Design and Implementation of a Hybrid Sliding Mode Controller with Nonlinear Surface for Trajectory Tracking of a Mobile Manipulator

This work presents the implementation of a Sliding Mode Controller (SMC) for a mobile manipulator, considering both a conventional version with a linear PI sliding surface and a proposed nonlinear variant (SMC+NLn). The nonlinear approach introduces an error-dependent gain in the discontinuous component of the control law to mitigate chattering effects. The dynamic model of the mobile manipulator was obtained by combining the kinematics of the robotic arm and the dynamics of the mobile base. Both controllers were tuned using genetic optimization algorithms, minimizing standard performance indices. The evaluation was carried out through simulations involving a reference trajectory that excites all degrees of freedom, as well as external disturbances emulated by variations in the Jacobian matrix. The results show that the SMC+NLn outperforms the conventional SMC in all tested scenarios, achieving lower tracking errors, reduced control effort, and significantly attenuated oscillations in the discontinuous component. In disturbance rejection tests, the nonlinear controller exhibited faster recovery and smoother transient response while maintaining similar steady-state behavior to the linear version near the reference. The proposed method improves performance without increasing implementation complexity, making it suitable for future validation on real systems to evaluate practical limitations, actuator impact, and robustness against unmodeled dynamics.