Stabilization of Three-Dimensional Collective Motion

TL;DR

This paper introduces a control methodology for stabilizing collective formations of identical particles in 3D space, leveraging Lie group structures and consensus algorithms to handle various communication topologies.

Contribution

It presents a novel stabilization approach for 3D collective motion using Lie group theory and consensus estimators, accommodating dynamic communication networks.

Findings

Stabilization of parallel, circular, and helical formations achieved.

Control laws derived for all-to-all communication scenarios.

Extended to networks with unidirectional and time-varying links.

Abstract

This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the stabilization problem is reduced to a consensus problem on the Lie algebra. The resulting equilibria correspond to parallel, circular and helical formations. We first derive the stabilizing control laws in the presence of all-to-all communication. Providing each agent with a consensus estimator, we then extend the results to a general setting that allows for unidirectional and time-varying communication topologies.