发表机构
University of Maryland; Boston University; Nanyang Technological University（马里兰大学; 波士顿大学; 南洋理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出GJK-CBF，利用GJK算法获取见证对并直接构造梯度，无需可微优化，实现SE(3)上凸刚体的高效碰撞避免，并在多机器人交换、狭缝导航及机械臂场景中验证了其无碰撞性和低保守性。
AI 中文摘要
凸体之间的碰撞避免是机器人学中的一个基本问题。控制障碍函数（CBFs）因其计算效率高，为实时安全滤波提供了一个实用的框架。对于一般凸体，精确的分离度量（如距离或缩放因子）通常通过优化计算。现有的CBF公式通常通过可微优化（diffOpt）获得所需的梯度，这增加了计算开销。相比之下，我们利用Gilbert-Johnson-Keerthi（GJK）算法获得当前的见证对——即实现最小距离或穿透深度的点对——并构建一个称为GJK-CBF的CBF，其梯度直接从见证对的相对刚体运动中构造，无需借助diffOpt。该公式适用于2D和3D环境中的广泛凸体对类别，前提是每个一对一交互中至少有一个是严格凸的。所提出的GJK-CBF在各种场景中得到了验证，包括2D和3D中的多机器人位置交换、3D中通过垂直狭缝的导航，以及其在机械臂上的适用性。结果表明，在所有场景中均实现了无碰撞运动，同时减少了由几何近似引入的保守性，尤其是在狭窄环境中。
英文摘要
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 each one-to-one interaction is strictly convex. The proposed GJK-CBF is validated in various scenarios, including multi-robot position swapping in both 2D and 3D, navigation through a vertical slit in 3D, and its applicability to manipulators. The results demonstrate collision-free motion across all scenarios while reducing the conservativeness introduced by geometric approximations, particularly in narrow environments.
Comments8 pages, 4 figures. Demo video: https://youtu.be/eDvscHhGIj0. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Code will be released upon publication
