Output Feedback Backup Control Barrier Functions: Safety Guarantees Under Input Bounds and State Estimation Error

TL;DR

This paper introduces Output Feedback Backup Control Barrier Functions (O-bCBFs) to ensure safety guarantees for control systems with input bounds and state estimation errors, addressing uncertainties in real-world scenarios.

Contribution

It develops a novel approach that uses an uncertainty envelope around estimated flows to guarantee safety despite state estimation errors and input constraints.

Findings

Ensures safety of the true state using an uncertainty envelope around estimated flows.

Guarantees the existence of a feasible control input under input constraints with state uncertainty.

Provides a method to maintain safety despite imperfect state information.

Abstract

Guaranteeing the safety of controllers is vital for real-world applications, but is markedly difficult when the states are not perfectly known and when the control inputs are bounded. Backup control barrier functions (bCBFs) use predictions of the flow under a prescribed controller to achieve safety in the presence of bounded inputs and perfect state information. However, when only an estimate of the true state is known, this flow may not be precisely computed, as the initial condition is unknown. Furthermore, the true flow evolves using feedback from the estimated state, thus introducing coupling between known and unknown flows. To address these challenges, we propose a technique that leverages an uncertainty envelope centered around the estimated flow and show that ensuring the safety of this envelope guarantees that the true state satisfies the safety constraints. Additionally, we show that in the presence of state uncertainty, using the resulting Output Feedback Backup Control Barrier Functions (O-bCBFs), there always exists a feasible control input that can guarantee the safety of the true state, even in the presence of input constraints.