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In this study, we propose a real-time model predictive control method which simultaneously optimizes obstacle avoidance trajectory and wheel positions using an embedded CPU. The proposed method generates both obstacle avoidance path and dynamical wheel positions on the basis of passage width so that a good balance between stability and mobility is achieved. To implement the algorithm into low speed on-board CPUs, we reduce the computational cost of the model predictive control without using mathematical functions in the index function. Thus the proposed real-time optimization method can be applied to low speed on-board CPUs used in commercially-produced vehicles. Furthermore, we conducted experiments using an embedded CPU to verify feasibility and efficacy of the proposed method.