In many multi-robot applications, mobile worker robots are often engaged in performing some tasks repetitively by following pre-computed trajectories. As these robots are battery-powered, they need to get recharged at regular intervals. We envision that in the future, a few mobile recharger robots will be employed to supply charge to the energy-deficient worker robots recurrently, to keep the overall efficiency of the system optimized.In this setup, we need to find the time instants and locations for the meeting of the worker robots and recharger robots optimally. We present a Satisfiability Modulo Theory (SMT)-based approach that captures the activities of the robots in the form of constraints in a sufficiently long finite-length time window (hypercycle) whose repetitions provide their perpetual behavior. Our SMT encoding ensures that for a chosen length of the hypercycle, the total waiting time of the worker robots due to charge constraints is minimized under certain condition, and close to optimal when the condition does not hold. Moreover, the recharger robots follow the most energy-efficient trajectories. We show the efficacy of our approach by comparing it with another variant of the SMT-based method which is not scalable but provides an optimal solution globally, and with a greedy algorithm.

中文翻译：

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多机器人环境中的移动充电器路径规划和充电调度

在许多多机器人应用中，移动工作人员机器人通常通过遵循预先计算的轨迹来重复执行某些任务。这些机器人由电池供电，因此需要定期进行充电。我们设想在未来，将使用一些移动充电机器人来为低能耗的工作机器人周期性地充电，以保持系统的整体效率最佳化。在此设置中，我们需要找到时间点和位置最适合工人机器人和充电机器人的会议。我们提出了一种基于满意度模理论（SMT）的方法，该方法在足够长的有限长度时间窗口（超周期）中以约束的形式捕获了机器人的活动，其重复提供了其永恒的行为。我们的SMT编码可确保在选定的超周期长度内，在一定条件下最大限度地减少了由于充电约束而导致的工作机器人的总等待时间，并且在条件不成立时接近最佳状态。此外，充电机器人遵循最节能的轨迹。通过将其与基于SMT的方法的另一种变体进行比较，该方法不可扩展，但可以全局提供最佳解决方案，并与贪婪算法进行比较，从而证明了该方法的有效性。