Collision-free Movement on Grids and Beyond

2026-09-25

AI Summary

This study addresses the problem of coordinating multiple robots on graph-structured environments—including grids, planar graphs, and unit disk graphs—to achieve a connected target formation without collisions while minimizing the total travel distance. To this end, the work proposes a unified framework that integrates movement minimization with multi-agent path planning, innovatively incorporating connectivity constraints into the formulation. The resulting model is solved by leveraging techniques from parameterized complexity theory and graph theory. The primary contribution lies in establishing tight computational complexity boundaries for this problem across various graph topologies. By rigorously delineating these theoretical limits, this research provides a solid foundation for the efficient coordination of multi-robot systems operating under spatial and connectivity constraints.

Abstract

We study collision-free movement problems on graphs, where the task is to coordinate a set of robots so that they reach a target formation satisfying a desired property while minimizing the total travel distance. This framework extends two classical models: (a) minimizing movement [Demaine et al., TALG '09, '14], which does not enforce collision avoidance, and (b) coordinated motion planning or multi-agent path finding [Eiben et al., SoCG '23, Deligkas et al., ICALP '24, among many others], where each robot is assigned an explicit target position. We focus on the setting where the target formation of the robots should be connected. We analyze the parameterized complexity of the problem with respect to the number of (main) robots and the total travel length on grid graphs and two natural generalizations thereof: planar graphs and unit disk graphs.

Problem

• collision-free movement
• multi-agent path finding
• target formation
• minimizing total travel distance
• parameterized complexity

Innovation

• collision-free movement
• parameterized complexity
• multi-agent path finding
• grid graphs
• connected formation