GJK-CBF: SE(3)上の凸剛体衝突回避のための制御バリア関数
GJK-CBF: Control Barrier Functions for Convex Rigid Body Collision Avoidance on SE(3)
GJKアルゴリズムで凸剛体間の最近傍点対を求め、その相対運動から直接勾配を構成する制御バリア関数を提案し、微分可能最適化を不要にした。2D/3Dのマルチロボット交換や狭所通過、マニピュレータで衝突回避を実証した。
詳しい要約
1. どんなもの？
2. 先行研究と比べてどこがすごい？
3. 技術・手法の肝は？
4. どうやって有効だと検証した？
5. 議論はある？
6. 次に読むべき論文は？
※ AIが要旨から生成した要約です。正確性は原文をご確認ください。
著者: Yi-Hsuan Chen, Shuo Liu, Wei Xiao, Michael Otte, Calin Belta
分類: cs.RO, eess.SY
原文アブストラクト
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.
