Optimal Temporal Logic Planning in Probabilistic Semantic Maps

TL;DR

This paper presents a method for robot motion planning under temporal logic constraints in probabilistic semantic maps, reducing the stochastic control problem to a deterministic shortest path problem with probabilistic guarantees, and demonstrating efficiency with A* search.

Contribution

It introduces a novel approach to handle uncertainty in semantic maps by converting stochastic control problems into deterministic ones with probabilistic guarantees, enabling efficient planning.

Findings

The method guarantees satisfaction of LTL specifications with probability delta.

The approach achieves optimal solutions efficiently using A* search.

Validated in simulated environments with differential-drive robots.

Abstract

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.