Collision detection between objects is critical for simulation, control, and learning for robotic systems. However, existing collision detection routines are inherently non-differentiable, limiting their applications in gradient-based optimization tools. In this work, we propose DCOL: a fast and fully differentiable collision-detection framework that reasons about collisions between a set of composable and highly expressive convex primitive shapes. This is achieved by formulating the collision detection problem as a convex optimization problem that solves for the minimum uniform scaling applied to each primitive before they intersect. The optimization problem is fully differentiable with respect to the configurations of each primitive and is able to return a collision detection metric and contact points on each object, agnostic of interpenetration. We demonstrate the capabilities of DCOL on a range of robotics problems from trajectory optimization and contact physics, and have made an open-source implementation available.

翻译：物体间的碰撞检测对于机器人系统的仿真、控制与学习至关重要。然而，现有碰撞检测程序本质上是不可微的，这限制了其在基于梯度的优化工具中的应用。本文提出DCOL：一种快速且完全可微的碰撞检测框架，能够对一组可组合且高表达力的凸基元形状之间的碰撞进行推理。该方法通过将碰撞检测问题转化为凸优化问题实现——该优化求解的是各基元在发生相交前所需的最小均匀缩放比例。该优化问题对各基元的构型完全可微，且能返回碰撞检测度量及每个物体上的接触点，且与物体相互穿透程度无关。我们在轨迹优化和接触物理等多个机器人学问题中展示了DCOL的能力，并提供了开源实现。