Anytime Single-Step MAPF Planning with Anytime PIBT

TL;DR

The paper tackles rapid, collision-free single-step MAPF planning under time budgets by enhancing PIBT with an anytime DFS approach. Anytime PIBT preserves the initial PIBT solution and then iteratively improves the single-step cost using pruning and disjoint agent groups (DJAGs), with theoretical convergence to the optimal single-step solution when given sufficient time. The authors prove convergence properties and demonstrate substantial per-timestep improvements in single-step costs for large agent sets, though improvements in full-horizon costs are limited when integrated with LaCAM/LaCAM*. The grouping mechanism and dynamic regrouping are central to scalability and optimality guarantees, suggesting promising directions for incorporating group costs and congestion-aware heuristics in future MAPF work.

Abstract

PIBT is a popular Multi-Agent Path Finding (MAPF) method at the core of many state-of-the-art MAPF methods including LaCAM, CS-PIBT, and WPPL. The main utility of PIBT is that it is a very fast and effective single-step MAPF solver and can return a collision-free single-step solution for hundreds of agents in less than a millisecond. However, the main drawback of PIBT is that it is extremely greedy in respect to its priorities and thus leads to poor solution quality. Additionally, PIBT cannot use all the planning time that might be available to it and returns the first solution it finds. We thus develop Anytime PIBT, which quickly finds a one-step solution identically to PIBT but then continuously improves the solution in an anytime manner. We prove that Anytime PIBT converges to the optimal solution given sufficient time. We experimentally validate that Anytime PIBT can rapidly improve single-step solution quality within milliseconds and even find the optimal single-step action. However, we interestingly find that improving the single-step solution quality does not have a significant effect on full-horizon solution costs.

Figures (4)

• Figure 1: The left example shows six agents with preferred actions denoted in arrows. The orange agent with higher priority would push back the blue agents, when an optimal single-step plan would have the orange agent move back instead. Anytime PIBT first detects initial disjoint agent groups through an initial modified PIBT call. Then Anytime PIBT solves each group by recursing through possible actions and agents in PIBT's order. It stores encountered better solutions and prunes intermediate solutions based on the accumulated penalty.
• Figure 2: We visualize the per timestep normalized f-values for 500 agents on map den520d. The normalized f-value is the solution f-value minus the lower-bound f-value (e.g. sum of each agent's best action). At every timestep, we plot the initial PIBT solution value (blue) and the solution after running Anytime PIBT for 1 second (orange).
• Figure 3: We run Anytime PIBT and store the f-value improvements compared to PIBT's initial solution at different timeouts. Deadlines are in additional milliseconds to the initial PIBT call (e.g., deadline of 0 is identical to PIBT).
• Figure 4: Evaluating PIBT vs Anytime PIBT

Theorems & Definitions (5)

• Definition 1: Disjoint Agent Groups
• Lemma 1
• proof
• Theorem 1
• proof