Abstract
Welding robot path planning gradually has increasingly widespread attention in automatic production on account of improving the production efficiency in the actual production process. It is a combinational optimization problem to find an optimal welding path for the robot manipulator by arranging the sequence and directions of welding seams. To solve the problem with two objectives, path length and energy consumption, this paper proposed an improved discrete MOEA/D based on a hybrid environment selection (DMOEA/D-HES) with a parallel scheme to search the optimal sequence and directions simultaneously for welding seams. The discretized reproduction and adaptive neighborhood provide a larger search range in solution space to overcome difficulties in duplication and uneven distribution of solutions. Adaptive decomposition method and improved hybrid environment selection promote solutions converge to the optimal direction and further balance convergence and diversity. Eight TSPLIB problems were tested with the proposed algorithm and the other four algorithms. Besides, the algorithm is compared with four multi-objective evolutionary algorithms (MOEAs) on the multi-objective welding robot path planning on the balance beam. The test results indicate DMOEA/D-HES outperforms other algorithms on convergence with a competitive diversity, which is effective to be applied in the actual welding process.
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Funding
This work is supported by the National Science Foundation of China (Nos. 61973120, 62076095, 61673175, 61573144), the Programme of Introducing Talents of Discipline to Universities (the 111 Project) under Grant B17017, and Fundamental Research Funds of the Central Universities, 222201917006.
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Appendices
Appendix 1
The table of welding seams formed by both ends.
Seams number | Start node | End node | Joints’ number | Start node | End node |
|---|---|---|---|---|---|
1 | 1 | 2 | 41 | 51 | 52 |
2 | 2 | 3 | 42 | 52 | 53 |
3 | 3 | 4 | 43 | 53 | 54 |
4 | 4 | 5 | 44 | 18 | 54 |
5 | 5 | 6 | 45 | 17 | 55 |
6 | 6 | 7 | 46 | 16 | 56 |
7 | 7 | 8 | 47 | 13 | 44 |
8 | 8 | 9 | 48 | 12 | 45 |
9 | 9 | 10 | 49 | 44 | 45 |
10 | 10 | 11 | 50 | 9 | 57 |
11 | 11 | 12 | 51 | 8 | 58 |
12 | 12 | 13 | 52 | 7 | 59 |
13 | 13 | 14 | 53 | 59 | 60 |
14 | 14 | 15 | 54 | 60 | 61 |
15 | 15 | 16 | 55 | 61 | 62 |
16 | 16 | 17 | 56 | 6 | 62 |
17 | 17 | 18 | 57 | 5 | 63 |
18 | 18 | 19 | 58 | 4 | 64 |
19 | 19 | 20 | 59 | 1 | 37 |
Appendix 2
The table of the coordinates for welding nodes in three dimensions.
Node number | x/mm | y/mm | z/mm | Node number | x/mm | y/mm | z/mm |
|---|---|---|---|---|---|---|---|
