This article seeks to develop the dynamic model of a mobile robot for controlling purposes while the effects of uncertainties and longitudinal and lateral slip are assumed. The rise in the number of state variables and considering the effects of nonlinear parameters due to slip modeling can complicate the control procedure of wheeled mobile manipulators. In addition, the existence of uncertainties as well as holonomic and nonholonomic constraints would increase this complexity even more. On the one side, as wheels are considered to slip, unwanted movements due to slippage affect the movement of the manipulator and the manipulator may not be able to track the desired path. On the other side, the movement of weighted links of the manipulator constantly changes the normal forces of the wheels. As traction forces are dependent on these normal forces, the path tracked by the platform would be affected. Given these conditions, employing a robust control methodology and developing an optimal algorithm to reduce the effects of uncertainties and wheels slip seems mandatory. To this aim, a sliding mode control (SMC) strategy is formulated in this study. Furthermore, the suggested algorithm is optimized using a state-dependent Riccati equation to reduce the consumed torque and increase the accuracy of the system. Simulations are conducted, and the presented algorithm is also checked with the experimental setup of a Scout robot. Simulation results show that the optimal sliding mode control (OSMC) successfully decreases sudden jumps due to slippage in the system. In addition, the consumed power of wheels and arm for SMC decreases from 9.15 and 1.02 N⋅m to, respectively, 1.46 and 0.54 N⋅m for OSMC.

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