Four-wheel redundantly-actuated mobile robot (FRMR) offers high controllability and maneuverability for automation applications. However, the robot dynamics and actuator failures are normally omitted in existing kinematic control schemes, which may lead to steering vibration and degraded robustness. To deal with these problems, a fault-tolerant dynamic control method is developed for precise trajectory tracking of the FRMR, which utilizes a two-level structure to cover the wheel-ground interactions and possible actuator failures. In the high level, with a novel fractional-order sliding mode control, this method offers an effective way to regulate the steering angle and eliminate the rotation chattering simultaneously. For the redundantly-actuated issue, a robust allocation solution is presented in the lower level to straightly determine optimal driving torques with full considerations of actuator failures and optimization efficiency. The convergence and stability of the achieved FRMR system are guaranteed theoretically. The experimental comparative results verify that higher tracking precision and enhanced robustness can be obtained using our proposed method. INDEX TERMS Fault-tolerant dynamic control, four-wheel redundantly-actuated mobile robot, fractional-order sliding mode control, wheel-ground interactions.