# Activated Backstepping with Control Barrier Functions for the Safe Navigation of Automated Vehicles

## TL;DR

This paper presents activated backstepping, a new control synthesis method combining control barrier functions with an activation mechanism, enabling less conservative safety guarantees for automated vehicle navigation.

## Contribution

It introduces activated backstepping, a novel approach to synthesize less conservative control barrier functions for high-relative-degree safety constraints.

## Key findings

- Successfully applied to an inverted pendulum example
- Achieved collision-free navigation in simulated automated vehicle scenarios
- Demonstrated geometric interpretation and advantages over existing methods

## Abstract

This paper introduces a novel safety-critical control method through the synthesis of control barrier functions (CBFs) for systems with high-relative-degree safety constraints. By extending the procedure of CBF backstepping, we propose activated backstepping - a constructive method to synthesize valid CBFs. The novelty of our method is the incorporation of an activation function into the CBF, which offers less conservative safe sets in the state space than standard CBF backstepping. We demonstrate the proposed method on an inverted pendulum example, where we explain the underlying geometric meaning in the state space and provide comparisons with existing CBF synthesis techniques. Finally, we implement our method to achieve collision-free navigation for automated vehicles using a kinematic bicycle model in simulation.