In this paper, a robust model predictive control (MPC) scheme using neural network based optimization has been developed to stabilize a physically constrained mobile robot. By applying a state scaling transformation, the intrinsic controllability of a mobile robots can be regained by incorporation into the control input u1 an additional exponential decaying term. An MPC based control method is then designed for the robot in the presence of external disturbances. The MPC optimization can be formulated as a convex nonlinear minimization problem and a primal-dual neural network (PDNN) is adopted to solve this optimization problem over a finite receding horizon. The computational efficiency of MPC has been improved by the proposed neuro-dynamic approach. Experimental studies under various dynamic conditions have been performed to demonstrate the performance of the proposed approach.Index Terms-Robust nonholonomic mobile robots, Scaling transformation, Model predictive control(MPC), Primal-dual neural network (PDNN).