A NESO-TD-based dual-loop integral sliding mode control framework for robust trajectory tracking of wheeled mobile robots

Wheeled mobile robots (WMRs) operating on rough outdoor compacted hard ground are susceptible to disturbances caused by model uncertainties and terrain variations, which may degrade trajectory tracking accuracy and robustness. To address this issue, this study proposes a unified dual-loop integral sliding mode control framework based on a nonlinear extended state observer (NESO) and a tracking differentiator (TD) for robust trajectory tracking of WMRs. At the kinematic level, an integral sliding mode surface based on the fal function is designed, and a kinematic controller with a hyperbolic tangent reaching law is developed to generate smooth desired velocity signals. At the dynamic level, an integral sliding mode controller integrating an improved TD and a third-order NESO is constructed. The TD employs a combination of hyperbolic tangent, inverse hyperbolic sine, and power functions to smoothly extract the desired velocities and their derivatives. Meanwhile, the third-order NESO estimates the lumped disturbances of the system in real time and provides feedforward compensation. In addition, a continuous reaching law combining power and hyperbolic tangent terms is designed to effectively reduce chattering. Finally, the proposed method is validated through MATLAB/Simulink simulations and experiments on a physical WMR platform. Compared with the conventional sliding mode control (SMC), the proposed method achieves faster reference trajectory tracking and effectively reduces tracking errors under various trajectories, with an average reduction of approximately 45.5% in the pose tracking RMSE. Under strong impulse disturbances, abrupt trajectory changes, and payload variations, the proposed method demonstrates superior disturbance rejection capability and dynamic response performance. Experimental results on rough, hard-compacted outdoor ground further verify the effectiveness and robust tracking capability of the proposed method.