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

翻译：在办公室等环境中，机器人两点间导航的持续时长会随时间推移而变化。例如，由于午休时段走廊挤满同向行人，前往厨房所需时间可能更长。本研究针对此类环境中的路径规划问题展开，任务以度量区间时序逻辑（MITL）——一种能精确表达时间约束的丰富机器人任务规范语言——进行描述。我们的目标是寻找一种能最大化机器人MITL任务时间鲁棒性的策略。作为解决方案的第一步，我们定义了一种混合整数线性规划方法，用于在变权重迁移系统上解决任务规划问题——该系统导航时长具有确定性但随每日时段变化。随后，我们将该规划器应用于马尔可夫决策过程中的MITL时间鲁棒性优化，其中物理位置间的导航时长具有不确定性，但延迟概率的时变分布已知。最后，我们针对马尔可夫决策过程开发了一种保留MITL时间鲁棒性保证的滚动时域规划器。通过机器人任务仿真，我们展示了规划算法的可扩展性。