<p>Path-following control for wheeled mobile robots operating on varying terrains constitutes a fundamental challenge in robotic motion control, as terrain variations directly impact steering dynamics. This study models steering dynamics as a first-order system, where the dynamic parameter is matched to specific terrains. To achieve terrain adaptation, Support Vector Machine (SVM) methodology enables real-time matching of steering dynamics parameters to identified terrains through instantaneous image recognition. By integrating time-varying steering dynamics with fundamental kinematics, we establish the control model and subsequently design a path-following controller for this time-varying system using Lyapunov stability theory. Comparative experiments conducted in variable terrain environments evaluated fixed-parameter versus terrain-adaptive parameter control across linear, square, and circular paths. The results demonstrate that when the dynamic parameter can adapt to terrain variations, the designed time-varying parameter path following controller enables the mobile robot to converge to the predefined path more rapidly with reduced overshoot.</p>