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Control Barrier Functions in Dynamic UAVs for Kinematic Obstacle Avoidance: A Collision Cone Approach

Manan Tayal, Rajpal Singh, Jishnu Keshavan, Shishir Kolathaya

TL;DR

A novel technique for safely navigating a quadrotor along a desired route while avoiding kinematic obstacles is introduced, using a new constraint formulation that employs control barrier functions (CBFs) and collision cones to ensure that the relative velocity between the quadrotor and the obstacle always avoids a cone of vectors that may lead to a collision.

Abstract

Unmanned aerial vehicles (UAVs), specifically quadrotors, have revolutionized various industries with their maneuverability and versatility, but their safe operation in dynamic environments heavily relies on effective collision avoidance techniques. This paper introduces a novel technique for safely navigating a quadrotor along a desired route while avoiding kinematic obstacles. We propose a new constraint formulation that employs control barrier functions (CBFs) and collision cones to ensure that the relative velocity between the quadrotor and the obstacle always avoids a cone of vectors that may lead to a collision. By showing that the proposed constraint is a valid CBF for quadrotors, we are able to leverage its real-time implementation via Quadratic Programs (QPs), called the CBF-QPs. Validation includes PyBullet simulations and hardware experiments on Crazyflie 2.1, demonstrating effectiveness in static and moving obstacle scenarios. Comparative analysis with literature, especially higher order CBF-QPs, highlights the proposed approach's less conservative nature. Simulation and Hardware videos are available here: https://tayalmanan28.github.io/C3BF-UAV/

Control Barrier Functions in Dynamic UAVs for Kinematic Obstacle Avoidance: A Collision Cone Approach

TL;DR

A novel technique for safely navigating a quadrotor along a desired route while avoiding kinematic obstacles is introduced, using a new constraint formulation that employs control barrier functions (CBFs) and collision cones to ensure that the relative velocity between the quadrotor and the obstacle always avoids a cone of vectors that may lead to a collision.

Abstract

Unmanned aerial vehicles (UAVs), specifically quadrotors, have revolutionized various industries with their maneuverability and versatility, but their safe operation in dynamic environments heavily relies on effective collision avoidance techniques. This paper introduces a novel technique for safely navigating a quadrotor along a desired route while avoiding kinematic obstacles. We propose a new constraint formulation that employs control barrier functions (CBFs) and collision cones to ensure that the relative velocity between the quadrotor and the obstacle always avoids a cone of vectors that may lead to a collision. By showing that the proposed constraint is a valid CBF for quadrotors, we are able to leverage its real-time implementation via Quadratic Programs (QPs), called the CBF-QPs. Validation includes PyBullet simulations and hardware experiments on Crazyflie 2.1, demonstrating effectiveness in static and moving obstacle scenarios. Comparative analysis with literature, especially higher order CBF-QPs, highlights the proposed approach's less conservative nature. Simulation and Hardware videos are available here: https://tayalmanan28.github.io/C3BF-UAV/
Paper Structure (20 sections, 2 theorems, 14 equations, 8 figures, 1 table)

This paper contains 20 sections, 2 theorems, 14 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Contribution and Paper Structure
  3. Organisation
  4. Preliminaries
  5. Quadrotor model
  6. Control barrier functions (CBFs)
  7. Safety Filter Design
  8. Collision Cone CBF (C3BF) candidate for quadrotors
  9. Collision Cone CBFs on Quadrotor
  10. 3D CBF candidate
  11. Projection CBF candidate
  12. Comparison with Higher Order CBFs
  13. Results and Discussions
  14. Simulation setup
  15. Experimental Results
  16. ...and 5 more sections

Key Result

Theorem 1

Given the quadrotor model eqn:quadrotor_model, the proposed CBF candidate eqn:CC-CBF with $p_{\rm{rel}},v_{\rm{rel}}$ defined by eq:pos-vec-3D, eq:vel-vec-3D is a valid CBF defined for the set $\mathcal{D}$.

Figures (8)

  • Figure 1: World coordinates and body fixed coordinates of Crazyflie and Euler's angles defined in these coordinates
  • Figure 2: 3D CBF candidate: The dimensions of the obstacle are comparable to each other, it can be assumed as a sphere
  • Figure 3: Projection CBF candidate: One of the dimensions, of the obstacle, is bigger than the other dimensions, it can be assumed as a cylinder.
  • Figure 4: Comparison of HO-CBF with C3BF. Here we are trying to compare the $\phi'$ and $\phi$ obtained from the two CBF formulations. It can be observed that $\phi'$ (pink cone) is dependent on $v_{rel}$, while $\phi$ (yellow cone) is a constant. The HO-CBF guarantees safety for a set that is not only smaller but also dependent on $v_{rel}$ as shown by the pink cone. Hence, HO-CBF is more conservative compared to C3BF.
  • Figure 5: Interaction with static obstacles: overtaking (a), (b), and braking (c) behavior of the quadrotor, Section \ref{['section: 3D-CBF']}.In all these cases the reference velocity of the quadrotor is 1m/s.
  • ...and 3 more figures

Theorems & Definitions (3)

  • Definition 1: Control barrier function (CBF)
  • Theorem 1
  • Theorem 2