Safe Controller Synthesis with Tunable Input-to-State Safe Control Barrier Functions

TL;DR

This paper introduces tunable input-to-state safe control barrier functions (TISSf-CBFs) that enable the synthesis of less conservative, provably safe controllers for systems with varying input disturbances, enhancing robustness in uncertain environments.

Contribution

It generalizes input to state safety (ISSf) with TISSf-CBFs, allowing for tunable, less conservative safety guarantees under state-dependent disturbances.

Findings

TISSf-CBFs guarantee safety under varying disturbances.

Demonstrated on a control system with input disturbance.

Applied to a safe cruise control for a heavy-duty truck.

Abstract

To bring complex systems into real world environments in a safe manner, they will have to be robust to uncertainties - both in the environment and the system. This paper investigates the safety of control systems under input disturbances, wherein the disturbances can capture uncertainties in the system. Safety, framed as forward invariance of sets in the state space, is ensured with the framework of control barrier functions (CBFs). Concretely, the definition of input to state safety (ISSf) is generalized to allow the synthesis of non-conservative, tunable controllers that are provably safe under varying disturbances. This is achieved by formulating the concept of tunable input to state safe control barrier functions (TISSf-CBFs) which guarantee safety for disturbances that vary with state and, therefore, provide less conservative means of accommodating uncertainty. The theoretical results are demonstrated with a simple control system with input disturbance and also applied to design a safe connected cruise controller for a heavy duty truck.