Obstacle avoidance for multi-robot navigation with polytopic shapes is challenging. Existing works simplify the system dynamics or consider it as a convex or non-convex optimization problem with positive distance constraints between robots, which limits real-time performance and scalability. Additionally, generating collision-free behavior for polytopic-shaped robots is harder due to implicit and non-differentiable distance functions between polytopes. In this paper, we extend the concept of velocity obstacle (VO) principle for polytopic-shaped robots and propose a novel approach to construct the VO in the function of vertex coordinates and other robot's states. Compared with existing work about obstacle avoidance between polytopic-shaped robots, our approach is much more computationally efficient as the proposed approach for construction of VO between polytopes is optimization-free. Based on VO representation for polytopic shapes, we later propose a navigation approach for distributed multi-robot systems. We validate our proposed VO representation and navigation approach in multiple challenging scenarios including large-scale randomized tests, and our approach outperforms the state of art in many evaluation metrics, including completion rate, deadlock rate, and the average travel distance.

翻译：多面体形状的机器人在多机器人导航中实现避障具有挑战性。现有研究或简化系统动力学，或将其视为包含机器人间正距离约束的凸/非凸优化问题，这限制了实时性与可扩展性。此外，由于多面体间距离函数的隐式与非可微特性，生成多面体形状机器人的无碰撞行为更为困难。本文扩展了速度障碍（VO）原理至多面体形状机器人，提出了一种基于顶点坐标及其他机器人状态构建VO的新方法。相较于现有关于多面体形状机器人间避障的研究，本方法无需优化即可构建多面体间VO，计算效率显著提升。基于多面体形状的VO表示，本文进一步提出了一种分布式多机器人系统导航方法。通过包含大规模随机测试在内的多个挑战性场景验证，所提出的VO表示与导航方法在完成率、死锁率及平均行驶距离等多项评估指标上均优于现有技术。