🤖 AI Summary
Real-time collision-free control of general ellipsoidal agents in multi-agent systems remains challenging due to non-convex safety constraints and computational inefficiency. Method: This paper proposes a novel Control Barrier Function (CBF) framework grounded in hyperplane separation and dual cone theory. Its core innovation lies in explicitly embedding the separating hyperplane constraint into the CBF dynamics, enabling a single-layer convex optimization formulation—eliminating the need for conventional multi-stage or iterative optimization schemes. Contribution/Results: Theoretical analysis guarantees strict safety for arbitrarily shaped ellipsoids. Compared to state-of-the-art approaches, the method reduces computational latency significantly, achieving millisecond-level response times and 100% collision avoidance success rates in both high-dynamic simulations and real-world robotic experiments. It thus achieves a unique balance of real-time performance, geometric generality, and provable reliability.
📝 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.