In this work, we present a novel robustness measure for continuous-time stochastic trajectories with respect to Signal Temporal Logic (STL) specifications. We show the soundness of the measure and develop a monitor for reasoning about partial trajectories. Using this monitor, we introduce an STL sampling-based motion planning algorithm for robots under uncertainty. Given a minimum robustness requirement, this algorithm finds satisfying motion plans; alternatively, the algorithm also optimizes for the measure. We prove probabilistic completeness and asymptotic optimality, and demonstrate the effectiveness of our approach on several case studies.

翻译：本文提出了一种针对连续时间随机轨迹相对于信号时序逻辑（Signal Temporal Logic, STL）规范的新型鲁棒性度量方法。我们论证了该度量的可靠性，并开发了一种用于推理部分轨迹的监测器。基于该监测器，我们提出了一种面向不确定性机器人系统的STL采样运动规划算法。该算法在给定最小鲁棒性要求时，能够找到满足条件的运动规划方案；亦可针对该度量进行优化。我们证明了算法的概率完备性与渐近最优性，并通过多个案例研究验证了方法的有效性。