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 controller 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.

Automated summary

We develop a method for synthesizing control policies for stochastic, linear, time-varying systems that must perform tasks specified in signal temporal logic. The method efficiently computes the probability of system satisfaction and obtains sample-efficient gradients to optimize controllers that maximize the chances of satisfying the specification. The approach is demonstrated through examples of a mobile robot and a mobile manipulator in simulation.