In this paper, an optimal control approach is used to solve a two-dimensional path planning problem for a differential drive mobile robot. Two optimal control algorithms are presented and analyzed, which consist of a novel implementation of a linear quadratic tracker (LQT), and a dynamic programming (DP) scheme. The algorithms are applied to the task of GPS navigation with obstacle avoidance. The methods aim to find an optimal path where the tracking error to the GPS target is minimized, while avoiding the obstacles present on the vehicle's map. The LQT algorithm minimizes the tracking error to the goal point, while simultaneously maximizing the distance to obstacles. It also makes use of a fuzzy logic system to adjust the optimization parameters according to different environmental scenarios.
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