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Table 1. Assembly results.
Bunny
Star
Tower
Dog
272
258
304
507
Volume [unit]*
704
758
728
1266
Number of support blocks
25
14
46
24
Number of subassemblies
Assembly planning time [s]
13.42
11.29
6.16
56.05
Assembling time [min]
24.10
22.25
28.14
43.40
Assembly speed [blocks/min]
11.29
11.59
10.80
11.68
Number of blocks
(with support blocks)
1 unit = 1 × 1 block volume = 48 mm3.
Table 2. Assembly results of previous study (Sugimoto et al., 2017).
Bunny 1
Bunny 2
Duck
281
262
565
Number of support blocks
31
12
44
Number of subassemblies
Assembly planning time [s]
1.11
1.11
4.33
Assembling time [min]
38
34
134
Assembly speed [blocks/min]
7.4
7.7
4.2
Number of blocks
(with support blocks)
(a) Unit size
Figure 1. Nanoblocks.
(b) Each size of nanoblock
2×2
(a) Even layer
1×2
(c) Support
2×1
(b) Odd layer
Figure 2. Arrangement of blocks (Maeda et al., 2016).
(a) The floating red block cannot be
assembled.
Figure 3. Assembly failure patterns.
(b) Assembly order may lead an assembly failure.
We must place block B before block A.
1×1
(a) The top block fulfills condition (ii)
Figure 4. Case stable.
Figure 5. Case inclusion.
Figure 6. Case partial inclusion.
(b) The top block fulfills condition (iii)
(a) The green block is not assemblable without adjacent block.
(b) The right green block become assemblable due to an adjacent block (the left green block).
Figure 7. Case adjacent support.
(a) 𝑃𝑃(𝐶𝐶𝑘𝑘 ) shares no region with 𝑃𝑃�𝐶𝐶̂𝑘𝑘𝑖𝑖 �.
(b) 𝑃𝑃�𝐶𝐶̂𝑘𝑘1 � does not share region with 𝑃𝑃(𝐶𝐶𝑘𝑘 ) though 𝑃𝑃�𝐶𝐶̂𝑘𝑘2 � does.
Figure 8. Case unassemblable.
Figure 9. Adding support blocks for unassemblable blocks.
Figure 10. Dividing into subassemblies.
(a) 𝑛𝑛block = 2, 𝑛𝑛stud = 2
Figure 11. Block indices of the green blocks.
(b) 𝑛𝑛block = 2, 𝑛𝑛stud = 4
Figure 12. Vertical placement can cause collision between the edges of the blocks.
Figure 13. Inclined placement avoids collision. It raises success probability.
Figure 14. Experimental setup. The robot picks a block from the bottom of the block supplier
according to the placement order. The block is placed to the assembly pad.
Figure 15. Grasp studs of a nanoblock to carry it (Maeda et al., 2016).
(a) CAD model*.
(b) Block model
(c) Subassemblies
(d) Final assembly
(Thingiverse 2019A)
Figure 16. A bunny.
(a) CAD model*.
(b) Block model
(c) Subassemblies
(d) Final assembly
(Thingiverse 2019B)
Figure 17. A star.
(a) CAD model*.
(Thingiverse 2019C)
Figure 18. A tower.
(b) Block model
(c) Final assembly
(a) CAD model*.
(b) Block model
(Thingiverse 2019D)
Figure 19. A dog.
Figure 20. A scene in dog model assembly.
(c) Subassemblies
(d) Final assembly
...