We consider energy-aware planning for an unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) team operating in a stochastic environment. The UAV must visit a set of air points in minimum time while respecting energy constraints, relying on the UGV as a mobile charging station. Unlike prior work that assumed deterministic travel times or used fixed robustness margins, we model travel times as random variables and bound the probability of failure (energy depletion) across the entire mission to a user-specified risk level. We formulate the problem as a Mixed-Integer Program and propose PRO-SPECT, a polynomial-time algorithm that generates risk-bounded plans. The algorithm supports both offline planning and online re-planning, enabling the team to adapt to disturbances while preserving the risk bound. We provide theoretical results on solution feasibility and time complexity. We also demonstrate the performance of our method via numerical comparisons and simulations.

翻译：针对在随机环境中运行的无人机（UAV）与无人车（UGV）协作团队，本文提出一种能量感知规划方法。无人机需在满足能量约束的前提下，依靠作为移动充电站的无人车，以最短时间访问一组空中点位。不同于以往假设行程时间确定性或采用固定鲁棒裕度的研究，本文将行程时间建模为随机变量，并将整个任务期间发生能量耗尽失效的概率约束至用户指定的风险水平。我们将该问题形式化为混合整数规划，并提出PRO-SPECT——一种可生成风险有界规划方案的多项式时间算法。该算法同时支持离线规划与在线重规划，使团队能够在保持风险界的前提下适应扰动。我们给出了关于解可行性与时间复杂度的理论结果，并通过数值对比与仿真验证了方法的性能。