用动态抛物线约束提升非完整机器人避障能力，可应对100个动态障碍物场景。
Beyond Collision Cones: Dynamic Obstacle Avoidance for Nonholonomic Robots via Dynamic Parabolic Control Barrier Functions
- 以动态抛物线定义安全边界，自适应距离与相对速度变化
- 在含100个动态障碍物的密集场景中成功率显著提升
- 适合需高安全性避障的移动机器人系统应用
控制屏障函数（CBFs）是保障自主系统安全的强大工具，但在复杂动态环境中应用于非完整机器人仍面临挑战。现有方法多依赖碰撞锥或速度障碍约束，仅考虑相对速度方向，导致保守性过高，易使基于CBF的二次规划不可行，尤其在密集场景中。为此，我们提出动态抛物线控制屏障函数（DPCBF），采用抛物线形安全边界，其顶点与曲率随障碍物距离及相对速度大小动态调整，构建更宽松的安全约束。理论证明该方法适用于受输入约束的运动学自行车模型。大量对比仿真显示，基于DPCBF的控制器在导航成功率和QP可行性方面均显著优于基线方法。该方法成功实现对最多100个动态障碍物环境的导航，而传统碰撞锥方法在此类场景中因不可行而失效。
原文摘要 · Abstract (English)
Control Barrier Functions (CBFs) are a powerful tool for ensuring the safety of autonomous systems, yet applying them to nonholonomic robots in cluttered, dynamic environments 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. Extensive 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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。