Model-free source seeking of exponentially convergent unicycle: theoretical and robotic experimental results

TL;DR

This paper presents a novel model-free extremum seeking control method for a unicycle robot that guarantees exponential convergence to the target point, supported by theoretical analysis, simulations, and real robotic experiments.

Contribution

It introduces a new extremum seeking design that converges exponentially for higher-degree objective functions, validated through theoretical, simulation, and robotic experiments.

Findings

The proposed design achieves exponential convergence to the extremum point.

The method is robust to initial conditions, measurement delays, and noise.

Experimental results confirm practical effectiveness on a robotic platform.

Abstract

This paper introduces a novel model-free, real-time unicycle-based source seeking design. This design autonomously steers the unicycle dynamic system towards the extremum point of an objective function or physical/scalar signal that is unknown expression-wise, but accessible via measurements. A key contribution of this paper is that the introduced design converges exponentially to the extremum point of objective functions (or scalar signals) that behave locally like a higher-degree power function (e.g., fourth-degree polynomial function) as opposed to locally quadratic objective functions, the usual case in literature. We provide theoretical results and design characterization, supported by a variety of simulation results that demonstrate the robustness of the proposed design, including cases with different initial conditions and measurement delays/noise. Also, for the first time in the literature, we provide experimental robotic results that demonstrate the effectiveness of the proposed design and its exponential convergence ability. These experimental results confirm that the proposed exponentially convergent extremum seeking design can be practically realized on a physical robotic platform under real-world sensing and actuation constraints.