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Event-Triggered Source Seeking Control for Nonholonomic Systems

Victor Hugo Pereira Rodrigues, Tiago Roux Oliveira, Miroslav Krstic

TL;DR

The paper tackles locating a signal source with a nonholonomic unicycle in GPS-denied environments. It develops an event-triggered source seeking control (ET-SSC) that updates inputs only at state-dependent triggering times and uses time-scaling and averaging to analyze the slow dynamics. The main contributions are the first ET-SSC framework for source seeking, a Lyapunov/averaging stability proof showing local exponential stability of the average system and practical convergence to a neighborhood of the source, and a guaranteed Zeno-free operation via a minimum dwell time. Simulations validate that ET-SSC achieves similar performance to continuous-time SSC while significantly reducing actuation and communication, enabling arbitrarily large inter-sampling times. The work advances resource-aware control for autonomous navigation in GPS-denied environments.

Abstract

This paper introduces an event-triggered source seeking control (ET-SSC) for autonomous vehicles modeled as the nonholonomic unicycle. The classical source seeking control is enhanced with static-triggering conditions to enable aperiodic and less frequent updates of the system's input signals, offering a resource-aware control design. Our convergence analysis is based on time-scaling combined with Lyapunov and averaging theories for systems with discontinuous right-hand sides. ET-SSC ensures exponentially stable behavior for the resulting average system, leading to practical asymptotic convergence to a small neighborhood of the source point. We guarantee the avoidance of Zeno behavior by establishing a minimum dwell time to prevent infinitely fast switching. The performance optimization is aligned with classical continuous-time source seeking algorithms while balancing system performance with actuation resource consumption. Our ET-SSC algorithm, the first of its kind, allows for arbitrarily large inter-sampling times, overcoming the limitations of classical sampled-data implementations for source seeking control.

Event-Triggered Source Seeking Control for Nonholonomic Systems

TL;DR

The paper tackles locating a signal source with a nonholonomic unicycle in GPS-denied environments. It develops an event-triggered source seeking control (ET-SSC) that updates inputs only at state-dependent triggering times and uses time-scaling and averaging to analyze the slow dynamics. The main contributions are the first ET-SSC framework for source seeking, a Lyapunov/averaging stability proof showing local exponential stability of the average system and practical convergence to a neighborhood of the source, and a guaranteed Zeno-free operation via a minimum dwell time. Simulations validate that ET-SSC achieves similar performance to continuous-time SSC while significantly reducing actuation and communication, enabling arbitrarily large inter-sampling times. The work advances resource-aware control for autonomous navigation in GPS-denied environments.

Abstract

This paper introduces an event-triggered source seeking control (ET-SSC) for autonomous vehicles modeled as the nonholonomic unicycle. The classical source seeking control is enhanced with static-triggering conditions to enable aperiodic and less frequent updates of the system's input signals, offering a resource-aware control design. Our convergence analysis is based on time-scaling combined with Lyapunov and averaging theories for systems with discontinuous right-hand sides. ET-SSC ensures exponentially stable behavior for the resulting average system, leading to practical asymptotic convergence to a small neighborhood of the source point. We guarantee the avoidance of Zeno behavior by establishing a minimum dwell time to prevent infinitely fast switching. The performance optimization is aligned with classical continuous-time source seeking algorithms while balancing system performance with actuation resource consumption. Our ET-SSC algorithm, the first of its kind, allows for arbitrarily large inter-sampling times, overcoming the limitations of classical sampled-data implementations for source seeking control.

Paper Structure

This paper contains 15 sections, 1 theorem, 80 equations, 1 figure.

Table of Contents

  1. INTRODUCTION
  2. PROBLEM FORMULATION
  3. Linear Velocity $v(t)$ and the Angular Velocity $\omega(t)$
  4. Estimation Error Dynamics
  5. Gradient Estimate and its Dynamics
  6. State Feedback based on Gradient Estimate
  7. Emulation of the Continuous-Time Extremum Seeking
  8. Event-Triggered Control Design
  9. Rescaling of Time
  10. Closed-Loop Average System
  11. STABILITY ANALYSIS
  12. SIMULATION RESULTS
  13. CONCLUSIONS
  14. Stability Analysis
  15. Avoidance of Zeno Behavior

Key Result

Theorem 1

Consider the closed-loop average dynamics of the gradient estimate (eq:dhatG_ETSSC_v_5), the average error vector (eq:Eav_event_1) and the average static event-triggering mechanism given by Definition def:averageStaticEvent. Under Assumptions assumption1--assumption2 and considering the quadratic ma where $a=\frac{3}{2}a_{3}$, and $\omega = \omega_{3}$. In addition, there exists a lower bound $\ta

Figures (1)

  • Figure :

Theorems & Definitions (3)

  • Definition 1: Static Triggering Condition
  • Definition 2: Average Static Triggering Condition
  • Theorem 1