Stochastic Robustness Interval for Motion Planning with Signal Temporal Logic

TL;DR

This paper introduces a new robustness measure for stochastic trajectories against STL specifications, enabling probabilistically complete and asymptotically optimal motion planning under uncertainty.

Contribution

It develops a novel robustness measure, a monitor for partial trajectories, and an STL sampling-based planning algorithm with proven theoretical guarantees.

Findings

The method ensures probabilistic completeness.

It achieves asymptotic optimality.

Effective in multiple case studies.

Abstract

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.