Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Global Attitude Synchronization for Heterogeneous Multi-agent Systems on SO(3)

Mouaad Boughellaba, Soulaimane Berkane, Abdelhamid Tayebi

TL;DR

This work addresses global attitude synchronization for heterogeneous rigid bodies evolving on $SO(3)$ under a tree-structured interaction graph. It first develops a continuous distributed scheme with almost global asymptotic stability and then introduces two global hybrid schemes: one with angular velocity measurements and one velocity-free that relies on auxiliary dynamics. A generic potential on $SO(3)^M\times\mathbb{R}^M$ is used to design the hybrid controllers, ensuring a unique global attractor and eliminating undesired equilibria; the velocity-free version compensates the lack of velocity information via an auxiliary system. Simulations on a seven-satellite network illustrate faster convergence and robustness of the hybrid controllers, highlighting practical benefits for sensor-bearing and scalable multi-agent platforms. The results advance global synchronization on $SO(3)$ for heterogeneous agents and lay groundwork for extending to time-varying/topology-delayed networks.

Abstract

In this paper, we address the problem of attitude synchronization for a group of rigid body systems evolving on SO(3). The interaction among these systems is modeled through an undirected, connected, and acyclic graph topology. First, we present an almost global continuous distributed attitude synchronization scheme with rigorously proven stability guarantees. Thereafter, we propose two global distributed hybrid attitude synchronization schemes on SO(3). The first scheme is a hybrid control law that leverages angular velocities and relative orientations to achieve global alignment to a common orientation. The second scheme eliminates the dependence on angular velocities by introducing dynamic auxiliary variables, while ensuring global asymptotic attitude synchronization. This velocity-free control scheme relies exclusively on attitude information. The proposed schemes are applicable to heterogeneous multi-agent systems, where agents may have distinct inertia matrices. Simulation results are provided to illustrate the effectiveness of the proposed distributed attitude synchronization schemes.

Global Attitude Synchronization for Heterogeneous Multi-agent Systems on SO(3)

TL;DR

This work addresses global attitude synchronization for heterogeneous rigid bodies evolving on under a tree-structured interaction graph. It first develops a continuous distributed scheme with almost global asymptotic stability and then introduces two global hybrid schemes: one with angular velocity measurements and one velocity-free that relies on auxiliary dynamics. A generic potential on is used to design the hybrid controllers, ensuring a unique global attractor and eliminating undesired equilibria; the velocity-free version compensates the lack of velocity information via an auxiliary system. Simulations on a seven-satellite network illustrate faster convergence and robustness of the hybrid controllers, highlighting practical benefits for sensor-bearing and scalable multi-agent platforms. The results advance global synchronization on for heterogeneous agents and lay groundwork for extending to time-varying/topology-delayed networks.

Abstract

In this paper, we address the problem of attitude synchronization for a group of rigid body systems evolving on SO(3). The interaction among these systems is modeled through an undirected, connected, and acyclic graph topology. First, we present an almost global continuous distributed attitude synchronization scheme with rigorously proven stability guarantees. Thereafter, we propose two global distributed hybrid attitude synchronization schemes on SO(3). The first scheme is a hybrid control law that leverages angular velocities and relative orientations to achieve global alignment to a common orientation. The second scheme eliminates the dependence on angular velocities by introducing dynamic auxiliary variables, while ensuring global asymptotic attitude synchronization. This velocity-free control scheme relies exclusively on attitude information. The proposed schemes are applicable to heterogeneous multi-agent systems, where agents may have distinct inertia matrices. Simulation results are provided to illustrate the effectiveness of the proposed distributed attitude synchronization schemes.
Paper Structure (17 sections, 6 theorems, 74 equations, 8 figures)

This paper contains 17 sections, 6 theorems, 74 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation
  4. Graph Theory
  5. Hybrid Systems Framework
  6. Problem Statement
  7. Distributed Attitude Synchronization on $SO(3)$
  8. Distributed Hybrid Feedback for Global Attitude Synchronization on $SO(3)$
  9. Generic Potential Function on $SO(3)^M\times \mathbb{R}^M$
  10. Distributed Hybrid Feedback for Global Attitude Synchronization on $SO(3)$ with Velocity Measurements
  11. Distributed Hybrid Feedback for Global Attitude Synchronization on $SO(3)$ without Velocity Measurements
  12. SIMULATION
  13. CONCLUSIONS
  14. Proof of Theorem \ref{['theorem_continuous']}
  15. Proof of Lemma \ref{['lem_cp_pf']}
  16. ...and 2 more sections

Key Result

Theorem 1

Let a network of $N$ agents rotate according to the rigid-body rotational dynamics given in R_dynamics_i. Assume that the measurement measurement_model_R is available and the interaction graph $\mathcal{G}$ is an undirected tree. Consider the dynamics R_bar_dynamics_k-w_dynamics_k with control torqu

Figures (8)

  • Figure 1: A network of seven satellites with an interaction graph.
  • Figure 2: A network of seven satellites with an oriented interaction graph.
  • Figure 3: The time evolution of the relative attitude associated with each edge.
  • Figure 4: The time evolution of the angular velocity of each agent.
  • Figure 5: The time evolution of the auxiliary variable $\xi_k$ associated with each edge considering Hybrid Controller.
  • ...and 3 more figures

Theorems & Definitions (21)

  • Theorem 1
  • proof
  • Remark 1
  • Remark 2
  • Proposition 1
  • proof
  • Remark 3
  • Remark 4
  • Lemma 1
  • proof
  • ...and 11 more