This work is inspired by the problem of planning sequences of operations, as welding, in car manufacturing stations where multiple industrial robots cooperate. The goal is to minimize the station cycle time, \emph{i.e.} the time it takes for the last robot to finish its cycle. This is done by dispatching the tasks among the robots, and by routing and scheduling the robots in a collision-free way, such that they perform all predefined tasks. We propose an iterative and decoupled approach in order to cope with the high complexity of the problem. First, collisions among robots are neglected, leading to a min-max Multiple Generalized Traveling Salesman Problem (MGTSP). Then, when the sets of robot loads have been obtained and fixed, we sequence and schedule their tasks, with the aim to avoid conflicts. The first problem (min-max MGTSP) is solved by an exact branch and bound method, where different lower bounds are presented by combining the solutions of a min-max set partitioning problem and of a Generalized Traveling Salesman Problem (GTSP). The second problem is approached by assuming that robots move synchronously: a novel transformation of this synchronous problem into a GTSP is presented. Eventually, in order to provide complete robot solutions, we include path planning functionalities, allowing the robots to avoid collisions with the static environment and among themselves. These steps are iterated until a satisfying solution is obtained. Experimental results are shown for both problems and for their combination. We even show the results of the iterative method, applied to an industrial test case adapted from a stud welding station in a car manufacturing line.

翻译：本研究受汽车制造工位中多台工业机器人协作规划操作序列（如焊接）问题的启发。目标是最小化工位循环时间，即最后一台机器人完成其工作周期所需的时间。通过分配机器人任务，并以无碰撞方式对机器人进行路径规划和调度，使其完成所有预定义任务来实现这一目标。我们提出一种迭代解耦方法以应对该问题的高复杂性。首先，忽略机器人之间的碰撞，得到一个最小-最大多广义旅行商问题（MGTSP）。随后，在确定并固定机器人负载集后，我们对其任务进行排序和调度，以避免冲突。第一个问题（最小-最大MGTSP）通过精确的分支定界法求解，其中通过结合最小-最大集合划分问题解与广义旅行商问题（GTSP）解来提出不同的下界。第二个问题通过假设机器人同步运动来处理：提出了一种将同步问题转化为GTSP的新颖变换。最终，为提供完整的机器人解决方案，我们引入路径规划功能，使机器人能够避免与静态环境及彼此发生碰撞。这些步骤迭代进行，直至获得满意解。针对两个问题及其组合，展示了实验结果。我们甚至展示了迭代方法应用于汽车制造生产线中螺柱焊接工位的工业测试案例结果。