Universal Barrier Functions for Safety and Stability of Constrained Nonlinear Systems

TL;DR

This paper introduces the Universal Barrier Function (UBF), a novel tool for synthesizing controllers that ensure safety and stability in constrained nonlinear systems, with theoretical guarantees and practical demonstrations.

Contribution

We propose the Universal Barrier Function (UBF), a new unified approach for safe and stabilizing control synthesis for nonlinear systems with complex safety and input constraints.

Findings

UBF-QP guarantees safe and stabilizing control inputs.

Existence of UBF is proven under mild conditions.

Numerical simulations validate the approach's effectiveness.

Abstract

In this paper, we address the problem of synthesizing safe and stabilizing controllers for nonlinear systems subject to complex safety specifications and input constraints. We introduce the Universal Barrier Function (UBF), a single continuously differentiable scalar-valued function that encodes both stability and safety criteria while accounting for input constraints. Using the UBF, we formulate a Quadratic Program (UBF-QP) to generate control inputs that are both safe and stabilizing under input constraints. We demonstrate that the UBF-QP is feasible if a UBF exists. Furthermore, under mild conditions, we prove that a UBF always exists. The proposed framework is then extended to systems with higher relative degrees. Finally, numerical simulations illustrate the effectiveness of our proposed approach.