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.
@article{arxiv.2210.04813,
title = {Stochastic Robustness Interval for Motion Planning with Signal Temporal Logic},
author = {Roland B. Ilyes and Qi Heng Ho and Morteza Lahijanian},
journal= {arXiv preprint arXiv:2210.04813},
year = {2023}
}