Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Feasibility-Enhanced Control Barrier Function Method for Multi-UAV Collision Avoidance

Qishen Zhong, Junlong Wu, Jian Yang, Guanwei Xiao, Junqi Wu, Zimeng Jiang, Pingan Fang

Abstract

This paper presents a feasibility-enhanced control barrier function (FECBF) framework for multi-UAV collision avoidance. In dense multi-UAV scenarios, the feasibility of the CBF quadratic program (CBF-QP) can be compromised due to internal incompatibility among multiple CBF constraints. To address this issue, we analyze the internal compatibility of CBF constraints and derive a sufficient condition for internal compatibility. Based on this condition, a sign-consistency constraint is introduced to mitigate internal incompatibility. The proposed constraint is incorporated into a decentralized CBF-QP formulation using worst-case estimates and slack variables. Simulation results demonstrate that the proposed method significantly reduces infeasibility and improves collision avoidance performance compared with existing baselines in dense scenarios. Additional simulations under varying time delays demonstrate the robustness of the proposed method. Real-world experiments validate the practical applicability of the proposed method.

A Feasibility-Enhanced Control Barrier Function Method for Multi-UAV Collision Avoidance

Abstract

This paper presents a feasibility-enhanced control barrier function (FECBF) framework for multi-UAV collision avoidance. In dense multi-UAV scenarios, the feasibility of the CBF quadratic program (CBF-QP) can be compromised due to internal incompatibility among multiple CBF constraints. To address this issue, we analyze the internal compatibility of CBF constraints and derive a sufficient condition for internal compatibility. Based on this condition, a sign-consistency constraint is introduced to mitigate internal incompatibility. The proposed constraint is incorporated into a decentralized CBF-QP formulation using worst-case estimates and slack variables. Simulation results demonstrate that the proposed method significantly reduces infeasibility and improves collision avoidance performance compared with existing baselines in dense scenarios. Additional simulations under varying time delays demonstrate the robustness of the proposed method. Real-world experiments validate the practical applicability of the proposed method.
Paper Structure (17 sections, 5 theorems, 25 equations, 6 figures, 2 tables)

This paper contains 17 sections, 5 theorems, 25 equations, 6 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARY
  3. Notations
  4. Control Barrier Function
  5. Unmanned Aerial Vehicle Kinematic Model
  6. Problem Formulation
  7. METHOD
  8. Centralized CBF-QP
  9. Feasibility Analysis and Sign-Consistency Constraint
  10. Decentralized CBF-QP with Sign-Consistency Constraint
  11. EXPERIMENTS
  12. Simulation Configurations and Parameters
  13. Simulation Setup and Evaluation Metrics
  14. Comparison with Baselines
  15. Evaluation of Time Delay Robustness
  16. ...and 2 more sections

Key Result

Lemma 1

Given a control barrier function $h$, any locally Lipschitz continuous controller $k : \mathcal{X} \to \mathbb{R}^m$ such that the control input $\mathbf{u} = k(\mathbf{x})$ satisfies renders the set $\mathcal{C}$ forward invariant, where denotes the time derivative of $h$ along the closed-loop system trajectories.

Figures (6)

  • Figure 1: Illustration of internal compatibility and incompatibility among multiple CBF constraints in multi-UAV collision avoidance. Compatibility refers to the existence of at least one control input that simultaneously satisfies all CBF constraints within the admissible input bounds. Internal compatibility specifically denotes the mutual consistency of the CBF constraints themselves, meaning that their intersection is non-empty without considering the admissible input bounds. Each ellipse represents a CBF constraint, while the circle denotes the admissible input bounds.
  • Figure 2: The cones of the sign-consistency constraint \ref{['Eq52']} . $\beta_1<\beta_2<\beta_3$ are the half-apex angles of these cones, respectively.
  • Figure 3: Overview of the proposed FECBF method.
  • Figure 4: Illustration of three representative and challenging simulation scenarios used for performance evaluation. The gray shaded region denotes the ground plane, while the points with halo and arrows represent the positions and velocity vectors of the UAVs, respectively. (a) Convergence scenario; (b) Dual-circle scenario, depicted from a top view; (c) Head-on scenario.
  • Figure 5: Time delay simulation results for all three scenarios with $n = 150$. The bottom-right subfigure shows the results for the dual-circle scenario with $\tau$ ranging from $3$ s to $5$ s at intervals of $0.2$ s, while the remaining subfigures show results for $\tau \in \{1, 3, 5\}$ s.
  • ...and 1 more figures

Theorems & Definitions (9)

  • Definition 1: CBF, ames2016control
  • Lemma 1
  • Remark 1: Velocity-dependent safety margin
  • Lemma 2
  • Lemma 3
  • proof
  • Lemma 4
  • Theorem 1: Sign-consistency condition
  • proof