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Model-Free Source Seeking by a Novel Single-Integrator with Attenuating Oscillations and Better Convergence Rate: Robotic Experiments

Shivam Bajpai, Ahmed A. Elgohary, Sameh A. Eisa

TL;DR

An amended design of the simple single-integrator control-affine structure known in ESC literature is proposed and it can functions effectively to achieve a model-free, real-time source seeking of light with attenuated oscillations using only local measurements of the light intensity.

Abstract

In this paper we validate, including experimentally, the effectiveness of a recent theoretical developments made by our group on control-affine Extremum Seeking Control (ESC) systems. In particular, our validation is concerned with the problem of source seeking by a mobile robot to the unknown source of a scalar signal (e.g., light). Our recent theoretical results made it possible to estimate the gradient of the unknown objective function (i.e., the scalar signal) incorporated in the ESC and use such information to apply an adaptation law which attenuates the oscillations of the ESC system while converging to the extremum (i.e., source). Based on our previous results, we propose here an amended design of the simple single-integrator control-affine structure known in ESC literature and show that it can functions effectively to achieve a model-free, real-time source seeking of light with attenuated oscillations using only local measurements of the light intensity. Results imply that the proposed design has significant potential as it also demonstrated much better convergence rate. We hope this paper encourages expansion of the proposed design in other fields, problems and experiments.

Model-Free Source Seeking by a Novel Single-Integrator with Attenuating Oscillations and Better Convergence Rate: Robotic Experiments

TL;DR

An amended design of the simple single-integrator control-affine structure known in ESC literature is proposed and it can functions effectively to achieve a model-free, real-time source seeking of light with attenuated oscillations using only local measurements of the light intensity.

Abstract

In this paper we validate, including experimentally, the effectiveness of a recent theoretical developments made by our group on control-affine Extremum Seeking Control (ESC) systems. In particular, our validation is concerned with the problem of source seeking by a mobile robot to the unknown source of a scalar signal (e.g., light). Our recent theoretical results made it possible to estimate the gradient of the unknown objective function (i.e., the scalar signal) incorporated in the ESC and use such information to apply an adaptation law which attenuates the oscillations of the ESC system while converging to the extremum (i.e., source). Based on our previous results, we propose here an amended design of the simple single-integrator control-affine structure known in ESC literature and show that it can functions effectively to achieve a model-free, real-time source seeking of light with attenuated oscillations using only local measurements of the light intensity. Results imply that the proposed design has significant potential as it also demonstrated much better convergence rate. We hope this paper encourages expansion of the proposed design in other fields, problems and experiments.
Paper Structure (8 sections, 1 theorem, 11 equations, 11 figures, 1 algorithm)

This paper contains 8 sections, 1 theorem, 11 equations, 11 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Control-Affine Extremum Seeking with Attenuating Oscillations using Geometric-Based Kalman Filtering
  3. Main Results
  4. Novel Single-Integrator-Like Source Seeking Design
  5. Simulations and Experimentation of the Proposed Design with Known Objective Function
  6. Experimentation of the Proposed Design for Model-free, Real-time Source Seeking of Light
  7. Comments on Stability from Experimentation
  8. Conclusive Remarks and Future Work

Key Result

Theorem 1

Let A1-A4 be satisfied with some $\omega \in (\omega^*,\infty), \omega^* >0$ and suppose $\exists \; t^* >t_0 =0$ such that $\forall t>t^*$ and $|J_i(t,\bm{z})| \le 1/t^p$ with some $p>1$ then (i) the equilibrium point $\hat{\bm{z}}^* \in \mathscr{C}$ is locally asymptotically stable for the estimat

Figures (11)

  • Figure 1: Simple diagram explaining ESC systems.
  • Figure 2: Sensor-based source seeking
  • Figure 3: The proposed ESC design in pokhrel2023control.
  • Figure 4: Overview of the experimental setup.
  • Figure 5: Proposed amended single-integrator design with GEKF and optional High/Low Pass Filters (HPF/LPS).
  • ...and 6 more figures

Theorems & Definitions (1)

  • Theorem 1