Handling Disjunctions in Signal Temporal Logic Based Control Through Nonsmooth Barrier Functions

TL;DR

This paper introduces a novel control approach using nonsmooth control barrier functions for complex spatio-temporal tasks specified by Signal Temporal Logic, reducing conservativeness and enabling handling of disjunctions.

Contribution

It develops a nonsmooth, time-varying control barrier function framework that exploits piece-wise smoothness and overcomes gradient vanishing, expanding applicability to complex STL tasks.

Findings

Reduces conservativeness in control barrier functions.

Enables handling of disjunctions in STL-based control.

Demonstrates effectiveness in simulation example.

Abstract

For a class of spatio-temporal tasks defined by a fragment of Signal Temporal Logic (STL), we construct a nonsmooth time-varying control barrier function (CBF) and develop a controller based on a set of simple optimization problems. Each of the optimization problems invokes constraints that allow to exploit the piece-wise smoothness of the CBF for optimization additionally to the common gradient constraint in the context of CBFs. In this way, the conservativeness of the control approach is reduced in those points where the CBF is nonsmooth. Thereby, nonsmooth CBFs become applicable to time-varying control tasks. Moreover, we overcome the problem of vanishing gradients for the considered class of constraints which allows us to consider more complex tasks including disjunctions compared to approaches based on smooth CBFs. As a well-established and systematic method to encode spatiotemporal constraints, we define the class of tasks under consideration as an STL-fragment. The results are demonstrated in a relevant simulation example.