Robustness-based Synthesis for Stochastic Systems under Signal Temporal Logic Tasks

We develop a method for synthesizing control policies for stochastic, linear, time-varying systems that must perform tasks specified in signal temporal logic. We build upon an efficient, sampling-based framework that computes the probability of the system satisfying its specification. By exploiting the properties of linear systems and robustness score in temporal logic specifications, we obtain sample-efficient gradients of the satisfaction probability with respect to con-troller parameters. Therefore, by applying gradient descent we obtain locally optimized controllers that maximize the chances of satisfying the specification. We demonstrate our approach through examples of a mobile robot and a mobile manipulator in simulation.