Optimal Path Planning With Opacity-Preserving Temporal Logic Specifications Using Bipartite Synthesizers

This paper investigates an optimal planning prob-lem with the requirement of preventing high-level mission specifications from being revealed to the intruder. We assume that the behavior of the robotic system at some specific locations is partially observable, and the intruder is modeled as a passive observer for the observable behavior and the corresponding overall transition cost of the trajectories. We first use the transition system to model the robot system. Then, we say that the transition system is LTL-based opaque with respect to high-level mission specifications if the intruder cannot infer the exact behavior of the system via the observable sequence of the system. We design a synthesizer for the product automaton of the transition system and the Büchi automaton to find the evolutions of possible reachable states. Based on the synthesizer, the corresponding run can be synthesized in which the optimality, correctness, and opacity can be guaranteed.