Control Barrier Function for Linearizable Systems with High Relative Degrees from Signal Temporal Logics: A Reference Governor Approach
Kaier Liang, Mingyu Cai, Cristian-Ioan Vasile
TL;DR
The paper tackles safety-critical navigation under Signal Temporal Logic ($STL$) tasks for high relative-degree, feedback-linearizable systems. It introduces an explicit reference governor-guided control barrier function (ERG-guided $CBF$) framework that enables the use of first-order $CBF$s to manage safety and STL satisfaction in high-order dynamics, augmented by a dynamic safety margin and a navigation field. A gradient-based, differentiable tuning approach (DiffTune) optimizes control parameters to reduce STL task completion time and improve tracking of the governor. The methodology is validated through simulations on a double integrator and a quadrotor, showing superior performance over traditional high-order $CBF$ methods in constrained environments with narrow passages, and demonstrating practical impact for safe, STL-compliant autonomous navigation.
Abstract
This paper considers the safety-critical navigation problem with Signal Temporal Logic (STL) tasks. We developed an explicit reference governor-guided control barrier function (ERG-guided CBF) method that enables the application of first-order CBFs to high-order linearizable systems. This method significantly reduces the conservativeness of the existing CBF approaches for high-order systems. Furthermore, our framework provides safety-critical guarantees in the sense of obstacle avoidance by constructing the margin of safety and updating direction of safe evolution in the agent's state space. To improve control performance and enhance STL satisfaction, we employ efficient gradient-based methods for iteratively learning optimal parameters of ERG-guided CBF. We validate the algorithm through both high-order linear and nonlinear systems. A video demonstration can be found on: \url{https://youtu.be/ZRmsA2FeFR4}