A Dynamic Programming Approach for Cooperative Pallet-Loading Manipulators

In a high-speed palletizing machine, packages of various sizes are inserted on a conveyor belt. Then, cooperating multiple robotic manipulators move them to obtain a desired final layout. The throughput of this palletizing process critically hinges upon the strategic selection of the insertion sequence and the careful choice of robot manipulations. Pursuing a higher throughput in this context holds great importance due to its potential to enhance productivity, however, reaching such goal constitutes a challenging task. Indeed, the problem of maximizing the throughput of the palletizing machine is a nontrivial one and, despite its relevant importance in industrial settings, it has not received much attention in existing literature. In this work, we present a Dynamic Programming-based algorithm, together with some reduction techniques, that allows finding the shortest packages sequence and the corresponding robot manipulations that maximize production. We include some numerical experiments on randomly generated problems and on actual industrial scenarios, which show the good performance of the proposed method. Note to Practitioners—This work is motivated by the need of high-speed palletizing machine manufacturers to automate the generation of packages sequences, and the corresponding robot manipulations tasks assignment. We solve this problem with a Dynamic Programming-based algorithm. The benefit of the proposed method is twofold. On one hand, it allows palletizing machines manufacturers not to waste their employees’ time on the often lengthy task of manually planning packages sequences and manipulations. On the other hand, the proposed approach allows minimizing the time required to assemble an assigned layout, increasing the overall throughput of the production chain. The proposed algorithm can be implemented in any programming language of choice (e.g., C++) and integrated by manufacturers in their production software. The main limitation of this approach is the computational time which grows exponentially with the number of packages. However, given that the application is an off-line one, this approach allows handling most of the industrial layouts, which usually consist of a few tens of packages, in a reasonable amount of time. As future developments, the approach could be generalized to handle more complicated manipulator movements and/or allow robots to manipulate each package more than once. This would add a layer of complexity that would require nontrivial tailored solution strategies in order to handle these new degrees of freedom.