SC3BF: Shifted Collision Cone Control Barrier Function for Dynamic Obstacle Avoidance

2026-10-06

AI Summary

This study addresses the excessive conservatism of traditional velocity-space Control Barrier Function (CBF) collision cones, which reject all relative velocities directed toward obstacles. To overcome this limitation, we propose a shifted collision cone CBF method that introduces a state-dependent allowance mechanism, enabling robots to dynamically approach obstacles based on distance and velocity. We theoretically prove the existence of a non-zero safety margin and derive its closed-form solution without requiring assumptions on minimum forward velocity or clearance margins. Integrated with quadratic programming optimization and a kinematic bicycle model, experiments in multi-moving-obstacle scenarios demonstrate that the proposed method significantly improves goal-reaching rates compared to baseline approaches while reducing nominal control modifications by approximately 50%.

Abstract

The collision cone used by velocity-space control barrier functions is conservative: it rejects every relative velocity aimed into an obstacle, however slow. We propose the \emph{shifted collision-cone CBF} (SC3BF), which adds a state-dependent \emph{allowance} to the cone condition, so the robot may approach the obstacle at a rate that grows with distance and with its own speed. SC3BF is enforced by an ordinary quadratic program, and its safe set is forward invariant under bounded inputs without a minimum forward speed or a clearance margin. We prove that a nonzero allowance preserving safety always exists, and derive one in closed form. Against three velocity-space baselines on a kinematic bicycle among up to $100$ moving obstacles, SC3BF reaches the goal more often and modifies the nominal input less than half as much.

Problem

• Dynamic Obstacle Avoidance
• Control Barrier Function
• Collision Cone
• Velocity Space

Innovation

• Control Barrier Function
• Collision Cone
• Dynamic Obstacle Avoidance
• Quadratic Programming
• Shifted Collision-Cone