Distributed Hybrid Feedback for Global Pose Synchronization of Multiple Rigid Body Systems on $SE(3)$

TL;DR

This paper introduces a novel distributed hybrid feedback control method on the Lie group SE(3) for achieving global pose synchronization among multiple rigid bodies, ensuring stability and robustness.

Contribution

It develops a new potential function and hybrid control scheme directly on SE(3), providing global stability guarantees for pose synchronization.

Findings

Achieves global asymptotic stability in pose synchronization

Demonstrates effectiveness through numerical simulations

Introduces a new potential function on SE(3) for control design

Abstract

This paper investigates the problem of pose synchronization for multiple rigid body systems evolving on the matrix Lie group $\SE(3)$. We propose a distributed hybrid feedback control scheme with global asymptotic stability guarantees using relative pose and group velocity measurements. The key idea consists of constructing a new potential function on $\SE(3) \times \mathbb{R}$ with a generalized non-diagonal weighting matrix, and a set of auxiliary scalar variables with continuous-discrete hybrid dynamics. Based on the new potential function and the auxiliary scalar variables, a geometric distributed hybrid feedback designed directly on $\SE(3)$ is proposed to achieve global pose synchronization. Numerical simulation results are presented to illustrate the performance of the proposed distributed hybrid control scheme.