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Motion planning under uncertainty for an autonomous system can be formulatedas a Markov Decision Process with a continuous state space. In this paper, wepropose a novel solution to this decision-theoretic planning problem thatdirectly obtains the continuous value function with only the first and secondmoments of the transition probabilities, alleviating the requirement for anexplicit transition model in the literature. We achieve this by expressing thevalue function as a linear combination of basis functions and approximating theBellman equation by a partial differential equation, where the value functioncan be naturally constructed using a finite element method. We have validatedour approach via extensive simulations, and the evaluations reveal that tobaseline methods, our solution leads to in terms of path smoothness, traveldistance, and time costs.

State-Continuity Approximation of Markov Decision Processes via Finite Element Methods for Autonomous System Planning