Shortest Path Set Induced Vertex Ordering and its Application to Distributed Distance Optimal Multi-agent Formation Path Planning

TL;DR

This paper introduces a vertex ordering method that improves distributed scheduling for multi-agent formation path planning, ensuring optimal convergence time on various graph types.

Contribution

It reveals a fundamental vertex ordering structure that enables faster, distributed scheduling algorithms for multi-agent formation planning, extending to complex graph types.

Findings

Distributed scheduling matches centralized convergence time.

Vertex ordering enables faster, scalable algorithms.

Method applies to graphs with non-uniform capacities and edge lengths.

Abstract

For the task of moving a group of indistinguishable agents on a connected graph with unit edge lengths into an arbitrary goal formation, it was previously shown that distance optimal paths can be scheduled to complete with a tight convergence time guarantee, using a fully centralized algorithm. In this study, we show that the problem formulation in fact induces a more fundamental ordering of the vertices on the underlying graph network, which directly leads to a more intuitive scheduling algorithm that assures the same convergence time and runs faster. More importantly, this structure enables a distributed scheduling algorithm once individual paths are assigned to the agents, which was not possible before. The vertex ordering also readily extends to more general graphs - those with non-unit capacities and edge lengths - for which we again guarantee the convergence time until the desired formation is achieved.