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This paper presents an optimal control scheme based on model-based predictive control (MPC) for a wheeled mobile robot (WMR) with nonholonomic constraints. It is shown that, by using MPC, some advantages can be obtained, such as the ability to handle constraints due to state or input limitations and performance improvement. To solve some problems with other MPCs for WMRs, this paper proposes to formulate a cost function in polar coordinates. Considerations regarding the computational effort of the MPC are developed with the purpose of analysing the viability of the proposed technique in real-time.