1 | 128.3 | − 1.3 | 19.0 | 41 | − 93.8 | − 50.8 | − 19.0 |
2 | 133.8 | − 1.3 | 19.0 | 42 | − 147.5 | − 50.8 | − 19.0 |
3 | 133.8 | − 1.3 | 20.3 | 43 | − 147.5 | − 49.5 | − 19.0 |
4 | 85.0 | − 1.3 | 20.3 | 44 | − 143.0 | − 49.5 | − 19.0 |
5 | 29.5 | − 1.3 | 25.3 | 45 | − 143.0 | − 49.5 | 19.0 |
6 | 26.8 | − 1.3 | 26.0 | 46 | − 147.5 | − 49.5 | 19.0 |
7 | − 26.8 | − 1.3 | 26.0 | 47 | − 147.5 | − 50.8 | 19.0 |
8 | − 29.5 | − 1.3 | 25.3 | 48 | − 93.8 | − 50.8 | 19.0 |
9 | − 85.0 | − 1.3 | 20.3 | 49 | 85.0 | − 49.5 | − 20.3 |
10 | − 133.8 | − 1.3 | 20.3 | 50 | 29.5 | − 78.9 | − 25.3 |
11 | − 133.8 | − 1.3 | 19.0 | 51 | 26.8 | − 80.4 | − 26.0 |
12 | − 128.3 | − 1.3 | 19.0 | 52 | 25.0 | − 81.3 | − 26.0 |
13 | − 128.3 | − 1.3 | − 19.0 | 53 | − 25.0 | − 81.3 | -26.0 |
14 | − 133.8 | − 1.3 | − 19.0 | 54 | − 26.8 | − 80.4 | − 26.0 |
15 | − 133.8 | − 1.3 | − 20.3 | 55 | − 29.5 | − 78.9 | − 25.3 |
16 | − 85.0 | − 1.3 | − 20.3 | 56 | − 85.0 | − 49.5 | − 20.3 |
17 | − 29.5 | − 1.3 | − 25.3 | 57 | − 85.0 | − 49.5 | 20.3 |
18 | − 26.8 | − 1.3 | − 26.0 | 58 | − 29.5 | − 78.9 | 25.3 |
19 | 26.8 | − 1.3 | − 26.0 | 59 | − 26.8 | − 80.4 | 26.0 |
20 | 29.5 | − 1.3 | − 25.3 | 60 | − 25.0 | − 81.3 | 26.0 |
21 | 85.0 | − 1.3 | − 20.3 | 61 | 25.0 | − 81.3 | 26.0 |
22 | 133.8 | − 1.3 | − 20.3 | 62 | 26.8 | − 80.4 | 26.0 |
23 | 133.8 | − 1.3 | − 19.0 | 63 | 29.5 | − 78.9 | 25.32 |
24 | 128.3 | − 1.3 | − 19.0 | 64 | 85.0 | − 49.5 | 20.3 |
25 | − 85.3 | − 50.8 | − 20.3 | 65 | − 147.4 | − 39.9 | − 20.3 |
26 | − 85.3 | − 50.8 | 20.3 | 66 | − 101.3 | − 39.9 | − 20.3 |
27 | − 25.3 | − 82.6 | − 27.5 | 67 | − 93.8 | − 47.4 | − 20.3 |
28 | − 25.3 | − 82.6 | 27.5 | 68 | − 93.8 | − 50.8 | − 20.3 |
29 | 25.3 | − 82.6 | − 27.5 | 69 | − 147.4 | − 39.9 | 20.3 |
30 | 25.3 | − 82.6 | 27.5 | 70 | − 101.3 | − 39.9 | 20.3 |
31 | 85.3 | − 50.8 | − 20.3 | 71 | − 93.8 | − 47.4 | 20.3 |
32 | 85.3 | − 50.8 | 20.3 | 72 | − 93.8 | − 50.8 | 20.3 |
33 | 93.8 | − 50.8 | − 19.0 | 73 | 147.4 | − 39.9 | 20.3 |
34 | 147.5 | − 50.8 | − 19.0 | 74 | 101.3 | − 39.9 | 20.3 |
35 | 147.5 | − 49.5 | − 19.0 | 75 | 93.8 | − 47.4 | 20.3 |
36 | 143.0 | − 49.5 | − 19.0 | 76 | 93.8 | − 50.8 | 20.3 |
37 | 143.0 | − 49.5 | 19.0 | 77 | 147.4 | − 39.9 | − 20.3 |
38 | 147.5 | − 49.5 | 19.0 | 78 | 101.3 | − 39.9 | − 20.3 |
39 | 147.5 | − 50.8 | 19.0 | 79 | 93.8 | − 47.4 | − 20.3 |
40 | 93.75 | − 50.8 | 19.0 | 80 | 93.8 | − 50.8 | − 20.3 |
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Zhou, X., Wang, X. & Gu, X. Welding robot path planning problem based on discrete MOEA/D with hybrid environment selection. Neural Comput & Applic 33, 12881–12903 (2021). https://doi.org/10.1007/s00521-021-05939-2
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DOI: https://doi.org/10.1007/s00521-021-05939-2