We propose a variant of alternating direction method of multiplier (ADMM) to solve constrained trajectory optimization problems. Our ADMM framework breaks a joint optimization into small sub-problems, leading to a low iteration cost and decentralized parameter updates. Our method inherits the theoretical properties of primal interior point method (P-IPM), i.e., guaranteed collision avoidance and homotopy preservation, while being orders of magnitude faster. We have analyzed the convergence and evaluated our method for time-optimal multi-UAV trajectory optimizations and simultaneous goal-reaching of multiple robot arms, where we take into consider kinematics-, dynamics-limits, and homotopy-preserving collision constraints. Our method highlights 10-100 times speedup, while generating trajectories of comparable qualities as state-of-the-art P-IPM solver.
翻译:我们提出了一种交替方向的乘数优化方法(ADMM),以解决受限轨道优化问题。我们的ADMM框架打破了对小小问题的共同优化,导致了低迭代成本和分散化参数更新。我们的方法继承了原始内点方法(P-IPM)的理论特性,即保证避免碰撞和同质保护,同时速度更快。我们分析了我们对于多机器人武器的时间-最佳多自动飞行器轨道优化和同步目标触控方法的趋同性,并评估了这种方法,我们从中考虑了运动学、动态限制和同质保持碰撞限制。我们的方法突出10-100倍的加速,同时生成了类似特性的轨迹,作为最先进的P-IPM解答器。