GJK-CBF: Control Barrier Functions for Convex Rigid Body Collision Avoidance on SE(3)
arXiv:2610.04910v1 Announce Type: new Abstract: Collision avoidance among convex bodies is a fundamental problem in robotics. Control Barrier Functions (CBFs) provide a practical framework for real-time safety filtering due to their computational efficiency. For general convex bodies, exact separation measures, such as distance or scaling factor, are typically computed through optimization. Existing CBF formulations often obtain the required gradient via differentiable optimization (diffOpt), adding computational overhead. In contrast, we leverage the Gilbert-Johnson-Keerthi (GJK) algorithm to obtain the current witness pair---the pair of points realizing the minimum distance or penetration depth---and formulate a CBF, termed GJK-CBF, whose gradient is constructed directly from the relative rigid-body motion of the witness pair, without resorting to diffOpt. This formulation applies to both 2D and 3D environments across a broad class of convex body pairs, provided that at least one in