Explicit Control Barrier Function-based Safety Filters and their Resource-Aware Computation

TL;DR

This paper introduces a resource-aware, closed-form implementation of control barrier function safety filters that enables high-frequency, efficient safety enforcement in control systems.

Contribution

It provides a novel closed-form controller expression for CBF-based safety filters, improving computational efficiency and enabling resource-aware safety filtering.

Findings

Closed-form solutions enable high-frequency safety filtering.

Partitioning the state-space allows efficient, region-specific control.

The approach is applicable to aerospace control and safe reinforcement learning.

Abstract

This paper studies the efficient implementation of safety filters that are designed using control barrier functions (CBFs), which minimally modify a nominal controller to render it safe with respect to a prescribed set of states. Although CBF-based safety filters are often implemented by solving a quadratic program (QP) in real time, the use of off-the-shelf solvers for such optimization problems poses a challenge in applications where control actions need to be computed efficiently at very high frequencies. In this paper, we introduce a closed-form expression for controllers obtained through CBF-based safety filters. This expression is obtained by partitioning the state-space into different regions, with a different closed-form solution in each region. We leverage this formula to introduce a resource-aware implementation of CBF-based safety filters that detects changes in the partition region and uses the closed-form expression between changes. We showcase the applicability of our approach in examples ranging from aerospace control to safe reinforcement learning.