Constant Bearing Pursuit on Branching Graphs

TL;DR

This paper generalizes cyclic pursuit with constant bearing laws to branching graphs, analyzing stability and equilibria, and enabling flexible agent participation for robust collective robot behaviors.

Contribution

It introduces a generalized pursuit framework on branching graphs, analyzes equilibria and stability, and enhances system robustness by allowing agents to join or leave seamlessly.

Findings

Existence of relative and shape equilibria established.

Necessary stability conditions for 3-agent systems derived.

Framework supports flexible agent participation without disrupting collective motion.

Abstract

Cyclic pursuit frameworks provide an efficient way to create useful global behaviors out of pairwise interactions in a collective of autonomous robots. Earlier work studied cyclic pursuit with a constant bearing (CB) pursuit law, and has demonstrated the existence of a variety of interesting behaviors for the corresponding dynamics. In this work, by attaching multiple branches to a single cycle, we introduce a modified version of this framework which allows us to consider any weakly connected pursuit graph where each node has an outdegree of 1. This provides a further generalization of the cyclic pursuit setting. Then, after showing existence of relative equilibria (rectilinear or circling motion), pure shape equilibria (spiraling motion) and periodic orbits, we also derive necessary conditions for stability of a 3-agent collective. By paving a way for individual agents to join or leave a collective without perturbing the motion of others, our approach leads to improved reliability of the overall system.