Enforcing Mixed State-Input Constraints with Multiple Backup Control Barrier Functions: A Projection-based Approach

TL;DR

This paper introduces a novel control framework that enforces mixed state-input safety constraints using backup control barrier functions, employing a projection-based method to handle complex constraints efficiently.

Contribution

It generalizes backup CBFs to manage multiple decoupled constraints and converts mixed constraints into state constraints via projection, simplifying synthesis.

Findings

Successfully applied to an inverted pendulum example

Enforces constraints on angle, torque, and power simultaneously

Eliminates need for saturating backup control laws in certain cases

Abstract

Ensuring the safety of control systems often requires the satisfaction of constraints on states (such as position or velocity), control inputs (such as force), and a mixture of states and inputs (such as power that depends on both velocity and force). This paper presents a safety-critical control framework for enforcing mixed state-input constraints through a generalization of backup control barrier functions (backup CBFs). First, we extend the backup CBF approach to maintain multiple decoupled state and input constraints using a single backup set-backup controller pair. Second, we address mixed state-input constraints by converting them into state constraints using a projection from the state-input space to the state space along the backup controller. In the special case of decoupled state and input constraints, the proposed method simplifies the synthesis of backup CBFs by eliminating the need for saturating backup control laws. Finally, we demonstrate the efficacy of the proposed method on an inverted pendulum example, where constraints on the angle (state), torque (input), and power (mixture of state and input) are satisfied simultaneously.