In this paper we propose a method of presenting a special case of Value Function as a solution to POMDP in mobile robot navigation. By using this new method the Value Function complexity will be reduced and more intuitive. We also propose a new reinforcement learning method to solve the Value Function. This reinforcement learning is based on Bellman Equation augmented with A* like heuristic during update iteration. The result of this new Value Function is validated with This particle filter is simulaed in Matlab and also experimented physically using a simple autonomous mobile robot built with Lego Mindstorms NXT with 3 ultrasonic sonar and RWTH Mindstorms NXT Toolbox for Matlab to connect the robot to Matlab. This simulation and experiment also incorporate particle filter localization from previous research. The simulation and experiment show that the Value Function can be utilized very well.
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