Collision-free Control Barrier Functions for General Ellipsoids via Separating Hyperplane

Abstract

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.