椭球体对象实时可行无碰撞运动规划
摘要
碎片化轨迹的在线碰撞规划是机器人和自动驾驶应用中的基础任务。本文重新审视了椭球体对象之间的碰撞规避问题，采用可微分约束方法。若两个椭球体不重叠，当且仅当它们中心点之间向量的终点不位于它们的Minkowski和的内部。我们采用参数化的Minkowski和近似方法，该方法可在任意给定方向上变得紧密。 resulting collision avoidance constraint is included in an optimal control problem (OCP) and evaluated in comparison to the separating-hyperplane approach. Not only do we observe that the Minkowski-sum formulation is computationally more efficient in our experiments, but also that using pre-determined over-approximation parameters based on warm-start trajectories leads to a very limited increase in suboptimality. This gives rise to a novel real-time scheme for collision-free motion planning with model predictive control (MPC). Both the real-time feasibility and the effectiveness of the constraint formulation are demonstrated in challenging real-world experiments.
引用
@article{arxiv.2409.12007,
title = {Real-Time-Feasible Collision-Free Motion Planning For Ellipsoidal Objects},
author = {Yunfan Gao and Florian Messerer and Niels van Duijkeren and Boris Houska and Moritz Diehl},
journal= {arXiv preprint arXiv:2409.12007},
year = {2025}
}
备注
This version corrects a typographical error in the proof of Lemma 3. Although the original proof contained a mistake, the statement of the lemma remains valid and unchanged