A Collision Cone Approach for Control Barrier Functions

¹ Cyber-Physical Systems, Indian Institute of Science, Bangalore ² System Design Engineering, University of Waterloo ³ Mechanical Engineering, Indian Institute of Science, Bangalore

Abstract

This work presents a unified approach for collision avoidance using Collision-Cone Control Barrier Functions (CBFs) in both ground (UGV) and aerial (UAV) unmanned vehicles. We propose a novel CBF formulation inspired by collision cones, commonly used in trajectory planning, to ensure safety by constraining the relative velocity between the vehicle and the obstacle to always point away from each other. The efficacy of this approach is demonstrated through simulations and hardware implementations on the Turtlebot, Stoch-Jeep (Ackermann), and Crazyflie 2.1 quadrotor robot, showcasing its effectiveness in avoiding collisions with dynamic obstacles in both ground and aerial settings. The real-time controller is developed using CBF Quadratic Programs (QPs) formulation. Comparative analysis with existing CBF-QPs, particularly Higher-Order CBF (HOCBF), highlights the less conservative nature of the proposed approach. Overall, this research contributes to a novel control formation that can give a guarantee for collision avoidance in unmanned vehicles by modifying the control inputs from existing path-planning controllers, enhancing the vehicle's maneuverability and safety in dynamic environments.

Method Overview

A collision cone is the set of relative-velocity directions that, if followed, would eventually bring the vehicle into contact with an obstacle. Draw the two lines from the vehicle that are tangent to a circle of radius r enclosing the obstacle (obstacle size plus vehicle width); every relative-velocity vector that falls between those two lines is on a collision course. Staying safe just means keeping the relative-velocity vector outside that cone, i.e. always pointing it away from the obstacle.

The pink wedge is the collision cone: any relative velocity inside it (red) is on a collision course, anything outside it (green) is safe.

This geometric picture turns into a single scalar safety function h(x) = ⟨p_rel, v_rel⟩ + ∥p_rel∥ ∥v_rel∥ cosφ, where p_rel and v_rel are the relative position and velocity between vehicle and obstacle, and φ is the cone's half-angle (cosφ = √(∥p_rel∥² − r²) / ∥p_rel∥). Enforcing h(x) ≥ 0 as a control barrier function constraint in a QP filter is exactly the condition that the relative-velocity vector stays outside the cone.

Compared to a Higher-Order CBF (HOCBF) built the same way, C3BF lets the effective margin scale with ∥v_rel∥ instead of using a fixed constant γ. A fixed γ makes the estimated cone widen as relative speed increases — overly conservative at high speed — whereas C3BF's speed-scaled margin tracks the true collision cone much more tightly, which is what lets the vehicle maneuver closer to obstacles while still guaranteeing safety.

BibTeX

@ARTICLE{11407993, author={Tayal, Manan and Giri Goswami, Bhavya and Rajgopal, Karthik and Singh, Rajpal and Tejas Rao, M. and Keshavan, Jishnu and Jagtap, Pushpak and Nadubettu Yadukumar, Shishir}, journal={IEEE Transactions on Control Systems Technology}, title={A Collision Cone Approach for Control Barrier Functions}, year={2026}, volume={34}, number={3}, pages={1297-1310}, keywords={Quadrotors;Collision avoidance;Safety;Bicycles;Wheels;Real-time systems;Vehicle dynamics;Robots;Autonomous aerial vehicles;Vectors;Collision cone;control barrier function (CBF);real-time obstacle avoidance;safety-critical control}, doi={10.1109/TCST.2026.3661160}}

A Collision Cone Approach for Control Barrier Functions

Abstract

Method Overview

Simulation Results

Obstacle avoidance on UGVs (Unicycle & Bicycle Models)

Obstacle avoidance on UAV (Quadrotor Model)

Hardware Experiments

Obstacle avoidance on Turlebot (Unicycle Model)

Obstacle avoidance on Stoch-Jeep (Bicycle Model)

Obstacle avoidance on Crazyflie 2.1 (Quadrotor Model)

BibTeX