Reinforcement Learning Based Temporal Logic Control with Soft Constraints Using Limit-deterministic Generalized Buchi Automata

This paper studies the control synthesis of motion planning subject to uncertainties. The uncertainties are considered in robot motions and environment properties, giving rise to the probabilistic labeled Markov decision process (PL-MDP). A Model-Free Reinforcement The learning (RL) method is developed to generate a finite-memory control policy to satisfy high-level tasks expressed in linear temporal logic (LTL) formulas. Due to uncertainties and potentially conflicting tasks, this work focuses on infeasible LTL specifications, where a relaxed LTL constraint is developed to allow the agent to revise its motion plan and take violations of original tasks into account for partial satisfaction. And a novel automaton is developed to improve the density of accepting rewards and enable deterministic policies. We proposed an RL framework with rigorous analysis that is guaranteed to achieve multiple objectives in decreasing order: 1) satisfying the acceptance condition of relaxed product MDP and 2) reducing the violation cost over long-term behaviors. We provide simulation and experimental results to validate the performance.