before they intersect. The optimization problem is fullydifferentiable with respect to the configurations of each primitive and is ableto return a collision detection metric and contact points on each object,agnostic of interpenetration. We demonstrate the capabilities of DCOL on arange of robotics problems from trajectory optimization and contact physics,and have made an open-source implementation available.

Differentiable Collision Detection for a Set of Convex Primitives