  This paper addresses the online motion planning problem of mobile robots
under complex high-level tasks. The robot motion is modeled as an uncertain
Markov Decision Process (MDP) due to limited initial knowledge, while the task
is specified as Linear Temporal Logic (LTL) formulas. The proposed framework
enables the robot to explore and update the system model in a Bayesian way,
while simultaneously optimizing the asymptotic costs of satisfying the complex
temporal task. Theoretical guarantees are provided for the synthesized outgoing
policy and safety policy. More importantly, instead of greedy exploration under
the classic ergodicity assumption, a safe-return requirement is enforced such
that the robot can always return to home states with a high probability. The
overall methods are validated by numerical simulations.
