Robust multirobot coordination using priority encoded homotopic constraints

TL;DR

This paper introduces a formal framework for multirobot coordination using priority-based homotopy classes, providing a control law that ensures safe navigation even under kinodynamic constraints and unexpected events.

Contribution

It formalizes priorities as a binary relation, proves the uniqueness of priority graphs for homotopy classes, and develops a control law for safe, flexible navigation within these classes.

Findings

Priority graphs uniquely encode homotopy classes of solutions.

Robust control law enables safe navigation under kinodynamic constraints.

Deviations from planned trajectories are possible without collisions or re-planning.

Abstract

We study the problem of coordinating multiple robots along fixed geometric paths. Our contribution is threefold. First we formalize the intuitive concept of priorities as a binary relation induced by a feasible coordination solution, without excluding the case of robots following each other on the same geometric path. Then we prove that two paths in the coordination space are continuously deformable into each other if and only if they induce the \emph{same priority graph}, that is, the priority graph uniquely encodes homotopy classes of coordination solutions. Finally, we give a simple control law allowing to safely navigate into homotopy classes \emph{under kinodynamic constraints} even in the presence of unexpected events, such as a sudden robot deceleration without notice. It appears the freedom within homotopy classes allows to much deviate from any pre-planned trajectory without ever colliding nor having to re-plan the assigned priorities.