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.

翻译：本文提出了一种GPU加速的优化框架，用于解决受控对象与障碍物均可建模为有限凸多面体并集的碰撞规避问题。基于尺度碰撞检测与凸优化的强对偶性，提出了一种新型碰撞规避约束。在此约束条件下，高维非凸碰撞规避优化问题可依照交替方向乘子法（ADMM）范式分解为多个低维二次规划问题。进一步地，这些低维二次规划问题可通过GPU并行求解，从而显著减少计算时间。通过高保真仿真验证了所提方法的有效性与实用性。