State-Continuity Approximation of Markov Decision Processes via Finite Element Methods for Autonomous System Planning
This addresses motion planning under uncertainty for autonomous systems, offering a novel method that reduces reliance on explicit transition models, though it appears incremental in its application of finite element methods to this domain.
The paper tackles motion planning under uncertainty for autonomous systems by proposing a novel method that directly obtains the continuous value function using only first and second moments of transition probabilities, eliminating the need for an explicit transition model. The approach is validated through simulations, showing improvements in path smoothness, travel distance, and time costs compared to baseline methods.
Motion planning under uncertainty for an autonomous system can be formulated as a Markov Decision Process with a continuous state space. In this paper, we propose a novel solution to this decision-theoretic planning problem that directly obtains the continuous value function with only the first and second moments of the transition probabilities, alleviating the requirement for an explicit transition model in the literature. We achieve this by expressing the value function as a linear combination of basis functions and approximating the Bellman equation by a partial differential equation, where the value function can be naturally constructed using a finite element method. We have validated our approach via extensive simulations, and the evaluations reveal that to baseline methods, our solution leads to in terms of path smoothness, travel distance, and time costs.