用分离超平面实现椭球体无碰撞控制，计算更高效。
Collision-free Control Barrier Functions for General Ellipsoids via Separating Hyperplane
- 基于对偶锥推导椭球体无碰撞条件，引入分离超平面扩展系统动态。
- 仅需单层优化，相比现有方法显著降低计算时间。
- 理论证明安全约束有效，适用于机器人避障等实际场景。
本文提出一种基于控制屏障函数（CBFs）与分离超平面的通用椭球体无碰撞避障方法。首先，利用对偶锥概念解析推导出一般椭球体的无碰撞条件，并通过将分离超平面引入系统动态，将其嵌入CBF框架中，实现高效可靠的碰撞规避。所提方法在理论上严格证明了其有效性，确保安全约束得以满足。该方法仅需单层优化，相比当前最优方法显著降低了计算耗时。数值仿真与真实实验验证了算法的有效性与实用性。
原文摘要 · Abstract (English)
This paper presents a novel collision avoidance method for general ellipsoids based on control barrier functions (CBFs) and separating hyperplanes. First, collision-free conditions for general ellipsoids are analytically derived using the concept of dual cones. These conditions are incorporated into the CBF framework by extending the system dynamics of controlled objects with separating hyperplanes, enabling efficient and reliable collision avoidance. The validity of the proposed collision-free CBFs is rigorously proven, ensuring their effectiveness in enforcing safety constraints. The proposed method requires only single-level optimization, significantly reducing computational time compared to state-of-the-art methods. Numerical simulations and real-world experiments demonstrate the effectiveness and practicality of the proposed algorithm.
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。