Control Barrier Functions for Systems with Multiple Control Inputs

TL;DR

This paper extends High Order Control Barrier Functions to systems with multiple control inputs, proposing two methods to handle the relative degree problem and improve QP feasibility for safety guarantees.

Contribution

It introduces two novel approaches for HOCBFs in multi-input systems, addressing the relative degree challenge and enhancing control feasibility.

Findings

The methods improve QP feasibility under control bounds.

Demonstrated effectiveness on a two-input bicycle model.

Comparison shows trade-offs between the two proposed methods.

Abstract

Control Barrier Functions (CBFs) are becoming popular tools in guaranteeing safety for nonlinear systems and constraints, and they can reduce a constrained optimal control problem into a sequence of Quadratic Programs (QPs) for affine control systems. The recently proposed High Order Control Barrier Functions (HOCBFs) work for arbitrary relative degree constraints. One of the challenges in a HOCBF is to address the relative degree problem when a system has multiple control inputs, i.e., the relative degree could be defined with respect to different components of the control vector. This paper proposes two methods for HOCBFs to deal with systems with multiple control inputs: a general integral control method and a method which is simpler but limited to specific classes of physical systems. When control bounds are involved, the feasibility of the above mentioned QPs can also be significantly improved with the proposed methods. We illustrate our approaches on a unicyle model with two control inputs, and compare the two proposed methods to demonstrate their effectiveness and performance.