Beyond Collision Cones: Dynamic Obstacle Avoidance for Nonholonomic Robots Via Dynamic Parabolic Control Barrier Functions
Hun Kuk Park, Taekyung Kim, Dimitra Panagou
AI summary
Problem
Existing CBF methods rely on fixed collision cones that only consider relative velocity angles, causing excessive conservatism and frequent quadratic program infeasibility in cluttered, dynamic settings.
Approach
The authors introduce a Dynamic Parabolic Control Barrier Function (DPCBF) that replaces fixed cones with a parabolic safety boundary whose curvature and position adapt in real-time based on obstacle distance and relative speed.
Key results
- Proves DPCBF validity for kinematic bicycle models under input constraints
- Achieves significantly higher navigation success rates in dense environments
- Resolves QP infeasibility issues common to collision-cone baselines
- Successfully navigates scenarios with up to 100 dynamic obstacles
Why it matters
Provides a practical, provably safe navigation framework for autonomous vehicles and mobile robots operating in crowded, real-world conditions.
Abstract
Control Barrier Functions (CBFs) are a powerful tool for ensuring the safety of autonomous systems, yet applying them to nonholonomic robots in cluttered, dynamic environ- ments remains an open challenge. State-of-the-art methods often rely on collision-cone or velocity-obstacle constraints which, by only considering the angle of the relative velocity, are inherently conservative and can render the CBF-based quadratic program infeasible, particularly in dense scenarios. To address this issue, we propose a Dynamic Parabolic Control Barrier Function (DPCBF) that defines the safe set using a parabolic boundary. The parabola’s vertex and curvature dynamically adapt based on both the distance to an obstacle and the magnitude of the relative velocity, creating a less restrictive safety constraint. We prove that the proposed DPCBF is valid for a kinematic bicycle model subject to input constraints. Ex- tensive comparative simulations demonstrate that our DPCBF- based controller significantly enhances navigation success rates and QP feasibility compared to baseline methods. Our approach successfully navigates through dense environments with up to 100 dynamic obstacles, scenarios where collision cone-based methods fail due to infeasibility. [Project Page]1 [Code] [Video]