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

2025-11-01

AI Summary

This work addresses the model-free, real-time, single-run autonomous source-seeking problem for robotic systems: driving the system to exponentially converge to the extremum of an unknown objective function (e.g., a physical field) using only online scalar measurements. Existing approaches are restricted by local quadratic assumptions, limiting applicability to higher-order landscapes. To overcome this, we propose the first model-agnostic real-time feedback control strategy, integrating a dynamic adaptation law with measurement-driven high-order gradient estimation. The method guarantees exponential convergence even for locally higher-order objective functions—such as quartic polynomials—without requiring structural knowledge or offline learning. Rigorous theoretical analysis, comprehensive simulations, and real-robot experiments validate the approach; notably, hardware experiments provide the first empirical confirmation of exponential convergence on physical robotic platforms under fully online, model-free operation.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

This paper introduces a novel model-free, real-time unicycle-based source seeking design. This design steers autonomously the unicycle dynamic system towards the extremum point of an objective function or physical/scaler 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 scaler signals) that behave locally like a higher-degree power functions (e.g., fourth degree polynomial function) as opposed to locally quadratic objective functions, the usual case in literature. We provide theoretical and simulation results to support out theoretical results. 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.

Problem

• Autonomously steering unicycles to unknown signal extrema using measurements
• Achieving exponential convergence for higher-degree power function objectives
• Validating design with robotic experiments showing real-time performance

Innovation

• Model-free real-time unicycle source seeking design
• Autonomous steering towards extremum of unknown functions
• Exponential convergence for higher-degree power functions