An operational space dynamic model of a redundantly actuated wheeled mobile robot taking into account the wheel-ground interaction is derived based on vehicle dynamics. The conditions for the robot to avoid slip are derived for both torque and motion. Two torque distribution schemes based on different criteria are proposed. The non-slip condition for motion is utilized to plan slip avoidance paths. The null space joint torques are utilized to fulfil the non-slip condition for torque and avoid actuator torque limits violation. Simulations results are presented to demonstrate the effects of wheel-ground interaction and performance of the proposed torque distribution schemes