Robust MITL Planning under Uncertain Navigation Times

In environments like offices, the duration of a robot's navigation betweentwo locations may vary over time. For instance, reaching a kitchen may takemore time during lunchtime since the corridors are crowded with people headingthe same way. In this work, we address the problem of routing in suchenvironments with tasks expressed in Metric Interval Temporal Logic (MITL) - arich robot task specification language that allows us to capture explicit timerequirements. Our objective is to find a strategy that maximizes the temporalrobustness of the robot's MITL task. As the first step towards a solution, wedefine a Mixed-integer linear programming approach to solving the task planningproblem over a Varying Weighted Transition System, where navigation durationsare deterministic but vary depending on the time of day. Then, we apply thisplanner to optimize for MITL temporal robustness in Markov Decision Processes,where the navigation durations between physical locations are uncertain, butthe time-dependent distribution over possible delays is known. Finally, wedevelop a receding horizon planner for Markov Decision Processes that preservesguarantees over MITL temporal robustness. We show the scalability of ourplanning algorithms in simulations of robotic tasks.