Output Feedback Backup Control Barrier Functions: Safety Guarantees Under Input Bounds and State Estimation Error
This addresses safety guarantees for real-world control applications where state information is imperfect and inputs are bounded, representing an incremental improvement over existing methods.
The paper tackles the problem of ensuring safety in control systems with bounded inputs and state estimation errors by proposing Output Feedback Backup Control Barrier Functions (O-bCBFs), which guarantee safety for the true state using an uncertainty envelope around the estimated flow, with feasibility proven under input constraints.
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.