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Predefined-Time Target Localization and Circumnavigation using Bearing-Only Measurements: Theory and Experiments

Donglin Sui, Mohammad Deghat

TL;DR

A novel adaptive target estimator is introduced that enables the agent to accurately localize the position of the unknown target with a tunable, predefined convergence time and a controller integrated with the estimator to steer the agent onto a circular trajectory centered at the target with a desired radius.

Abstract

This paper investigates the problem of controlling an autonomous agent to simultaneously localize and circumnavigate an unknown stationary target using bearing-only measurements (without explicit differentiation). To improve the convergence rate of target estimation, we introduce a novel adaptive target estimator that enables the agent to accurately localize the position of the unknown target with a tunable, predefined convergence time. Following this, we design a controller integrated with the estimator to steer the agent onto a circular trajectory centered at the target with a desired radius. The predefined-time stability of the overall system including the estimation and control errors are rigorously analyzed. Extensive simulations and experiments using unmanned aerial vehicles (UAVs) illustrate the performance and efficacy of the proposed estimation and control algorithms.

Predefined-Time Target Localization and Circumnavigation using Bearing-Only Measurements: Theory and Experiments

TL;DR

A novel adaptive target estimator is introduced that enables the agent to accurately localize the position of the unknown target with a tunable, predefined convergence time and a controller integrated with the estimator to steer the agent onto a circular trajectory centered at the target with a desired radius.

Abstract

This paper investigates the problem of controlling an autonomous agent to simultaneously localize and circumnavigate an unknown stationary target using bearing-only measurements (without explicit differentiation). To improve the convergence rate of target estimation, we introduce a novel adaptive target estimator that enables the agent to accurately localize the position of the unknown target with a tunable, predefined convergence time. Following this, we design a controller integrated with the estimator to steer the agent onto a circular trajectory centered at the target with a desired radius. The predefined-time stability of the overall system including the estimation and control errors are rigorously analyzed. Extensive simulations and experiments using unmanned aerial vehicles (UAVs) illustrate the performance and efficacy of the proposed estimation and control algorithms.

Paper Structure

This paper contains 18 sections, 12 theorems, 44 equations, 6 figures.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARIES
  3. Useful Lemmas
  4. Background and Notations
  5. Problem Statements
  6. PROPOSED ALGORITHM
  7. Target Estimator
  8. Circumnavigation Controller
  9. STABILITY ANALYSIS
  10. Preliminary Results
  11. Generalization
  12. Main Results
  13. Simulations
  14. Experiments
  15. Experimental Setup
  16. ...and 3 more sections

Key Result

Lemma II.1

If there exists a continuous radially unbounded function $V:\mathbb{R}^n\mapsto \mathbb{R}_{+}\cup \{0\}$ such that $\bm{x}\in M$ iff $V(\bm{x})=0$ and any solution $\bm{x}(t)$ of system eq:sample_dynamic_system satisfies for constants $T_c = T_c(\bm{\rho})>0$ and $p\in (0,1]$, then the set $M$ is GSPTA for system eq:sample_dynamic_system and the strong predefined time is $T_c$.

Figures (6)

  • Figure 1: Motion trail of a Crazyflie 2.1 quadcopter localizing and circumnavigating a stationary unknown target using the proposed control algorithms.
  • Figure 2: Problem geometry and notations.
  • Figure 3: Possible values of $\delta(t)$.
  • Figure 4: Comparative analysis of simulation results benchmarking the performance of the proposed method against established approaches from the literature.
  • Figure 5: (a) Schematic diagram of the flying arena; (b) Block diagram of the experimental system.
  • ...and 1 more figures

Theorems & Definitions (26)

  • Definition II.1: see for instance, chowdhary2013Concurrentpan2018Compositearanovskiy2023PreservingExcitation
  • Definition II.2: sanchez-torres2018Class
  • Lemma II.1: sanchez-torres2018Class
  • Lemma IV.1
  • proof
  • Remark IV.1
  • Lemma IV.2
  • proof
  • Lemma IV.3
  • proof
  • ...and 16 more