Matrix Control Barrier Functions

TL;DR

This paper extends control barrier functions to matrix-valued functions, enabling the handling of more complex safe sets through semidefinite programming, with applications demonstrated in drone safety and obstacle avoidance.

Contribution

It introduces matrix control barrier functions for richer safe set descriptions and develops continuous safety filters using semidefinite programming.

Findings

Effective in maintaining drone network connectivity.

Successfully applied to nonsmooth obstacle avoidance.

Demonstrated continuity of safety filters in experiments.

Abstract

This paper generalizes the control barrier function framework by replacing scalar-valued functions with matrix-valued ones. Specifically, we develop barrier conditions for safe sets defined by matrix inequalities -- both semidefinite and indefinite. Matrix inequalities can be used to describe a richer class of safe sets, including nonsmooth ones. The safety filters constructed from our proposed matrix control barrier functions via semidefinite programming (CBF-SDP) are shown to be continuous. Our matrix formulation naturally provides a continuous safety filter for Boolean-based control barrier functions, notably for disjunctions (OR), without relaxing the safe set. We illustrate the effectiveness of the proposed framework with applications in drone network connectivity maintenance and nonsmooth obstacle avoidance, both in simulations and hardware experiments.