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When a wheeled autonomous robot drives with wheel slips, the velocity and posture control becomes difficult. An ideal automatic driving control system should be able to comply with changes in slip conditions so as to optimise the control performance. Using dual heuristic programming and multi-layer perceptron neural networks, an adaptive critic anti-slip control design is developed to achieve this goal. The critic structure enables neural network learning by satisfying the Bellman equation so that the inclination of the action performance can be assessed to improve the control parameters. A slip model of the robot vehicle is derived. The adaptive critic anti-slip control system is verified extensively by computer simulation. The result shows that the performance is significantly better than that of using traditional fuzzy control.