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Distributed Circumnavigation Using Bearing Based Control with Limited Target Information

Kushal Pratap Singh, Manvi Bengani, Darshit Mittal, Twinkle Tripathy

TL;DR

This work addresses circumnavigation of a stationary target by a heterogeneous team of unicycle robots under limited target information. It introduces a bearing-based distributed guidance law for followers and a CC-trajectory-based strategy for leaders, proving global asymptotic stability for the entire group. The stability proof leverages Zubov's theorem to certify convergence and its region of attraction, with information propagation along the communication graph guaranteeing coordinated circumnavigation. The approach is validated with simulations and hardware experiments on TurtleBots using an OptiTrack system, demonstrating robust convergence to concentric circular formations under realistic sensing and actuation constraints.

Abstract

In this paper, we address the problem of circumnavigation of a stationary target by a heterogeneous group comprising of $\textbf{n}$ autonomous agents, having unicycle kinematics. The agents are assumed to have constant linear speeds, we control only the angular speeds. Assuming limited sensing capabilities of the agents, in the proposed framework, only a subset of agents, termed as \textit{leaders}, know the target location. The rest, termed as \textit{followers}, do not. We propose a distributed guidance law which drives all the agents towards the desired objective; global asymptotic stability (GAS) is ensured by using Zubov's theorem. The efficacy of the approach is demonstrated through both numerical simulations and hardware experiments on the TurtleBots utilising OptiTrack motion capture system.

Distributed Circumnavigation Using Bearing Based Control with Limited Target Information

TL;DR

This work addresses circumnavigation of a stationary target by a heterogeneous team of unicycle robots under limited target information. It introduces a bearing-based distributed guidance law for followers and a CC-trajectory-based strategy for leaders, proving global asymptotic stability for the entire group. The stability proof leverages Zubov's theorem to certify convergence and its region of attraction, with information propagation along the communication graph guaranteeing coordinated circumnavigation. The approach is validated with simulations and hardware experiments on TurtleBots using an OptiTrack system, demonstrating robust convergence to concentric circular formations under realistic sensing and actuation constraints.

Abstract

In this paper, we address the problem of circumnavigation of a stationary target by a heterogeneous group comprising of autonomous agents, having unicycle kinematics. The agents are assumed to have constant linear speeds, we control only the angular speeds. Assuming limited sensing capabilities of the agents, in the proposed framework, only a subset of agents, termed as \textit{leaders}, know the target location. The rest, termed as \textit{followers}, do not. We propose a distributed guidance law which drives all the agents towards the desired objective; global asymptotic stability (GAS) is ensured by using Zubov's theorem. The efficacy of the approach is demonstrated through both numerical simulations and hardware experiments on the TurtleBots utilising OptiTrack motion capture system.
Paper Structure (9 sections, 4 theorems, 17 equations, 7 figures, 1 table)

This paper contains 9 sections, 4 theorems, 17 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Formulation
  4. Main Results
  5. Distributed guidance law for followers
  6. Guidance law for leaders
  7. Simulation Results
  8. Experimental Validation
  9. Conclusion

Key Result

Lemma 1

(Zubov's Theorem) Consider the non-linear system $\dot{x}=f(x)$ with an equilibrium at the origin and let $G \subset \mathbb{R}^n$ be a domain containing the origin. Suppose there exist two functions $V:G\rightarrow \mathbb{R}$ and $h:\mathbb{R}^n \rightarrow \mathbb{R}$ with the following propertie Then, $x=0$ is asymptotically stable and $G$ is the region of attraction (ROA).

Figures (7)

  • Figure 1: Location of centres $\mathbf{o_A}$ and $\mathbf{o_B}$ of circles $\mathcal{C}_A$ and $\mathcal{C}_B$, respectively
  • Figure 2:
  • Figure 3: Leaders and followers are shown in blue and yellow, respectively.
  • Figure 4: A directed path within $\mathcal{G}_C$ terminating at the leader $l_m$.
  • Figure 5: Case $1$.
  • ...and 2 more figures

Theorems & Definitions (9)

  • Lemma 1
  • Lemma 2
  • Definition 1: Sensing graph
  • Definition 2: Communication graph
  • Lemma 3
  • proof
  • Remark 1
  • Theorem 1
  • proof