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.

翻译：本文提出了一种新颖的无模型实时独轮车源追踪设计。该设计能够自主引导独轮车动态系统朝向目标函数或物理/标量信号的极值点运动，这些目标函数或信号在表达式层面未知，但可通过测量获取。本文的一个关键贡献在于：所提出的设计能够指数收敛至局部表现为高次幂函数（例如四次多项式函数）的目标函数（或标量信号）的极值点，这与文献中通常讨论的局部二次型目标函数情形形成对比。我们提供了理论结果与设计特性分析，并辅以多种仿真结果验证所提设计的鲁棒性，包括不同初始条件及测量延迟/噪声等情况。此外，我们在文献中首次提供了机器人实验结果，证明了所提设计的有效性及其指数收敛能力。这些实验结果证实，所提出的指数收敛极值搜索设计能够在真实世界的传感与执行约束下，于物理机器人平台上实际实现。