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Construction Automation with Bio-Inspired Hierarchical Extremely Modular Systems

Journal of Automation, Mobile Robotics and Intelligent Systems
Volume 19 (2025): Issue 2 (June 2025)
By:
Open Access
|Jun 2025

Figures & Tables

Figure 1.

Physical models of mathematical prime knots constructed with extremely modular Pipe-Z: 1) Trefoil (31); 2) Figure-eight knot (41); 3) Cinquefoil (51); 4) 63 knot
Physical models of mathematical prime knots constructed with extremely modular Pipe-Z: 1) Trefoil (31); 2) Figure-eight knot (41); 3) Cinquefoil (51); 4) 63 knot

Figure 2.

A computer rendering of an existing overpass retrofitted with two branches of Truss-Z, comprised of 47 modules on the left and 77 modules on the right
A computer rendering of an existing overpass retrofitted with two branches of Truss-Z, comprised of 47 modules on the left and 77 modules on the right

Figure 3.

1) A physical model of the spatial multi-branch structure based on PZ. The bud is based on a truncated pentagonal prism. Three additional “branching buds” based on a dodecahedron (12-gon) are indicated by yellow circles. This system is called PZ12* and is considered EMS-2. 2) An example ofa spatial multi-branch quasi-EMS. This structure is built with “Space-Cube”—a system of toy blocks based on the simplest space-filling polyhedron—the cube. This system is called SC3 for short
1) A physical model of the spatial multi-branch structure based on PZ. The bud is based on a truncated pentagonal prism. Three additional “branching buds” based on a dodecahedron (12-gon) are indicated by yellow circles. This system is called PZ12* and is considered EMS-2. 2) An example ofa spatial multi-branch quasi-EMS. This structure is built with “Space-Cube”—a system of toy blocks based on the simplest space-filling polyhedron—the cube. This system is called SC3 for short

Figure 4.

Examples of 3D PZ structures. The units have been added sequentially at various twists along the dotted arrow. 1) An arch; 2) a torus; 3&4) free-form pipes
Examples of 3D PZ structures. The units have been added sequentially at various twists along the dotted arrow. 1) An arch; 2) a torus; 3&4) free-form pipes

Figure 5.

Planar projections of EMS (1) and qEMS (2)
Planar projections of EMS (1) and qEMS (2)

Figure 6.

The nomenclature and encoding of EMS-2. On the left: the genotype (((1, ■, ■, (1, 0, 0, 1, 1, 1, 1)), (2, 1, IV, (1, 1, 1)), (3, 2, II, (1, 0, 1)), (4, 2, III, (1))), ((1, I, (0, 0,0,0,0,0,0,0,0)),(3,II,(0,1,1,1,1)),(3,III,(0,0,1, 0)), (3, IV, (1, 0, 1)), (4, II, (1, 0)), (4, III, (1, 1, 1, 0)))) tabulated for clarity. On the right: the corresponding phenotype. The obstacles are indicated by hatched areas. The terminals are indicated by Greek letters. In this case, the buds have a form of pentagons (indicated by black). Buds and bud faces are indexed with Arabic and Roman numerals, respectively. The corresponding elements are shown in the same colors. Stems and twigs are shown in “reddish” and “bluish” colors, respectively. The first unit is indicated by a thick black outline. It starts from the “virtual” unit shown by a gray dotted line
The nomenclature and encoding of EMS-2. On the left: the genotype (((1, ■, ■, (1, 0, 0, 1, 1, 1, 1)), (2, 1, IV, (1, 1, 1)), (3, 2, II, (1, 0, 1)), (4, 2, III, (1))), ((1, I, (0, 0,0,0,0,0,0,0,0)),(3,II,(0,1,1,1,1)),(3,III,(0,0,1, 0)), (3, IV, (1, 0, 1)), (4, II, (1, 0)), (4, III, (1, 1, 1, 0)))) tabulated for clarity. On the right: the corresponding phenotype. The obstacles are indicated by hatched areas. The terminals are indicated by Greek letters. In this case, the buds have a form of pentagons (indicated by black). Buds and bud faces are indexed with Arabic and Roman numerals, respectively. The corresponding elements are shown in the same colors. Stems and twigs are shown in “reddish” and “bluish” colors, respectively. The first unit is indicated by a thick black outline. It starts from the “virtual” unit shown by a gray dotted line

Figure 7.

