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

Fengyu Lin, Miaomiao Wang, Housheng Su, Abdelhamid Tayebi

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.

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

Abstract

This paper investigates the problem of pose synchronization for multiple rigid body systems evolving on the matrix Lie group . 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 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 is proposed to achieve global pose synchronization. Numerical simulation results are presented to illustrate the performance of the proposed distributed hybrid control scheme.
Paper Structure (13 sections, 49 equations, 2 figures)

This paper contains 13 sections, 49 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Special Euclidean Group $\operatorname{SE}(3)$
  5. Graph Theory
  6. Problem Statement
  7. Potential function design on $(\operatorname{SE}(3) \times \mathbb{R})^M$
  8. Potential Function on $\operatorname{SE}(3)$ and $\operatorname{SE}(3)\times \mathbb{R}$
  9. Generic Potential Function on $(\operatorname{SE}(3)\times \mathbb{R})^M$
  10. Hybrid Pose Synchronization Scheme
  11. SIMULATION
  12. Conclusion
  13. Proof of Lemma \ref{['lem:parameters']}

Figures (2)

  • Figure 1: The topology graph $\mathcal{G}$: (a) undirected; (b) undirected graph with an arbitrary orientation.
  • Figure 2: Simulation results for the distributed hybrid feedback \ref{['ex_controller']}.