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Planning over MAPF Agent Dependencies via Multi-Dependency PIBT

Zixiang Jiang, Yulun Zhang, Rishi Veerapaneni, Jiaoyang Li

Abstract

Modern Multi-Agent Path Finding (MAPF) algorithms must plan for hundreds to thousands of agents in congested environments within a second, requiring highly efficient algorithms. Priority Inheritance with Backtracking (PIBT) is a popular algorithm capable of effectively planning in such situations. However, PIBT is constrained by its rule-based planning procedure and lacks generality because it restricts its search to paths that conflict with at most one other agent. This limitation also applies to Enhanced PIBT (EPIBT), a recent extension of PIBT. In this paper, we describe a new perspective on solving MAPF by planning over agent dependencies. Taking inspiration from PIBT's priority inheritance logic, we define the concept of agent dependencies and propose Multi-Dependency PIBT (MD-PIBT) that searches over agent dependencies. MD-PIBT is a general framework where specific parameterizations can reproduce PIBT and EPIBT. At the same time, alternative configurations yield novel planning strategies that are not expressible by PIBT or EPIBT. Our experiments demonstrate that MD-PIBT effectively plans for as many as 10,000 homogeneous agents under various kinodynamic constraints, including pebble motion, rotation motion, and differential drive robots with speed and acceleration limits. We perform thorough evaluations on different variants of MAPF and find that MD-PIBT is particularly effective in MAPF with large agents.

Planning over MAPF Agent Dependencies via Multi-Dependency PIBT

Abstract

Modern Multi-Agent Path Finding (MAPF) algorithms must plan for hundreds to thousands of agents in congested environments within a second, requiring highly efficient algorithms. Priority Inheritance with Backtracking (PIBT) is a popular algorithm capable of effectively planning in such situations. However, PIBT is constrained by its rule-based planning procedure and lacks generality because it restricts its search to paths that conflict with at most one other agent. This limitation also applies to Enhanced PIBT (EPIBT), a recent extension of PIBT. In this paper, we describe a new perspective on solving MAPF by planning over agent dependencies. Taking inspiration from PIBT's priority inheritance logic, we define the concept of agent dependencies and propose Multi-Dependency PIBT (MD-PIBT) that searches over agent dependencies. MD-PIBT is a general framework where specific parameterizations can reproduce PIBT and EPIBT. At the same time, alternative configurations yield novel planning strategies that are not expressible by PIBT or EPIBT. Our experiments demonstrate that MD-PIBT effectively plans for as many as 10,000 homogeneous agents under various kinodynamic constraints, including pebble motion, rotation motion, and differential drive robots with speed and acceleration limits. We perform thorough evaluations on different variants of MAPF and find that MD-PIBT is particularly effective in MAPF with large agents.
Paper Structure (33 sections, 1 theorem, 13 figures, 5 tables, 5 algorithms)

This paper contains 33 sections, 1 theorem, 13 figures, 5 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Multi-Agent Path Finding
  4. MAPF Algorithms
  5. PIBT and Its Variants
  6. Agent Dependency Perspective of PIBT
  7. Multi-Dependence PIBT
  8. Overview
  9. Accepting the Tentative Path
  10. Add Hard Dependencies
  11. Add Soft Dependencies
  12. Backtracking
  13. Falling to Safe Paths
  14. Attempting to Replan
  15. MD-PIBT Hyperparameters
  16. ...and 18 more sections

Key Result

Theorem 1

MD-PIBT returns a collision-free solution.

Figures (13)

  • Figure 1: Multi-Dependence PIBT (MD-PIBT) builds and searches over an Agent Dependency Graph. Left shows an scenario for planning with a window size of 3, with initial path preferences drawn. Assume all agent's safe paths are waiting at their current location. (1) Let MD-PIBT start planning with A. A's path conflicts with B, D, and E's safe path, causing A to have hard dependencies on them (Def. \ref{['def:hard-agent-dependency']}, they must find non-safe paths for A's path to be valid). Thus, $B, D, E$ need to be planned next. Given multiple agents, we plan in alphabetical order. (2) When B plans, B's path collides with C and A's safe path. Since A is already planned, we record a soft dependency between B and A. (3-6) This logic continues until planning F. (7) F fails to find a collision-free path. When this occurs, F requires a parent (in this case C) to replan. The replan request unplans C which includes removing downstream dependencies and converting soft dependencies to C to hard dependencies. (8) Suppose that C replans by moving down, which does not intersect with F's safe path. Then F is not included in the AgDG. (9) After planning all agents in the AgDG, we can move on to plan other agents not in the AgDG (not depicted).
  • Figure 2: Success rate and runtime for different numbers of agents for one-shot MAPF with PM agents.
  • Figure 3: Success rate and runtime for different numbers of agents for one-shot MAPF with PMLA agents.
  • Figure 4: Distribution of the number of agent dependencies generated per agent per successful planning attempt, under different agent densities, with $w = 3$. $S$ and $L$ refers to the number of small and large agents, respectively.
  • Figure 5: Throughput and runtime with different numbers of agents for LMAPF with PM agents.
  • ...and 8 more figures

Theorems & Definitions (6)

  • Definition 1: Agent Dependencies
  • Definition 2: Hard Dependencies
  • Definition 3: Soft Dependencies
  • Definition 4: Agent Dependency Graph (AgDG)
  • Theorem 1
  • proof