In this paper, we apply a Markov Decision Process (MDP) to assure collision avoidance and specify optimal paths for evolution of an agent with nonlinear dynamics. We consider evolution of an autonomous wheeled robot in a motion field where a malicious agent has stochastic transitions over the field. By knowing the history of malicious agent transition as well as initial and goal destinations of the autonomous robot, the optimal path is obtained using the Bellman equation. We propose a novel finite time controller that assures reachability of desired way-points along the optimal path, where the optimal path is obtained without deriving the Hamiltonian.

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