SC2: the 2D projection of SC3 structure shown in Figure 3.2. The genotype is shown on the left, and the corresponding phenotype is shown on the right. The respective corresponding elements are shown in the same colors. The last unit of each stem functions as a bud and is indicated by a diagonal hatch
SC2: the 2D projection of SC3 structure shown in Figure 3.2. The genotype is shown on the left, and the corresponding phenotype is shown on the right. The respective corresponding elements are shown in the same colors. The last unit of each stem functions as a bud and is indicated by a diagonal hatch

Figure 8.

From the left: the genotype; top right: the corresponding tabulated genotype; on the bottom right: the corresponding phenotype
From the left: the genotype; top right: the corresponding tabulated genotype; on the bottom right: the corresponding phenotype

Figure 9.

Calculation of the difference between two exemplary genotypes. The differences for all corresponding branches are summed up and multiplied by the penalty weight wP. Missing corresponding branches are indicated by dashed arrows. The difference between the two empty lists is 0
Calculation of the difference between two exemplary genotypes. The differences for all corresponding branches are summed up and multiplied by the penalty weight wP. Missing corresponding branches are indicated by dashed arrows. The difference between the two empty lists is 0

Figure 10.

In this case, reaching error rE = 2.25 + 0.95 + 0.58 + 0.63 + 1.19 = 5.6. The number of units n = 54. Stems with branching units are indicated in gray. Twigs are white
In this case, reaching error rE = 2.25 + 0.95 + 0.58 + 0.63 + 1.19 = 5.6. The number of units n = 54. Stems with branching units are indicated in gray. Twigs are white

Figure 11.

Sub-figures 1, 2, 3, and 4 show allowable MTZs connecting five terminals with: 2, 3, 4, and 5 stems, respectively
Sub-figures 1, 2, 3, and 4 show allowable MTZs connecting five terminals with: 2, 3, 4, and 5 stems, respectively

Figure 12.

The final trial of the Evolution Strategy-based experiment. For each phenotype, the generation number (g), the reaching error (rE), and the number of units (n) are shown in the bottom right corner. There has been no further improvement after 39 generations. Stems with branching units are indicated in gray. Twigs are white
The final trial of the Evolution Strategy-based experiment. For each phenotype, the generation number (g), the reaching error (rE), and the number of units (n) are shown in the bottom right corner. There has been no further improvement after 39 generations. Stems with branching units are indicated in gray. Twigs are white

Figure 13.

1) The best MTZ layout produced by Evolution Strategy. 2) The three-dimensional MTZ based on this layout
1) The best MTZ layout produced by Evolution Strategy. 2) The three-dimensional MTZ based on this layout

Steps for creating an Extremely Modular System or its transformation

StartTransformationOperator
General structure↓↴Add a stemaS [Gi, (ii, BFi, ui)]
Add twigsaT[Gi, ((p1, BF1, u1),(p2, BF2, u2),…,(pk, BFk, Uk))]
Remove branchesrB [Gi, ((p1, BF1), (p2, BF2), …,(pi, BFk))]
Substructure @ buds↲
↴
↓Displace branchesdB[Gi, (((pi, BFi),(pj, BFj)),…)]
Units @ branches↲
↴
↓Add units @ branchesaU[Gi,((p1,BF1,(v11,l11),…,(vk1,lk1)),…,(pj,BFj,(v1j,l1j),…,(vkj,lkj)))]
Remove units @ branchesrU[Gi,((p1,BF1,(l11,…,lk1),…,(pJ,BFJ,(l1j,…,lkJ)))]
Invert units @ branchesiU[Gi ((p1,BF1,(l11,…,lk1),…,(pj,BFj,(l1j,…,lkj)))]
End↲
DOI: https://doi.org/10.14313/jamris-2025-015 | Journal eISSN: 2080-2145 | Journal ISSN: 1897-8649
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Language: English
Page range: 59 - 64
Submitted on: Jan 4, 2024
Accepted on: Apr 4, 2024
Published on: Jun 26, 2025
Published by: Łukasiewicz Research Network – Industrial Research Institute for Automation and Measurements PIAP
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year
Keywords:
evolution strategy,
discrete structure encoding,
extremely modular system,
multi-branch structure
Related subjects:
Computer sciences,
Artificial intelligence,
Engineering,
Electrical engineering,
Control engineering, metrology and testing,
Mechanical engineering,
Fundamentals of mechanical engineering

© 2025 Ela Zawidzka, Machi Zawidzki, published by Łukasiewicz Research Network – Industrial Research Institute for Automation and Measurements PIAP
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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