[Paper Review] A Collision Cone Approach for Control Barrier Functions

Manan Tayal, Bhavya Giri Goswami+6 more|arXiv (Cornell University)|Mar 11, 2024

Robotic Path Planning Algorithms4 citations

TL;DR

This paper proposes Collision Cone Control Barrier Functions (C3BFs), a novel real-time safety framework that integrates collision cone geometry with control barrier functions to ensure collision avoidance for unmanned ground and aerial vehicles. By constraining relative velocity to avoid the collision cone, the method enables safe, non-conservative navigation around dynamic obstacles through quadratic program-based control, validated on TurtleBot, Stoch-Jeep, and Crazyflie 2.1 drones with superior performance over higher-order CBFs.

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, 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, 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 (CBF-QPs). Comparative analysis with the state-of-the-art CBFs 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.

Motivation & Objective

• To address the limitations of existing control barrier functions in handling dynamic obstacles and lacking geometric intuition.
• To develop a unified, real-time safety framework applicable to both ground (UGV) and aerial (UAV) vehicles.
• To provide formal collision avoidance guarantees using a geometrically intuitive approach based on relative velocity constraints.
• To outperform state-of-the-art higher-order CBFs in feasibility and safety under dynamic obstacle conditions.
• To validate the approach through simulations and hardware experiments on diverse robotic platforms.

Proposed method

• Formulates a new class of control barrier functions based on the geometric concept of collision cones, ensuring relative velocity between vehicle and obstacle points away from the cone.
• Derives CBF-QP formulations for unicycle, bicycle, and quadrotor dynamics to compute real-time, safe control inputs.
• Uses a safety filter architecture that operates as a fast, real-time controller over existing path planners.
• Applies the method to point mass, unicycle, bicycle, and quadrotor models with both static and moving obstacles.
• Employs a quadratic program to optimize control inputs while enforcing the C3BF constraints for forward invariance of safe sets.
• Validates the framework using PyBullet simulations and hardware experiments on TurtleBot3, Stoch-Jeep, and Crazyflie 2.1 with motion capture-based state estimation.

Experimental results

Research questions

• RQ1 Can a geometrically intuitive CBF formulation improve safety and reduce conservatism in dynamic obstacle avoidance?
• RQ2 How does the proposed C3BF approach compare to higher-order CBFs in terms of feasibility and collision avoidance performance?
• RQ3 Can the C3BF-QP framework ensure real-time safety guarantees across diverse robotic platforms including UGVs and UAVs?
• RQ4 Does the method maintain robustness in complex scenarios involving multiple static and dynamic obstacles?
• RQ5 Can the same safety filter be applied uniformly across different vehicle models with varying kinematics?

Key findings

• The C3BF approach successfully avoids collisions with dynamic obstacles in both simulation and hardware experiments on TurtleBot3, Stoch-Jeep, and Crazyflie 2.1.
• The C3BF-QP controller demonstrated robust performance in multi-obstacle environments, including long and spherical static obstacles.
• The method outperformed higher-order CBFs (HO-CBFs), which failed to avoid high-speed approaching obstacles and struggled with long obstacles in projection CBF cases.
• Hardware experiments confirmed real-time feasibility, with control commands computed and transmitted at 100 Hz using motion capture and onboard filtering.
• The controller maintained safe trajectories even in multi-agent scenarios with identical safety filters, demonstrating scalability and robustness.
• The C3BF framework provides formal safety guarantees while being less conservative than existing CBF-based methods.