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, 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 (B&B) 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.Note to Practitioners-This paper is motivated by the problem of planning robot operations in welding applications in the automotive industry. Here, a number of welding tasks have been introduced along the car body: the goal is to let the robots perform such tasks while minimizing the cycle time (or makespan). The main difficulties, from the manufacturing engineer perspective, lie in assigning the tasks to the robots, deciding the order and the timing of the operations, avoiding collisions between the robots and the environment, and among the robots themselves. We present in this work an iterative approach, consisting of two steps: first, sequences for the robot operations are computed in order to minimize the cycle time, while neglecting collisions among robots; then, given the assignment of tasks to robots, the operations are reordered and scheduled while avoiding conflicts among robots. Robot motions are also automatically computed to avoid collisions with the static environment. We show an optimal algorithm, for the first part, based on implicit enumeration (B&B) and introduce a novel suboptimal algorithm, for the second part, to synchronize the robots.These algorithms are iterated while fetching information about the problem that are hard to compute, thus following a lazy approach. Tests on problems adapted from the literature and from the automotive i...

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Sheet metal assemhiy is investment intense. Therefore, the equipment needs to he efficiently utilized. The balancing of welds has a significant influence on achievable production rate and equipment utilization. Robot line balancing is a complex problem, where each weld is to be assigned to a specific station and robot, such that line cycle time is minimized. Industrial robot line balancing has been manually conducted in computer aided engineering (CAE)-tools based on experience and trial and error rather than mathematical methods. However, recently an automatic method for robot line balancing was proposed by the authors. To reduce robot coordination cycle time losses, this method requires identical reach ability of all line stations. This limits applicability considerably since in most industrial lines, reach ability differs over the stations to further line reach ability and flexibility. Therefore, in this work we propose a novel generalized simulationbased method for automatic robot line balancing that allows any robot positioning. It reduces the need for robot coordination significantly by spatially separating the robot weld work loads. The proposed method is furthermore successfully demonstrated on automotive stud welding lines, with line cycle times lower than that of the corresponding running production programs. Moreover, algorithm central processing unit (CPU)-times are mere fractions of the lead times of existing CAE-tools.

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In the manufacturing industry, spray painting is often an important part of the manufacturing process. Especially in the automotive industry, the perceived quality of the final product is closely linked to the exactness and smoothness of the painting process. For complex products or low batch size production, manual spray painting is often used. But in large scale production with a high degree of automation, the painting is usually performed by industrial robots. There is a need to improve and simplify the generation of robot trajectories used in industrial paint booths. A novel method for spray paint optimization is presented, which can be used to smooth out a generated initial trajectory and minimize paint thickness deviations from a target thickness. The smoothed out trajectory is found by solving, using an interior point solver, a continuous non-linear optimization problem. A two-dimensional reference function of the applied paint thickness is selected by fitting a spline function to experimental data. This applicator footprint profile is then projected to the geometry and used as a paint deposition model. After generating an initial trajectory, the position and duration of each trajectory segment are used as optimization variables. The primary goal of the optimization is to obtain a paint applicator trajectory, which would closely match a target paint thickness when executed. The algorithm has been shown to produce satisfactory results on both a simple 2-dimensional test example, and a non-trivial industrial case of