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Real Time Safety of Fixed-wing UAVs using Collision Cone Control Barrier Functions

Aryan Agarwal, Ravi Agrawal, Manan Tayal, Pushpak Jagtap, Shishir Kolathaya

TL;DR

This work addresses real-time collision avoidance for high-speed fixed-wing UAVs in cluttered environments by developing Collision Cone Control Barrier Functions (C3BF) and implementing them as CBF-QP safety filters. It formulates a 3D Dubins-type UAV model, introduces a naive C3BF candidate and a backstepped extension, and demonstrates through simulations that the backstepped C3BF can extend safety to a larger state set while enabling smoother trajectories and lower control effort than existing CBFs. The key contributions are the CBF formulation for fixed-wing dynamics, the analysis of controllability limitations in the naive approach, and the backstepping enhancement that broadens safety guarantees, demonstrated against a baseline CBF. This work has practical implications for real-time, formally safe collision avoidance in UAVs operating near moving obstacles, laying groundwork for theoretical guarantees and broader obstacle scenarios.

Abstract

Fixed-wing UAVs have transformed the transportation system with their high flight speed and long endurance, yet their safe operation in increasingly cluttered environments depends heavily on effective collision avoidance techniques. This paper presents a novel method for safely navigating an aircraft along a desired route while avoiding moving obstacles. We utilize a class of control barrier functions (CBFs) based on collision cones to ensure the relative velocity between the aircraft and the obstacle consistently avoids a cone of vectors that might lead to a collision. By demonstrating that the proposed constraint is a valid CBF for the aircraft, we can leverage its real-time implementation via Quadratic Programs (QPs), termed the CBF-QPs. Validation includes simulating control law along trajectories, showing effectiveness in both static and moving obstacle scenarios.

Real Time Safety of Fixed-wing UAVs using Collision Cone Control Barrier Functions

TL;DR

This work addresses real-time collision avoidance for high-speed fixed-wing UAVs in cluttered environments by developing Collision Cone Control Barrier Functions (C3BF) and implementing them as CBF-QP safety filters. It formulates a 3D Dubins-type UAV model, introduces a naive C3BF candidate and a backstepped extension, and demonstrates through simulations that the backstepped C3BF can extend safety to a larger state set while enabling smoother trajectories and lower control effort than existing CBFs. The key contributions are the CBF formulation for fixed-wing dynamics, the analysis of controllability limitations in the naive approach, and the backstepping enhancement that broadens safety guarantees, demonstrated against a baseline CBF. This work has practical implications for real-time, formally safe collision avoidance in UAVs operating near moving obstacles, laying groundwork for theoretical guarantees and broader obstacle scenarios.

Abstract

Fixed-wing UAVs have transformed the transportation system with their high flight speed and long endurance, yet their safe operation in increasingly cluttered environments depends heavily on effective collision avoidance techniques. This paper presents a novel method for safely navigating an aircraft along a desired route while avoiding moving obstacles. We utilize a class of control barrier functions (CBFs) based on collision cones to ensure the relative velocity between the aircraft and the obstacle consistently avoids a cone of vectors that might lead to a collision. By demonstrating that the proposed constraint is a valid CBF for the aircraft, we can leverage its real-time implementation via Quadratic Programs (QPs), termed the CBF-QPs. Validation includes simulating control law along trajectories, showing effectiveness in both static and moving obstacle scenarios.
Paper Structure (14 sections, 2 theorems, 13 equations, 3 figures)

This paper contains 14 sections, 2 theorems, 13 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Control barrier functions (CBFs)
  4. Safety Filter Design
  5. Collision Cone CBF (C3BF) candidate for fixed wing UAVs
  6. Collision Cone CBFs on Fixed Wing UAV
  7. Fixed Wing UAV model
  8. Naive C3BF candidate
  9. C3BF Candidate with Backstepping
  10. Results and Discussions
  11. Simulation Setup
  12. C3BF - Naive vs Backstepped
  13. C3BF vs existing CBF
  14. Conclusions

Key Result

Theorem 1

Given the fixed wing UAV model eqn:kinematic_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 $\mathcal{C}$.

Figures (3)

  • Figure 1: Aircraft's linear and angular velocities defined in body-fixed frame. (X,Y,Z) represents earth-fixed frame.
  • Figure 2: 3D CBF candidate: The dimensions of the obstacle are comparable to each other, it can be assumed as a sphere
  • Figure 3: Aircraft's behaviour following C3BF: Obstacle incoming head-on to the aircraft (a), Comparision of aircraft's behaviour following C3BF and CBF in molnar2024collision for a static obstacle (b) and for constant velocity obstacle (c). In all three cases, the collision radius $r = 100m$.

Theorems & Definitions (3)

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