Density-Optimal Direction-Based Control Barrier Functions for Safety- Critical Collision Avoidance = 밀도 최적 방향 기반 제어 장벽 함수를 이용한 안전필수 충돌회피

다국어 초록 (Multilingual Abstract)

This study presents a safety-critical collision avoidance algorithm for UGVs and UAVs that ensures deadlock resolution and real-time computational efficiency. While collision avoidance for autonomous systems has been extensively studied, Control Barrier Functions (CBF) have recently emerged as a primary framework. This framework can be seamlessly integrated with existing control methods while maintaining computational efficiency via QP optimization. However, conventional methods often exhibit deadlock issues and conservativeness. Specifically, this deadlock phenomenon is mathematically driven by the opposing gradients between the nominal control input and the safety barrier constraints, which leads to a vanishing control effort in the axial direction. Furthermore, existing methods often exhibit excessive conservativeness in cluttered or narrow environments, resulting in suboptimal trajectories or navigation failures even before reaching the deadlock state. Inspired by the collision avoidance behaviors of bats in dense swarms, this study proposes a DOCBF that resolves conflicts heuristically by leveraging density- optimal spaces. To address the conservativeness issue, an enhanced distance- dependent formulation is introduced. Numerical results and Monte Carlo simulations confirm that the proposed method consistently resolves deadlocks and ensures zero collisions, even in high-density environments Keyword: Safety-Critical, Collision Avoidance, Control Barrier Function (CBF), Autonomous Vehicles, Deadlock Resolution

목차 (Table of Contents)

• Abstact i
• Table of Contents ii
• List of Tables iii
• List of Figures iv
• Chapter 1. Introduction 1
• 1.1. Background and Motivations 1
• 1.2. Literature Survey 2
• 1.3. Research Objectives and Contributions 5
• 1.3.1. Safety-Critical Control for UGVs 5
• 1.3.2. Safety-Critical Control for UAVs 5
• 1.4. Thesis Organization 6
• Chapter 2. Preliminaries 7
• 2.1. Control Barrier Function 7
• 2.2. Reciprocal Velocity Obstacle 9
• 2.3. Unmanned Ground Vehicle and Aerial Vehicle Dynamics 12
• 2.3.1. UGV Dynamics 12
• 2.3.2. UAV Dynamics 12
• Chapter 3. Controller Design 14
• 3.1. Density Potential Function 14
• 3.1.1. Motivation for density potential function 14
• 3.2. Density-Optimal Direction-Based CBF 18
• 3.2.1. DOCBF problem formulation 18
• 3.2.2. Design of the DOCBF Barrier Function in 2D 20
• 3.3. Simulation Results 22
• 3.3.1 Simulation Results in 2D 22
• 3.3.2 Simulation Results in 3D 31
• 3.3.3 Comparative Analysis 35
• Chapter 4. Conclusion 37
• Reference 38
• Abstract (in korean) 44