Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Distributed Attitude Estimation for Multi-agent Systems on $SO(3)$

Mouaad Boughellaba, Abdelhamid Tayebi

TL;DR

This work advances distributed attitude estimation for multi-agent systems evolving on $SO(3)$ by first delivering a continuous observer with almost global asymptotic stability and then a hybrid observer that attains global asymptotic stability through a switching mechanism augmented with time-varying edge variables. The hybrid framework provides a systematic construction of a global-attention attitude estimator, accompanied by an explicit design using relative attitude measurements and a structured parameter set guaranteeing stability. The authors extend the attitude estimation to bearing-based distributed pose estimation in 3D, achieving global convergence of poses up to a common translation and orientation. Simulations on a five-agent network validate the effectiveness of both schemes and highlight practical applicability, while also acknowledging the tree-graph assumption as a potential area for future relaxation.

Abstract

We consider the problem of distributed attitude estimation of multi-agent systems, evolving on $SO(3)$, relying on individual angular velocity and relative attitude measurements. The interaction graph topology is assumed to be an undirected tree. First, we propose a continuous nonlinear distributed attitude estimation scheme with almost global asymptotic stability guarantees. Thereafter, we proceed with the \textit{hybridization} of the proposed estimation scheme to derive a new hybrid nonlinear distributed attitude estimation scheme enjoying global asymptotic stabilization of the attitude estimation errors to a common constant orientation. In addition, the proposed hybrid attitude estimation scheme is used to solve the problem of pose estimation of $N$-vehicles navigating in a three-dimensional space, with global asymptotic stability guarantees, where the only available measurements are the local relative bearings and the individual linear velocities. Simulation results are provided to illustrate the effectiveness of the proposed estimation schemes.

Distributed Attitude Estimation for Multi-agent Systems on $SO(3)$

TL;DR

This work advances distributed attitude estimation for multi-agent systems evolving on by first delivering a continuous observer with almost global asymptotic stability and then a hybrid observer that attains global asymptotic stability through a switching mechanism augmented with time-varying edge variables. The hybrid framework provides a systematic construction of a global-attention attitude estimator, accompanied by an explicit design using relative attitude measurements and a structured parameter set guaranteeing stability. The authors extend the attitude estimation to bearing-based distributed pose estimation in 3D, achieving global convergence of poses up to a common translation and orientation. Simulations on a five-agent network validate the effectiveness of both schemes and highlight practical applicability, while also acknowledging the tree-graph assumption as a potential area for future relaxation.

Abstract

We consider the problem of distributed attitude estimation of multi-agent systems, evolving on , relying on individual angular velocity and relative attitude measurements. The interaction graph topology is assumed to be an undirected tree. First, we propose a continuous nonlinear distributed attitude estimation scheme with almost global asymptotic stability guarantees. Thereafter, we proceed with the \textit{hybridization} of the proposed estimation scheme to derive a new hybrid nonlinear distributed attitude estimation scheme enjoying global asymptotic stabilization of the attitude estimation errors to a common constant orientation. In addition, the proposed hybrid attitude estimation scheme is used to solve the problem of pose estimation of -vehicles navigating in a three-dimensional space, with global asymptotic stability guarantees, where the only available measurements are the local relative bearings and the individual linear velocities. Simulation results are provided to illustrate the effectiveness of the proposed estimation schemes.
Paper Structure (15 sections, 7 theorems, 78 equations, 6 figures)

This paper contains 15 sections, 7 theorems, 78 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Graph Theory
  5. Hybrid Systems Framework
  6. Problem Statement
  7. Distributed Attitude Estimation
  8. Continuous Distributed Attitude Estimation
  9. Hybrid Distributed Attitude Estimation
  10. Switching Mechanism Design for Multi-agent Systems
  11. Generic Hybrid Attitude Observer
  12. Explicit Hybrid Distributed Attitude Observer Design Using Relative Attitude Measurements
  13. Application to distributed pose estimation
  14. SIMULATION
  15. CONCLUSIONS

Key Result

Lemma 1

Consider the matrix $\textit{H}(t)$ obtained from the graph $\mathcal{G}$ with an arbitrary orientation of the edges, satisfying Assumption graph_ass. Then, $\forall t\geq 0$, $\textit{H}(t)x=0$ implies $x=0$.

Figures (6)

  • Figure 1: The actual formation, $\mathcal{G}(p)$, in $\mathbb{R}^3$.
  • Figure 2: The interaction graph $\mathcal{G}$: (a) without an orientation (b) with an orientation.
  • Figure 3: The time evolution of the relative attitude error norm, associated with each edge, for the Continuous observer and the Hybrid observer.
  • Figure 4: The time evolution of the hybrid variable $\xi_k$ associated with each edge.
  • Figure 5: The time evolution of the position estimation error norm.
  • ...and 1 more figures

Theorems & Definitions (28)

  • Remark 1
  • Lemma 1
  • proof
  • Remark 2
  • Theorem 1
  • proof
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • ...and 18 more