Online collision-free trajectory generation within a shared workspace is fundamental for most multi-robot applications. However, many widely-used methods based on model predictive control (MPC) lack theoretical guarantees on the feasibility of underlying optimization. Furthermore, when applied in a distributed manner without a central coordinator, deadlocks often occur where several robots block each other indefinitely. Whereas heuristic methods such as introducing random perturbations exist, no profound analyses are given to validate these measures. Towards this end, we propose a systematic method called infinite-horizon model predictive control with deadlock resolution. The MPC is formulated as a convex optimization over the proposed modified buffered Voronoi with warning band. Based on this formulation, the condition of deadlocks is formally analyzed and proven to be analogous to a force equilibrium. A detection-resolution scheme is proposed, which can effectively detect deadlocks online before they even happen. Once detected, it utilizes an adaptive resolution scheme to resolve deadlocks, under which no stable deadlocks can exist under minor conditions. In addition, the proposed planning algorithm ensures recursive feasibility of the underlying optimization at each time step under both input and model constraints, is concurrent for all robots and requires only local communication. Comprehensive simulation and experiment studies are conducted over large-scale multi-robot systems. Significant improvements on success rate are reported, in comparison with other state-of-the-art methods and especially in crowded and high-speed scenarios.

翻译：共享工作空间内的在线无碰撞轨迹生成是大多数多机器人应用的基础。然而，许多广泛使用的基于模型预测控制（MPC）的方法缺乏对底层优化可行性的理论保障。此外，在无中央协调器的分布式应用中，常出现多台机器人相互无限阻塞的死锁现象。尽管存在如引入随机扰动等启发式方法，但缺乏对这些措施有效性进行深入分析的依据。为此，我们提出一种系统性方法——具有死锁解决功能的无限时域模型预测控制。该MPC通过所提出的改进型带警告缓冲Voronoi图被建模为凸优化问题。基于此公式化表述，对死锁条件进行了形式化分析，并证明其与力平衡的类比关系。提出一种检测-解决机制，可在死锁实际发生前进行在线有效检测。一旦检测到死锁，该机制采用自适应解决策略，在微小条件下即可确保无稳定死锁存在。此外，所提出的规划算法在输入约束和模型约束下能保证每个时间步底层优化的递归可行性，对所有机器人并行执行，且仅需局部通信。针对大规模多机器人系统进行了全面的仿真与实验研究。与其他先进方法相比，特别是在拥挤和高速场景下，成功率得到显著提升。