Collision Detection Accelerated: An Optimization Perspective

TL;DR

This paper reformulates collision detection as a convex optimization problem, introducing an accelerated Frank-Wolfe based algorithm that significantly improves computational efficiency over traditional methods like GJK.

Contribution

It establishes a novel connection between collision detection and convex optimization, and develops an accelerated algorithm that outperforms existing approaches.

Findings

Up to two times faster collision detection times.

Significant reduction in iteration counts compared to GJK.

Effective on both convex and non-convex shapes.

Abstract

Collision detection between two convex shapes is an essential feature of any physics engine or robot motion planner. It has often been tackled as a computational geometry problem, with the Gilbert, Johnson and Keerthi (GJK) algorithm being the most common approach today. In this work we leverage the fact that collision detection is fundamentally a convex optimization problem. In particular, we establish that the GJK algorithm is a specific sub-case of the well-established Frank-Wolfe (FW) algorithm in convex optimization. We introduce a new collision detection algorithm by adapting recent works linking Nesterov acceleration and Frank-Wolfe methods. We benchmark the proposed accelerated collision detection method on two datasets composed of strictly convex and non-strictly convex shapes. Our results show that our approach significantly reduces the number of iterations to solve collision detection problems compared to the state-of-the-art GJK algorithm, leading to up to two times faster computation times.