Feedback Motion Planning for Stochastic Nonlinear Systems with Signal Temporal Logic Specifications

TL;DR

This paper presents a feedback motion planning framework for stochastic nonlinear systems that ensures high-probability satisfaction of complex temporal logic specifications using probabilistic reachable tubes and contraction-based control.

Contribution

It introduces a novel predicate erosion strategy transforming stochastic problems into deterministic STL trajectory optimizations with probabilistic guarantees.

Findings

Achieves high satisfaction probability (e.g., 99.99%) in simulations and real robot experiments.

Less conservative than existing methods, leading to higher success rates.

Demonstrates effectiveness on various robotic systems, including a quadrupedal robot.

Abstract

We study feedback motion planning for continuous-time stochastic nonlinear systems under signal temporal logic (STL) specifications. We propose a framework that synthesizes control policies for chance-constrained STL trajectory optimization problems, with the goal of ensuring that the closed-loop stochastic system satisfies a given STL formula with high probability (e.g., 99.99\%). Our approach is based on a predicate erosion strategy that transforms the intractable stochastic problem into a deterministic STL trajectory optimization problem with tightened STL formula constraints. The amount of erosion is determined by a probabilistic reachable tube (PRT) that bounds the deviation between the stochastic trajectory and an associated nominal trajectory. To compute such bounds, we leverage contraction theory and feedback design, and develop several tracking controllers. This yields a complete feedback motion planning pipeline which can be implemented by numerical optimizations. We demonstrate the efficacy and versatility of the proposed framework through simulations on several robotic systems and through experiments on a real-world quadrupedal robot, and show that it is less conservative and achieves higher specification satisfaction probability than representative baselines.