A Real-Time Rescheduling Algorithm for Multi-robot Plan Execution

TL;DR

Switchable-Edge Search (SES), an A*-style algorithm designed to find optimal passing orders, is proposed and it is proved the optimality of SES and its efficiency is evaluated via simulations.

Abstract

One area of research in multi-agent path finding is to determine how replanning can be efficiently achieved in the case of agents being delayed during execution. One option is to reschedule the passing order of agents, i.e., the sequence in which agents visit the same location. In response, we propose Switchable-Edge Search (SES), an A*-style algorithm designed to find optimal passing orders. We prove the optimality of SES and evaluate its efficiency via simulations. The best variant of SES takes less than 1 second for small- and medium-sized problems and runs up to 4 times faster than baselines for large-sized problems.

Figures (6)

• Figure 1: Example of converting a MAPF solution to a TPG. The solid arrows in the TPG represent Type 1 edges, and the dashed arrow represents a Type 2 edge.
• Figure 2: Example of reversing an edge in a TPG.
• Figure 3: Example of running ESES on the top-left STPG. The circled numbers denote the order of generating these STPGs.
• Figure 4: Runtime of ESES, GSES, and k-robust CBS. The dashed lines represent the mean of runtime, and the shaded areas denote the 0.4 to 0.6 quantile range. For trials that exceed the $90$-second time limit, we count it as $90$ seconds.
• Figure 5: Numbers of nodes explored and pruned by ESES and GSES on the warehouse map. Dashed lines represent the mean values. Shaded area between two lines for the same algorithm indicates the portion of pruned nodes.

Theorems & Definitions (43)

• Definition 1: MAPF
• Remark 1
• Definition 2: MAPF Solution
• Remark 2
• Definition 3: TPG
• Example 1
• Proposition 1: Cost
• Proposition 2: Collision-Free
• Definition 4: Deadlock
• Lemma 3: Deadlock $\iff$ Cycle