Compositions of Multiple Control Barrier Functions Under Input Constraints

TL;DR

This paper introduces a method to design multiple Control Barrier Functions (CBFs) that ensure feasible control inputs under input constraints, enabling safe operation of nonlinear systems through decoupled CBF design and guaranteed viability.

Contribution

It provides a novel approach to decouple the design of multiple CBFs and guarantees the feasibility of the combined control constraints under input limitations.

Findings

Decoupled CBF design ensures feasibility under input constraints.

The combined CBF set forms a viability domain.

Simulation demonstrates effective nonlinear orientation control.

Abstract

This paper presents a methodology for ensuring that the composition of multiple Control Barrier Functions (CBFs) always leads to feasible conditions on the control input, even in the presence of input constraints. In the case of a system subject to a single constraint function, there exist many methods to generate a CBF that ensures constraint satisfaction. However, when there are multiple constraint functions, the problem of finding and tuning one or more CBFs becomes more challenging, especially in the presence of input constraints. This paper addresses this challenge by providing tools to 1) decouple the design of multiple CBFs, so that a CBF can be designed for each constraint function independently of other constraints, and 2) ensure that the set composed from all the CBFs together is a viability domain. Thus, a quadratic program subject to all the CBFs simultaneously is always feasible. The utility of this methodology is then demonstrated in simulation for a nonlinear orientation control system.