Set-Based Control Barrier Functions for Scalable Safety Filter Design

TL;DR

This paper introduces set-based control barrier functions for large-scale linear systems, enabling scalable, tunable safety filters that integrate reachability analysis and MPC, with proven stability and reduced computational complexity.

Contribution

It proposes a novel set-based CBF framework using Minkowski functionals, facilitating scalable safety filter design for high-dimensional systems with convex constraints.

Findings

Successfully applied to high-dimensional systems and motion control tasks.

Achieved safety guarantees with reduced runtime via learning-based approximations.

Validated on an electric drive with short sampling times.

Abstract

Industrial control applications require high performance under strict constraints. Control barrier functions (CBFs) provide principled safety mechanisms, but constructing CBF-based safety filters for large-scale systems is challenging. We introduce set-based CBFs for linear systems with convex constraints by defining the barrier via the Minkowski functional of a control invariant set. This invariant set can be obtained from scalable computations, including reachability analysis and model predictive control (MPC). The approach yields tunable safety filters with dampened intervention and asymptotic stability of the set of safe states. We derive reformulations embedding set-based CBF constraints into convex optimization for common set representations and present learning-based approximations reducing runtime while preserving safety. We demonstrate the approach through simulations on a high-dimensional system and a motion control task, and validate the method experimentally on an electric drive with short sampling times.