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Multi-Agent Motion Planning For Differential Drive Robots Through Stationary State Search

Jingtian Yan, Jiaoyang Li

TL;DR

The paper tackles multi-agent motion planning for differential-drive robots by integrating kinodynamic constraints into a scalable framework. MASS combines a MAPF-based Level-1 planner, Stationary Safe Interval Path Planning (SSIPP) at Level 2, and speed-profile optimization at Level 3, augmented by Partial Stationary Expansion for scalability and an adaptive window for lifelong planning. It demonstrates substantial gains in throughput and solution quality on standard benchmarks and a warehouse simulator, outperforming post-processed MAPF and other baselines by up to 400%. The work delivers a practical, kinodynamics-aware MAMP solution for large teams of differential-drive robots with applicability to traffic, airports, and warehousing.

Abstract

Multi-Agent Motion Planning (MAMP) finds various applications in fields such as traffic management, airport operations, and warehouse automation. In many of these environments, differential drive robots are commonly used. These robots have a kinodynamic model that allows only in-place rotation and movement along their current orientation, subject to speed and acceleration limits. However, existing Multi-Agent Path Finding (MAPF)-based methods often use simplified models for robot kinodynamics, which limits their practicality and realism. In this paper, we introduce a three-level framework called MASS to address these challenges. MASS combines MAPF-based methods with our proposed stationary state search planner to generate high-quality kinodynamically-feasible plans. We further extend MASS using an adaptive window mechanism to address the lifelong MAMP problem. Empirically, we tested our methods on the single-shot grid map domain and the lifelong warehouse domain. Our method shows up to 400% improvements in terms of throughput compared to existing methods.

Multi-Agent Motion Planning For Differential Drive Robots Through Stationary State Search

TL;DR

The paper tackles multi-agent motion planning for differential-drive robots by integrating kinodynamic constraints into a scalable framework. MASS combines a MAPF-based Level-1 planner, Stationary Safe Interval Path Planning (SSIPP) at Level 2, and speed-profile optimization at Level 3, augmented by Partial Stationary Expansion for scalability and an adaptive window for lifelong planning. It demonstrates substantial gains in throughput and solution quality on standard benchmarks and a warehouse simulator, outperforming post-processed MAPF and other baselines by up to 400%. The work delivers a practical, kinodynamics-aware MAMP solution for large teams of differential-drive robots with applicability to traffic, airports, and warehousing.

Abstract

Multi-Agent Motion Planning (MAMP) finds various applications in fields such as traffic management, airport operations, and warehouse automation. In many of these environments, differential drive robots are commonly used. These robots have a kinodynamic model that allows only in-place rotation and movement along their current orientation, subject to speed and acceleration limits. However, existing Multi-Agent Path Finding (MAPF)-based methods often use simplified models for robot kinodynamics, which limits their practicality and realism. In this paper, we introduce a three-level framework called MASS to address these challenges. MASS combines MAPF-based methods with our proposed stationary state search planner to generate high-quality kinodynamically-feasible plans. We further extend MASS using an adaptive window mechanism to address the lifelong MAMP problem. Empirically, we tested our methods on the single-shot grid map domain and the lifelong warehouse domain. Our method shows up to 400% improvements in terms of throughput compared to existing methods.

Paper Structure

This paper contains 31 sections, 3 theorems, 5 equations, 7 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. MAPF Algorithms
  4. MAMP Algorithms
  5. Problem Formulation
  6. Lifelong MAMP$_{D}$
  7. MASS
  8. System Overview
  9. Stationary SIPP (SSIPP)
  10. SSIPP Node
  11. Main Algorithm
  12. Stationary Node Expansion
  13. Duplicate Detection
  14. Partial Stationary Expansion (PE)
  15. PE Node
  16. ...and 16 more sections

Key Result

Theorem 1

SSIPP is complete and returns the optimal solution if one exists when Level 3 is complete and optimal. Please refer to the Appendix for detailed proof.

Figures (7)

  • Figure 1: Speed profile of agent A (blue line: linear velocity, red line: angular velocity) generated by (a) MAPF, (b) MAPF+ADG, (c) SIPP-IP, (d) PSB, and (e) MASS. Agent A first moves upward (ACT1) while adjusting its speed to avoid collisions with agent B, performs an in-place rotation (ACT2), and then moves to the right (ACT3).
  • Figure 2: System overview. In (b), the green strips are safe intervals, the dark green strips are stationary safe intervals, and the gray boxes are temporal obstacles given by Level 1.
  • Figure 3: Illustration of the safe interval search process.
  • Figure 4: Limitation of directly applying RHCR to MASS. Solid circles are the current locations of agents and dashed circles are the expected start location for the next episode.
  • Figure 5: Success rate and average runtime across all maps. The success rate is the ratio of solved instances to all instances.
  • ...and 2 more figures

Theorems & Definitions (8)

  • Definition 1
  • Definition 2
  • Theorem 1: Completeness and optimality of SSIPP
  • Theorem 2: Completeness and optimality of SSIPP with PE
  • Lemma 1
  • proof
  • proof
  • proof