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. Starting from a collision-free initial trajectory, our method inherits the theoretical properties of primal interior point method (P-IPM), i.e., guaranteed collision avoidance and homotopy preservation throughout optimization, 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 an order of magnitude's speedup, while generating trajectories of comparable qualities as state-of-the-art P-IPM solver.
翻译:我们提出了一个交替方向的乘数优化方法(ADMM)的变式,以解决受限轨道优化问题。我们的ADMM框架打破了联合优化的小型子问题,导致低迭代成本和分散化参数更新。从最初的无碰撞轨迹开始,我们的方法继承了原始内点方法(P-IPM)的理论属性,即在整个优化过程中保证避免碰撞和同质保护,同时速度更快。我们分析了趋同性,并评估了我们对于多机器人武器的时间最佳多反流优化和同步目标影响的方法,我们从中考虑了运动学、动态-限制和同质-保持碰撞限制。我们的方法突出了数量级速度的顺序,同时生成了类似质量的轨迹,作为最先进的P-IP解答器。