  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.
