Generalized‐Udwadia–Kalaba‐Theory‐Based Robust Constraint Following Control Design for Wheeled Mobile Robot System With Equality and Inequality Constraints

Ensuring high‐precision trajectory tracking for wheeled mobile robots operating under complex constraints and uncertainties remains a critical challenge. To address this, we propose a robust constraint‐following control framework based on Generalized Udwadia‐Kalaba theory, capable of simultaneously enforcing both equality and inequality constraints while handling system uncertainty. First, based on the diffeomorphism transformation, the constrained state variables are mapped into the unconstrained space. Second, an error dynamic model of the WMR is integrated with a GUK‐based robust controller to make the variable precisely follow both equality and inequality constraints. Through Lyapunov analysis, we prove the system achieves uniform boundedness and uniform ultimate boundedness. Finally, simulations on the WMR demonstrate that the controller ensures precise constraint following without violating safety boundaries and outperforms existing methods in some aspects, including convergence speed and error performance.