Model-Free Source Seeking by a Novel Single-Integrator with Attenuating Oscillations and Better Convergence Rate: Robotic Experiments (2311.04330v2)

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.

• The paper introduces a GEKF-enabled single-integrator that substantially reduces oscillations while enhancing convergence in model-free source seeking tasks.
• The methodology leverages local gradient estimation with dynamic adaptation, enabling real-time adjustments in the control inputs.
• Experimental validation with a TB3 robot demonstrates improved performance over traditional methods, highlighting its potential for advanced robotic applications.

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

This paper investigates a model-free control technique for source seeking using a novel control-affine Extremum Seeking Control (ESC) system, achieved through significant modifications of the single-integrator architecture to include a Geometric-based Extended Kalman Filter (GEKF). The principal aim is to reduce oscillations while enhancing convergence rates in the presence of unknown signal sources, as demonstrated experimentally with a TurtleBot3 (TB3) robot.

The paper is built upon recent theoretical advancements by the authors' group, which allow for gradient estimation of the objective function by exclusively employing local measurements. Specifically, the objective in question is the light intensity targeted by a mobile robot. The paper contrasts its novel design with traditional control-affine ESC systems, such as the simple single-integrator, which are well-documented for their stability but criticized for persistent oscillations.

Methodology and Design

The proposed ESC design functions by empirically estimating the objective function's gradient and employing this information to implement a model-free adaptive control policy. The GEKF plays a pivotal role in refining gradient estimates, stabilizing the system around the extremum point, and dynamically adjusting input signal amplitudes based on proximity to the target source. Notably, the adaptation law attenuates control input oscillations, an attribute absent in prior single-integrator schemes.

The authors formally derive the stability conditions for the system, ensuring practical asymptotic stability with GEKF, as shown in theorem-backed narratives.

Experimental Validation

Experimental efforts primarily involved environmental trials with the TB3 robot tasked with seeking light sources, serving as a surrogate for evaluating the performance of both known objective functions and unquantified light intensities. These experimentation scenarios elicited several key observations:

1. Performance Comparison: When compared to traditional single-integrator methods, the GEKF-enabled design demonstrated superior oscillation mitigation and enhanced convergence rates.
2. Real-Time Adaptation: The ESC system adjusted dynamically under time-varying conditions, showcasing robustness in tracking moving targets—an attribute highlighting potential future applications.
3. Stability Achievement: Monitored performance using $J_x$ and $J_y$ terms validated stability as delineated in theoretical analyses.

Implications and Future Directions

The paper’s novel control-affine ESC design significantly benefits model-free real-time source seeking scenarios. Practically, this capability promises to broaden ESC applications in mobile robotics, unmanned vehicles, and more. Theoretically, these findings suggest a fertile territory for further exploration, such as characterizing the effects of GEKF on higher-order ESC systems or applying similar constructs to other domains requiring real-time gradient estimation.

Future research should explore the implications of GEKF-driven adaptability on convergence behaviors and seek to generalize the ESC frameworks to cope with time-variant extremum conditions—a remarkable functionality hinted at by the paper's moving-source tracking results.

Moreover, expanding the ESC systems to further accommodate such dynamic environments could unlock new capabilities in real-time autonomous navigation and adaptive sensing applications. Thus, this work not only solidifies the practical feasibility of the proposed ESC system in controlled environments but also lights the path for theoretical and applied advances in the field of control systems.