<p>To address the trajectory tracking control of wheeled mobile robots (WMRs) under sideslip conditions, this paper proposes a hierarchical observation strategy based on the dual-loop control structure of WMRs. By improving the traditional predefined-time prescribed performance function, precise adjustment of the convergence time is achieved. In the kinematic outer loop, an adaptive sliding mode observer is designed to estimate the sideslip velocity, which is combined with a predefined-time prescribed performance sliding mode controller. In the dynamic inner loop, a novel predefined-time disturbance observer and a prescribed performance sliding mode control are adopted. Theoretical analysis shows that disturbance observation error, position error, and velocity error all converge within the predefined time, and numerical simulations verify the effectiveness of the method.</p>