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Attitude Synchronization for Multi-Agent Systems on SO(3) Using Vector Measurements

Mouaad Boughellaba, Soulaimane Berkane, Abdelhamid Tayebi

TL;DR

This work addresses leaderless attitude synchronization for a network of rigid bodies on $SO(3)$ using only local inertial vector measurements. It develops two distributed schemes, one at the kinematic level and one at the dynamic level, under an undirected acyclic connected graph, and proves almost global asymptotic stability for both. The kinematic scheme relies on a vector-measurement–based feedback law, while the dynamic scheme augments it with angular-velocity dynamics and damping to achieve either a constant attitude or a synchronized constant-velocity motion. The results are supported by Lyapunov-based stability proofs and validated by simulations on an eight-satellite network, highlighting robustness to partial state exchange. The findings offer strong stability guarantees in a distributed setting and motivate future hybrid approaches to overcome global topological limitations on $SO(3)$.

Abstract

In this paper, we address the problem of leaderless attitude synchronization for a group of rigid body systems evolving on SO(3), relying on local measurements of some inertial (unit-length) vectors. The interaction graph among agents is assumed to be undirected, acyclic, and connected. We first present a distributed attitude synchronization scheme designed at the kinematic level of SO(3), followed by an extended scheme designed at the dynamic level. Both schemes are supported by a rigorous stability analysis, which establishes their almost global asymptotic stability properties. Finally, numerical simulations demonstrate the effectiveness of both distributed attitude synchronization schemes.

Attitude Synchronization for Multi-Agent Systems on SO(3) Using Vector Measurements

TL;DR

This work addresses leaderless attitude synchronization for a network of rigid bodies on using only local inertial vector measurements. It develops two distributed schemes, one at the kinematic level and one at the dynamic level, under an undirected acyclic connected graph, and proves almost global asymptotic stability for both. The kinematic scheme relies on a vector-measurement–based feedback law, while the dynamic scheme augments it with angular-velocity dynamics and damping to achieve either a constant attitude or a synchronized constant-velocity motion. The results are supported by Lyapunov-based stability proofs and validated by simulations on an eight-satellite network, highlighting robustness to partial state exchange. The findings offer strong stability guarantees in a distributed setting and motivate future hybrid approaches to overcome global topological limitations on .

Abstract

In this paper, we address the problem of leaderless attitude synchronization for a group of rigid body systems evolving on SO(3), relying on local measurements of some inertial (unit-length) vectors. The interaction graph among agents is assumed to be undirected, acyclic, and connected. We first present a distributed attitude synchronization scheme designed at the kinematic level of SO(3), followed by an extended scheme designed at the dynamic level. Both schemes are supported by a rigorous stability analysis, which establishes their almost global asymptotic stability properties. Finally, numerical simulations demonstrate the effectiveness of both distributed attitude synchronization schemes.

Paper Structure

This paper contains 11 sections, 2 theorems, 37 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Graph Theory
  5. Problem Statement
  6. Distributed Attitude Synchronization at the kinematic level
  7. Distributed Attitude Synchronization at the dynamic level
  8. SIMULATION
  9. CONCLUSIONS
  10. Proof of Theorem \ref{['theorem_1']}
  11. Proof of Theorem \ref{['theorem_2']}

Key Result

Theorem 1

Let a network of $N$ agents rotate according to the kinematics given in R_dynamics_i. Assume that the measurement vector_measurement is available and the interaction graph $\mathcal{G}$ is an undirected tree. Consider the dynamics R_bar_dynamics_k with feedback control fc_vector_meas. Then, the foll

Figures (4)

  • Figure 1: Interaction graph for a network of eight satellites.
  • Figure 2: Time evolution of the attitudes under the control \ref{['fc_vector_meas']}.
  • Figure 3: Time evolution of the attitudes and angular velocities under the control \ref{['torque_i']}, with $k_\omega=1$ and $\bar{k}_\omega =1$.
  • Figure 4: Time evolution of the attitudes and angular velocities under the control \ref{['torque_i']}, with $k_\omega = 0$ and $\bar{k}_\omega=1$. The satellites converge to a common time-varying attitude and a constant angular velocity.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof