The complicated task allocation, scheduling and planning problem with multiple stations and multiple robots commonly seen in spot welding production line design is studied in this paper. To deal with the highly coupled model combined with several task planning sub-problems, including robot cells design, robots allocation among cells, welding allocation among cells and robots, and welding scheduling for each robot, as well as numerous internal and external constraints, the traditional multi-robot task allocation (MRTA) framework is extended to a novel and uniform multi-station multi-robot (MS-MRTA) framework, and a sophisticated hierarchical optimization algorithm is proposed. Firstly, to establish the optimization model based on MS-MRTA framework as a whole, constraints such as reachability constraint, maximum speed and acceleration constraint, collision constraint and welding operation time constraint are considered, and the optimization objective is established based on the balance of welding tasks of each robot and each cell. Then, in order to solve the highly coupled model, a hierarchical optimization algorithm is proposed to divide the problem into three layers from top to bottom: the path planning of a single robot, welding task allocation among robots, and welding task allocation among cells. The path planning of a single robot is analogous to the Travelling Salesman Problem (TSP) solved by iterating the Lin-Kernighan-Helsgaun (LKH) solver with the trapezoidal acceleration and deceleration motion. To solve the welding task allocation among robots with numerous constraints, a regional assignment method was proposed which simplify the model and eliminate the accessibility constraint and collision constraint, and combined with genetic algorithm to solve the sub-problem iteratively. The welding task allocation among cells is solved based on the principle of balanced welding of each cell. Genetic algorithm is used to obtain the nested iterative solution of three sub-problems. The cases of actual door welding tasks are studied to verify the effectiveness of the proposed optimization algorithm. Compared with the method of long-term trial and error by experienced experts and two other more advanced algorithms, the proposed optimization algorithm results in a task assignment scheme with less welding time, less waiting time and an increase of welding operation productivity, which shows the effectiveness and feasibility of the multi-robot multi-station task allocation algorithm based on stepwise optimization.

本文研究了点焊生产线设计中常见的多工位多机器人的复杂任务分配、调度和规划问题。为了处理结合几个任务规划子问题的高耦合模型，包括机器人单元设计、单元间机器人分配、单元和机器人之间的焊接分配、每个机器人的焊接调度以及众多内部和外部约束，将传统的多机器人任务分配（MRTA）框架扩展为新颖统一的多站多机器人（MS-MRTA）框架，并提出了复杂的分层优化算法。首先，整体建立基于MS-MRTA框架的优化模型，可达性约束、最大速度和加速度约束等约束，考虑碰撞约束和焊接操作时间约束，根据各机器人和各单元焊接任务的平衡性建立优化目标。然后，为了解决高耦合模型，提出了一种分层优化算法，将问题从上到下分为三层：单个机器人的路径规划、机器人之间的焊接任务分配和单元之间的焊接任务分配。单个机器人的路径规划类似于通过使用梯形加速和减速运动迭代 Lin-Kernighan-Helsgaun (LKH) 求解器解决的旅行商问题 (TSP)。为解决多约束机器人之间的焊接任务分配，提出了一种简化模型并消除可达性约束和碰撞约束的区域分配方法，并结合遗传算法迭代求解子问题。根据各电芯平衡焊接的原则解决电芯间的焊接任务分配。遗传算法用于获得三个子问题的嵌套迭代解。对实际门焊接任务的案例进行了研究，以验证所提出的优化算法的有效性。与经验丰富的专家长期试错法和另外两种更先进的算法相比，所提出的优化算法导致任务分配方案的焊接时间更少，等待时间更少，焊接操作生产率提高，