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

arXiv: https://arxiv.org/abs/2310.05261 · HTML: https://mlsanity.com/paper/2310.05261/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2023.

## Built on by (most cited first, 3 of 3)

- [Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation](https://mlsanity.com/paper/2401.05629/) (2024)
- [Domain Adaptive Safety Filters via Deep Operator Learning](https://mlsanity.com/paper/2410.14528/) (2024)
- [CN-CBF: Composite Neural Control Barrier Function for Robot Navigation in Dynamic Environments](https://mlsanity.com/paper/2603.06921/) (2026)

## Abstract (arXiv)

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.