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This paper studies optimal motion planning subject to motion and environmentuncertainties. By modeling the system as a probabilistic labeled Markovdecision process (PL-MDP), the control objective is to synthesize afinite-memory policy, under which the agent satisfies complex high-level tasksexpressed as linear temporal logic (LTL) with desired satisfaction probability.In particular, the cost optimization of the trajectory that satisfies infinitehorizon tasks is considered, and the trade-off between reducing the expectedmean cost and maximizing the probability of task satisfaction is analyzed.Instead of using traditional Rabin automata, the LTL formulas are converted tolimit-deterministic B\"uchi automata (LDBA) with a reachability acceptancecondition and a compact graph structure. The novelty of this work lies inconsidering the cases where LTL specifications can be potentially infeasibleand developing a relaxed product MDP between PL-MDP and LDBA. The relaxedproduct MDP allows the agent to revise its motion plan whenever the task is notfully feasible and quantify the revised plan's violation measurement. Amulti-objective optimization problem is then formulated to jointly consider theprobability of task satisfaction, the violation with respect to original taskconstraints, and the implementation cost of the policy execution. Theformulated problem can be solved via coupled linear programs. To the best ofour knowledge, this work first bridges the gap between probabilistic planningrevision of potential infeasible LTL specifications and optimal controlsynthesis of both plan prefix and plan suffix of the trajectory over theinfinite horizons. Experimental results are provided to demonstrate theeffectiveness of the proposed framework.

Optimal Probabilistic Motion Planning with Potential Infeasible LTL Constraints