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A Conflict-Aware Optimal Goal Assignment Algorithm for Multi-Robot Systems

Aakash, Indranil Saha

TL;DR

This work proposes an efficient conflict-guided method to compute the next best assignment and introduces two more optimizations to the algorithm -- first for avoiding the unconstrained path computations between robot-goal pairs wherever possible, and the second to prevent duplicate constrained path computations for multiple robot-goal pairs.

Abstract

The fundamental goal assignment problem for a multi-robot application aims to assign a unique goal to each robot while ensuring collision-free paths, minimizing the total movement cost. A plausible algorithmic solution to this NP-hard problem involves an iterative process that integrates a task planner to compute the goal assignment while ignoring the collision possibilities among the robots and a multi-agent path-finding algorithm to find the collision-free trajectories for a given assignment. This procedure involves a method for computing the next best assignment given the current best assignment. A naive way of computing the next best assignment, as done in the state-of-the-art solutions, becomes a roadblock to achieving scalability in solving the overall problem. To obviate this bottleneck, we propose an efficient conflict-guided method to compute the next best assignment. Additionally, we introduce two more optimizations to the algorithm -- first for avoiding the unconstrained path computations between robot-goal pairs wherever possible, and the second to prevent duplicate constrained path computations for multiple robot-goal pairs. We extensively evaluate our algorithm for up to a hundred robots on several benchmark workspaces. The results demonstrate that the proposed algorithm achieves nearly an order of magnitude speedup over the state-of-the-art algorithm, showcasing its efficacy in real-world scenarios.

A Conflict-Aware Optimal Goal Assignment Algorithm for Multi-Robot Systems

TL;DR

This work proposes an efficient conflict-guided method to compute the next best assignment and introduces two more optimizations to the algorithm -- first for avoiding the unconstrained path computations between robot-goal pairs wherever possible, and the second to prevent duplicate constrained path computations for multiple robot-goal pairs.

Abstract

The fundamental goal assignment problem for a multi-robot application aims to assign a unique goal to each robot while ensuring collision-free paths, minimizing the total movement cost. A plausible algorithmic solution to this NP-hard problem involves an iterative process that integrates a task planner to compute the goal assignment while ignoring the collision possibilities among the robots and a multi-agent path-finding algorithm to find the collision-free trajectories for a given assignment. This procedure involves a method for computing the next best assignment given the current best assignment. A naive way of computing the next best assignment, as done in the state-of-the-art solutions, becomes a roadblock to achieving scalability in solving the overall problem. To obviate this bottleneck, we propose an efficient conflict-guided method to compute the next best assignment. Additionally, we introduce two more optimizations to the algorithm -- first for avoiding the unconstrained path computations between robot-goal pairs wherever possible, and the second to prevent duplicate constrained path computations for multiple robot-goal pairs. We extensively evaluate our algorithm for up to a hundred robots on several benchmark workspaces. The results demonstrate that the proposed algorithm achieves nearly an order of magnitude speedup over the state-of-the-art algorithm, showcasing its efficacy in real-world scenarios.
Paper Structure (22 sections, 4 theorems, 5 figures, 1 algorithm)

This paper contains 22 sections, 4 theorems, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem
  3. Preliminaries
  4. Problem Definition
  5. Example
  6. Algorithm
  7. Algorithm Description
  8. Conflict-Aware Assignment Computation.
  9. Heuristic Distance-Based Assignment Computation.
  10. Path Memoization.
  11. Example
  12. Theoretical Properties
  13. Correctness.
  14. Time complexity.
  15. Evaluation
  16. ...and 7 more sections

Key Result

Lemma 1

In a multi-robot application, if an assignment of robots to goals contains a set of conflicting robot-goal pairs (or edges) that escalates the assignment cost, then any other assignment containing the same set of conflicting robot-goal pairs will experience at least an equal escalation in its cost.

Figures (5)

  • Figure 1: An example problem
  • Figure 2: Applying Algorithm \ref{['algo1']} on Problem in Figure \ref{['fig:example-prob']}(\ref{['fig:ws']})
  • Figure 3: Computation Time Comparison with Baseline for Various Workspaces (X-axis: Runtime(s), Y-axis: Runtime(s)) (Leftmost four plots: $R = 50$, Rightmost four plots: $R = 100$)
  • Figure 4: Ablation Study for Various Workspaces (X-axis: Approaches, Y-axis: Runtime(s)) (Left: $R = 50$, Right: $R = 100$)
  • Figure 5: Scalability Comparison between Baseline ($\mathtt{h0m0p0}$) and Our Approach ($\mathtt{h1m1p1}$) (a) $OD = 20\%$, $WS: 200\times200$ (b) $R = 50$, $WS: 100\times100$ (c) $R = 50$, $OD: 20\%$

Theorems & Definitions (10)

  • Remark 1
  • Remark 2
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 1
  • proof
  • Theorem 2
  • proof