Time-Varying Soft-Maximum Control Barrier Functions for Safety in an A Priori Unknown Environment

TL;DR

This paper introduces a novel time-varying soft-maximum control barrier function method that ensures safety in unknown environments by combining local perception-based safe sets into a single, smooth, composite CBF for real-time control of robots.

Contribution

It proposes a new smooth, time-varying soft-maximum composite CBF that can handle arbitrary relative degrees and dynamically model safe sets from perception data.

Findings

Successfully applied to a nonholonomic ground robot with inertia.

Demonstrated real-time safety guarantees in unknown environments.

Effectively combines local safe sets into a global safety model.

Abstract

This paper presents a time-varying soft-maximum composite control barrier function (CBF) that can be used to ensure safety in an a priori unknown environment, where local perception information regarding the safe set is periodically obtained. We consider the scenario where the periodically obtained perception feedback can be used to construct a local CBF that models a local subset of the unknown safe set. Then, we use a novel smooth time-varying soft-maximum function to compose the N most recently obtained local CBFs into a single CBF. This composite CBF models an approximate union of the N most recently obtained local subsets of the safe set. Notably, this composite CBF can have arbitrary relative degree r. Next, this composite CBF is used as a rth-order CBF constraint in a real-time optimization to determine a control that minimizes a quadratic cost while guaranteeing that the state stays in a time-varying subset of the unknown safe set. We also present an application of the time-varying soft-maximum composite CBF method to a nonholonomic ground robot with nonnegligible inertia. In this application, we present a simple approach to generate the local CBFs from the periodically obtained perception data.