Stochastic Robustness Interval for Motion Planning with Signal Temporal Logic

In this work, we present a novel robustness mea- sure 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 proba- bilistic completeness and asymptotic optimality of the motion planner with respect to the measure, and demonstrate the effectiveness of our approach on several case studies.