Feedback Motion Planning for Stochastic Nonlinear Systems with Signal Temporal Logic Specifications
This work addresses the challenge of synthesizing control policies for stochastic systems with temporal logic constraints, which is important for safety-critical robotics applications.
The paper proposes a feedback motion planning framework for stochastic nonlinear systems under signal temporal logic (STL) specifications, achieving high satisfaction probability (e.g., 99.99%) via a predicate erosion strategy and probabilistic reachable tubes. Simulations and real-world quadruped experiments show it is less conservative and achieves higher satisfaction probability than baselines.
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.