SafeSpace: Aggregating Safe Sets from Backup Control Barrier Functions under Input Constraints

TL;DR

This paper introduces a method to combine multiple certified safe regions in control systems into a larger, unified safe set using enhanced control barrier functions, improving safety guarantees under input constraints.

Contribution

It extends the combinatorial CBF framework with an auxiliary variable for logical composition, enabling aggregation of multiple safe sets into a single certified safe region.

Findings

The framework yields a continuous safety filter over the aggregated safe set.

Demonstrated on spacecraft safety problems, expanding operational safety regions.

Abstract

Control barrier functions (CBFs) provide a principled framework for enforcing safety in control systems -- yet the certified safe operating region in practice is often conservative, especially under input bounds. In many applications, multiple smaller safe sets can be certified independently, e.g., around distinct equilibria with different stabilizing controllers. This paper proposes a framework for uniting such regions into a single certified safe set using \emph{combinatorial CBFs}. We refine the combinatorial CBF framework by introducing an auxiliary variable that enables logical compositions of individual CBFs. In the proposed framework, we show that such compositions yield a \emph{generalized combinatorial CBF} under a condition termed \emph{conjunctive compatibility}. Building on this result, we extend the framework to enable the aggregation of multiple implicit safe sets generated by the backup CBF framework. We show that the resulting CBF-based quadratic program yields a continuous safety filter over the aggregated safe region. The approach is demonstrated on two spacecraft safety problems, safe attitude control and safe station keeping, where multiple certified safe regions are combined to expand the operational envelope.