Safety-Critical Control using Optimal-decay Control Barrier Function with Guaranteed Point-wise Feasibility

TL;DR

This paper introduces an optimal-decay control barrier function approach that guarantees point-wise safety feasibility in robotics control, addressing infeasibility issues in existing quadratic program-based safety methods.

Contribution

It proposes a novel optimal-decay form for CBFs that ensures point-wise feasibility, improving safety-critical control under input constraints.

Findings

Guarantees point-wise safety feasibility inside the safe set

Validated through numerical simulations in adaptive cruise control

Addresses infeasibility issues in CLF-CBF-QP methods

Abstract

Safety is one of the fundamental problems in robotics. Recently, a quadratic program-based control barrier function (CBF) method has emerged as a way to enforce safety-critical constraints. Together with control Lyapunov function (CLF), it forms a safety-critical control strategy, named CLF-CBF-QP, which can mediate between achieving the control objective and ensuring safety, while being executable in real-time. However, once additional constraints such as input constraints are introduced, the CLF-CBF-QP may encounter infeasibility. In order to address the challenge that arises due to the infeasibility, we propose an optimal-decay form for safety-critical control wherein the decay rate of the CBF is optimized point-wise in time so as to guarantee point-wise feasibility when the state lies inside the safe set. The proposed control design is numerically validated using an adaptive cruise control example.