This paper presents a point stabilization method which is a hybrid form of Exact Euclidian Distance Transform (EEDT) and Model Predictive Control (MPC) theory. An optimal control problem is evaluated using a wheeled mobile robot's mathematical model. The model is represented in polar coordinates considering non-holonomic constraints. The optimal input parameters are obtained by solving a sequential quadratic cost function. The EEDT algorithm provides via-points starting from the initial

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... to the desired final coordinates. The line segments connected by these points form the shortest obstacle free static trajectory. Assuming that all of the occupied regions in the map are fully known, states of the mobile robot are constrained by avoiding the intersection of the obstacles and the planned path. Point stabilization phase is performed in a partial manner by applying MPC algorithm on consecutive via points. The overall stabilized trajectory between the start and goal is obtained by connecting the stabilized sub-trajectories. This approach provides a way to stabilize a trajectory without determining convex sub-regions on a non-convex map. The results on a simulated differentially driven mobile robot prove that the proposed algorithm gives satisfactory results for point stabilization problem in presence of static obstacles on a non-convex map.