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This paper presents a novel motion planning approach inspired by the Dynamic Programming (DP) for mobile robots and other autonomous vehicles. The proposed discrete- time algorithm enables a multi-degree of freedom vehicle to reach its destination through an arbitrary obstacle field in a minimum number of time steps. Furthermore, the resulting optimal path is guaranteed to posses the required degree of smoothness and incorporates the motion state constraints such as velocity, acceleration, and jerk limits. The algorithm is proven to terminate in a finite number of steps without its computational complexity increasing with the type or number of obstacles. The effectiveness of the algorithm is demonstrated on a mobile robot modeled as a point-mass in a 2-dimensional space subject to velocity and acceleration limits.