The Multi-Agent Path Finding (MAPF) problem involves planning collision-free paths for multiple agents in a shared environment. The majority of MAPF solvers rely on the assumption that an agent can arrive at a specific location at a specific timestep. However, real-world execution uncertainties can cause agents to deviate from this assumption, leading to collisions and deadlocks. Prior research solves this problem by having agents follow a Temporal Plan Graph (TPG), enforcing a consistent passing order at every location as defined in the MAPF plan. However, we show that TPGs are overly strict because, in some circumstances, satisfying the passing order requires agents to wait unnecessarily, leading to longer execution time. To overcome this issue, we introduce a new graphical representation called a Bidirectional Temporal Plan Graph (BTPG), which allows switching passing orders during execution to avoid unnecessary waiting time. We design two anytime algorithms for constructing a BTPG: BTPG-na\"ive and BTPG-optimized. Experimental results show that following BTPGs consistently outperforms following TPGs, reducing unnecessary waits by 8-20%.

翻译：多智能体路径规划（MAPF）问题涉及在共享环境中为多个智能体规划无碰撞路径。大多数MAPF求解器依赖于智能体能够在特定时间步到达特定位置的假设。然而，真实世界的执行不确定性可能导致智能体偏离这一假设，从而引发碰撞和死锁。先前研究通过让智能体遵循时间规划图（TPG）来解决该问题，强制执行MAPF计划中定义的每个位置的通行顺序。但本研究发现，TPG过于严格，因为在某些情况下满足通行顺序要求智能体不必要地等待，导致执行时间延长。为克服这一局限，我们提出了一种名为双向时间规划图（BTPG）的新型图表示方法，允许在执行过程中切换通行顺序以避免不必要的等待时间。我们设计了两种用于构建BTPG的随时算法：BTPG-naïve和BTPG-optimized。实验结果表明，遵循BTPG始终优于遵循TPG，可将不必要的等待时间减少8-20%。