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

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.