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

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.

GPU-Accelerated Optimization-Based Collision Avoidance

This paper proposes a GPU-accelerated optimization framework for collision avoidance problems where the controlled objects and the obstacles can be modeled as the finite union of convex polyhedra. A novel collision avoidance constraint is proposed based on scale-based collision detection and the strong duality of convex optimization. Under this constraint, the high-dimensional non-convex optimization problems of collision avoidance can be decomposed into several low-dimensional quadratic programmings (QPs) following the paradigm of alternating direction method of multipliers (ADMM). Furthermore, these low-dimensional QPs can be solved parallel with GPUs, significantly reducing computational time. High-fidelity simulations are conducted to validate the proposed method's effectiveness and practicality.