Gradient-Based STL Control with Application to Nonholonomic Systems

TL;DR

This paper develops gradient-based control methods for dynamical systems with temporal logic specifications, extending to nonholonomic systems like unicycles, and demonstrates their effectiveness through simulations.

Contribution

Introduces a class of gradient-based controllers with satisfaction guarantees, extended for unicycle dynamics, and explores their combination for complex tasks.

Findings

Controllers provide satisfaction guarantees for simple systems.

Extension of controllers to unicycle-like dynamics.

Simulation results demonstrate practical effectiveness.

Abstract

In this paper, we study the control of dynamical systems under temporal logic task specifications using gradient-based methods relying on quantitative measures that express the extent to which the tasks are satisfied. A class of controllers capable of providing satisfaction guarantees for simple systems and specifications is introduced and then extended for the case of unicycle-like dynamics. The possibility of combining such controllers in order to tackle more complex task specifications while retaining their computational efficiency is examined, and the practicalities related to an effective combination are demonstrated through a simulation study. The introduced framework for controller design lays ground for future work in the direction of effectively combining such elementary controllers for the purpose of aiding exploration in learning algorithms.