Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Collision Cone Approach for Control Barrier Functions

Manan Tayal, Bhavya Giri Goswami, Karthik Rajgopal, Rajpal Singh, Tejas Rao, Jishnu Keshavan, Pushpak Jagtap, Shishir Kolathaya

TL;DR

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 by modifying the control inputs from existing path-planning controllers.

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.

A Collision Cone Approach for Control Barrier Functions

TL;DR

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 by modifying the control inputs from existing path-planning controllers.

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.
Paper Structure (29 sections, 4 theorems, 43 equations, 16 figures, 1 table)

This paper contains 29 sections, 4 theorems, 43 equations, 16 figures, 1 table.

Table of Contents

  1. Introduction
  2. Contribution and Paper Structure
  3. Organisation
  4. Preliminaries
  5. Unicycle model
  6. Bicycle model
  7. Quadrotor model
  8. Control barrier functions (CBFs)
  9. Controller synthesis for real-time safety
  10. Classical CBFs and moving obstacle avoidance
  11. Ellipse-CBF Candidate
  12. Higher Order CBFs
  13. Collision Cone CBF (C3BF)
  14. Application to Unicycle
  15. Application to Bicycle
  16. ...and 14 more sections

Key Result

Theorem 1

Given the acceleration controlled unicycle model eqn:Acceleration controlled Unicycle model, the proposed CBF candidate eqn:CC-CBF with $p_{\rm{rel}},v_{\rm{rel}}$ defined by eq:positionvectorunicycle, eq:velocityvectorunicycle is a valid CBF defined for the set $\mathcal{D}$.

Figures (16)

  • Figure 1: Test setups: TurtleBot3 Burger; Stoch-Jeep; Crazyflie 2.1. respectively
  • Figure 2: Schematic of Unicycle (left); Bicycle model (right); Quadrotor model (down).
  • Figure 3: Construction of collision cone for an elliptical obstacle considering the ego-vehicle's dimensions (width: $w$).
  • Figure 4: 3D CBF candidate: The dimensions of the obstacle are comparable to each other, it can be assumed as a sphere
  • Figure 5: Projection CBF candidate: One of the dimensions, of the obstacle, is bigger than the other dimensions, it can be assumed as a cylinder.
  • ...and 11 more figures

Theorems & Definitions (13)

  • Remark 1
  • Definition 1: Control barrier function (CBF)
  • Theorem 1
  • proof
  • Remark 2
  • Theorem 2
  • proof
  • Remark 3
  • Theorem 3
  • proof
  • ...and 3 more