Ro-To-Go! Robust Reactive Control with Signal Temporal Logic

Abstract

Signal Temporal Logic robustness is a common objective for optimal robot control, but its dependence on history limits the robot's decision-making capabilities when used in model predictive control approaches. In this work, we introduce Signal Temporal Logic robustness-to-go, a new quantitative semantics for the logic that isolates the contributions of suffix trajectories. We prove its relationship to formula progression for Metric Temporal Logic, and show that the robustness-to-go depends only on the suffix trajectory and progressed formula. We implement robustness-to-go as the objective in a model predictive control algorithm and use formula progression to efficiently evaluate it online. We test the algorithm in simulation and compare it to model predictive control using other robustness measures. Our experiments show that using robustness-to-go improves performance compared to using traditional robustness.