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Nowadays, robotic cells are mostly designed with the main goal to meet the desired production rate without any consideration of the energy efficiency, therefore, it is often possible to achieve significant energy savings without downsizing the production. In our previous study, we established the mathematical formulation of the energy optimization problem, proposed a parallel heuristic, and optimized an existing robotic cell in Skoda Auto, the results of which revealed a 20% reduction in the energy consumption of robot drive systems. This study proposes a novel parallel Branch & Bound algorithm to optimize the energy consumption of robotic cells without deterioration in throughput. The energy saving is achieved by changing robot speeds and positions, applying robot power-saving modes (brakes, bus power off), and selecting an order of operations. The core part of the algorithm is our tight lower bound, based on convex envelopes. Besides the bounding, a Deep Jumping approach is introduced to guide the search to the promising parts of the Branch & Bound tree, and the parallelization accelerates the exploration of the tree. The experimental results revealed that the performance of the parallel algorithm scales almost linearly up to 12 processor cores, and the quality of obtained solutions is better or comparable to other existing works. |
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