Control Barrier Function for Linearizable Systems with High Relative Degrees from Signal Temporal Logics: A Reference Governor Approach

TL;DR

This paper introduces an ERG-guided CBF method for high-order linearizable systems that reduces conservativeness and guarantees obstacle avoidance, with iterative learning for improved STL satisfaction.

Contribution

It presents a novel ERG-guided CBF framework enabling first-order CBF application to high-order systems with safety guarantees and improved control performance.

Findings

Reduces conservativeness of CBF approaches for high-order systems

Provides safety guarantees for obstacle avoidance

Demonstrates effectiveness on linear and nonlinear systems

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}