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.
The authors would like to thank the entire personnel at the Geometry and Motion Planning Group, Fraunhofer-Chalmers Research Centre for Industrial Mathematics, for useful discussions and support in the implementation, in particular, D. Segerdahl. They also thank the anonymous referees and associate editor for their helpful suggestions
Authors and Affiliations
- Domenico Spensieri, Fraunhofer-Chalmers Centre
- Johan S. Carlson, Fraunhofer-Chalmers Centre
- Fredrik Ekstedt, Fraunhofer-Chalmers Centre
- Robert Bohlin, Fraunhofer-Chalmers Centre