Optimal Temporal Logic Planning in Probabilistic Semantic Maps
This addresses the challenge of ensuring correctness guarantees for robots in probabilistic semantic environments, representing an incremental improvement in planning methods.
The paper tackles robot motion planning under temporal logic constraints in uncertain semantic maps by formulating it as a stochastic optimal control problem and reducing it to a deterministic shortest path problem with a confidence parameter, achieving an optimal and efficient solution using the A* algorithm as demonstrated in simulations.
This paper considers robot motion planning under temporal logic constraints in probabilistic maps obtained by semantic simultaneous localization and mapping (SLAM). The uncertainty in a map distribution presents a great challenge for obtaining correctness guarantees with respect to the linear temporal logic (LTL) specification. We show that the problem can be formulated as an optimal control problem in which both the semantic map and the logic formula evaluation are stochastic. Our first contribution is to reduce the stochastic control problem for a subclass of LTL to a deterministic shortest path problem by introducing a confidence parameter $delta$. A robot trajectory obtained from the deterministic problem is guaranteed to have minimum cost and to satisfy the logic specification in the true environment with probability $delta$. Our second contribution is to design an admissible heuristic function that guides the planning in the deterministic problem towards satisfying the temporal logic specification. This allows us to obtain an optimal and very efficient solution using the A* algorithm. The performance and correctness of our approach are demonstrated in a simulated semantic environment using a differential-drive robot.