  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.
