Timescale-Separation-Based Source Seeking for USV

The primary objective of this study is to enable an unmanned surface vehicle (USV) to autonomously approach the extremum of an unknown scalar field using only real-time field measurements. To this end, a source-seeking method based on timescale separation is developed within a hierarchical control framework that divides the closed-loop system into a slow and a fast subsystem. The slow subsystem governs the gradual evolution of the USV pose and generates reference heading and surge commands from local scalar field information, providing a directional cue toward the field extremum. The fast subsystem applies actuator-level control inputs that ensure these references are tracked with sufficient accuracy through rapid corrective actions. A Lyapunov-based analysis is carried out to study the stability properties of the coupled slow–fast dynamics and to establish conditions under which convergence can be guaranteed in the presence of model nonlinearities and external disturbances. Numerical simulations are conducted to illustrate the resulting system behavior and to verify that the proposed framework maintains stable seeking performance under typical operating conditions.