In vehicle production factories, the vehicle painting process employs multiple robotic arms to simultaneously apply paint to car bodies advancing along a conveyor line. Designing paint paths for these robotic arms, which involves assigning car body areas to arms and determining paint sequences for each arm, remains a time-consuming manual task for engineers, indicating the demand for automation and design time reduction. The unique constraints of the painting process hinder the direct application of conventional robotic path planning techniques, such as those used in welding. Therefore, this paper formulates the design of paint paths as a hierarchical optimization problem, where the upper-layer subproblem resembles a vehicle routing problem (VRP), and the lower-layer subproblem involves detailed path planning. This approach allows the use of different optimization algorithms at each layer, and permits flexible handling of constraints specific to the vehicle painting process through the design of variable representation, constraints, repair operators, and an initialization process at the upper and lower layers. Experiments with three commercially available vehicle models demonstrated that the proposed method can automatically design paths that satisfy all constraints for vehicle painting with quality comparable to those created manually by engineers.

翻译：在汽车生产工厂中，车辆喷涂工序采用多台机械臂对沿传送线移动的车身同时进行喷漆作业。为这些机械臂设计喷涂路径——包括将车身区域分配给各机械臂并确定每台机械臂的喷涂顺序——目前仍是工程师需要耗费大量时间的手动任务，这表明该领域对自动化及设计时间缩减存在迫切需求。喷涂工艺特有的约束条件阻碍了传统机器人路径规划技术（如焊接领域所用方法）的直接应用。因此，本文提出将喷涂路径设计构建为层次优化问题：上层子问题类似于车辆路径规划问题（VRP），下层子问题则涉及详细路径规划。该方法允许在每层使用不同的优化算法，并通过设计上下两层的变量表示、约束条件、修复算子及初始化流程，灵活处理车辆喷涂工艺特有的约束。对三种市售车型的实验表明，所提方法能自动设计出满足所有车辆喷涂约束的路径，其质量可与工程师手动设计的路径相媲美。