Bidirectional Temporal Plan Graph: Enabling Switchable Passing Orders for More Efficient Multi-Agent Path Finding Plan Execution

TL;DR

A new graphical representation called a Bidirectional Temporal Plan Graph (BTPG), which allows switching passing orders during execution to avoid unnecessary waiting time, and two anytime algorithms for constructing a BTPG are designed: BTPG-naïve and BTPG-optimized.

Abstract

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-naïve and BTPG-optimized. Experimental results show that following BTPGs consistently outperforms following TPGs, reducing unnecessary waits by 8-20%.

Figures (14)

• Figure 1: Motivating examples. In Scenario 1 (2), the MAPF plan requries the agents to follow the arrows with the green agent passing through location F (E) before the blue agent.
• Figure 2: TPG for the scenario where 3 agents rotate in a cycle simultaneously.
• Figure 3: BTPG for the example depicted in \ref{['motivating2']}.
• Figure 4: In our 3,900 simulations, BTPG never performed worse than TPG. Thus ideally we could prove that BTPGs are strictly superior to TPGs. However, here we show a hand-crafted adversarial example where a BTPG leads to longer execution time than a TPG under a specific set of delays.
• Figure 5: Two cases of grouping: The left case is when one agent follows another agent; the right one is when two agents move along the same path in opposite directions. Red arrows depict the reversed edges of edge $(C,B)$.

Theorems & Definitions (12)

• Definition 1: TPG
• Definition 2: Rotation Cycle
• Definition 3: Bidirectional pair
• Definition 4: BTPG
• Lemma 1
• proof
• Lemma 2
• proof
• Corollary 1
• proof