# Digital Plan of Brickwork Layout for Robotic Bricklaying Technology

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions [10,11].

## 2. Methodology

## 3. Algorithm of the Converter from IFC Format

## 4. Mathematical Method of Connecting Discontinuous Axes of Objects Walls with an Orthogonal Layout

- Find the directional vector $\overrightarrow{b}$ for each axis:$$\overrightarrow{b}=\left[{b}_{1};{b}_{2}\right]={P}_{2i}-{P}_{1i}=\left[{x}_{2}-{x}_{1};{y}_{2}-{y}_{1}\right].$$
- Find the initial point, $S$, for each axis $a$:$$S\left[{x}_{0};{y}_{0}\right]={P}_{1i}\left[x;y\right].$$
- Write the axes in parametric form, as a system of equations [45]:$$\{\begin{array}{c}x={x}_{0}+{b}_{1}\xb7t\\ y={y}_{0}+{b}_{2}\xb7t\end{array}$$
- Write the axes $a$ in matrix form [45]:$${a}_{i}=\left(\begin{array}{cc}{x}_{0}& {b}_{1}\\ {y}_{0}& {b}_{2}\end{array}\right),$$

- Both parameters ${t}_{i}$ and ${t}_{j}$ lie in the interval $\langle 0,1\rangle $ and the intersection of the axes is found between the end points of the axes, which does not comply with the conditions for drawing objects; hence, ${c}_{i,j}=\varnothing $.
- Neither ${t}_{i}$ nor ${t}_{j}$ lies in the interval $\langle 0,1\rangle $ and the intersection of the axes is found outside the axis area delimited by the end points of the axes, which does not comply with the conditions for drawing objects; hence, ${c}_{i,j}=\varnothing $.
- Only one of ${t}_{i}$ or ${t}_{j}$ lies in the interval $\langle 0,1\rangle $ and the intersection of the axes is found between the end points on one axis and outside the area delimited by the end points on the second axis, which complies with the conditions for drawing objects. Hence, the co-ordinates of the intersection of the axes are calculated using the formulae below; that is, ${c}_{i,j}=\left[{x}_{ijc};{y}_{ijc}\right]$, where$$\{\begin{array}{c}{x}_{ijc}={P}_{1ix}+{t}_{i}\xb7\left({P}_{2ix}-{P}_{1ix}\right)\\ {y}_{ijc}={P}_{1iy}+{t}_{i}\xb7\left({P}_{2iy}-{P}_{1iy}\right)\end{array}$$$$\{\begin{array}{c}{x}_{ijc}={P}_{1jx}+{t}_{j}\xb7\left({P}_{2jx}-{P}_{1jx}\right)\\ {y}_{ijc}={P}_{1jy}+{t}_{j}\xb7\left({P}_{2jy}-{P}_{1jy}\right)\end{array}.$$

- Corner connection of the axes (see Figure 11, State 1), under the condition:$$\left\{\left|{d}_{1i,j}\right|\vee \left|{d}_{2i,j}\right|\right\}=\left\{\left|{d}_{3i,j}\right|\vee \left|{d}_{4i,j}\right|\right\}=\frac{w}{2}$$
- T-connection of the axes (see Figure 11, State 2) under the condition:$$\left\{\left|{d}_{1i,j}\right|\vee \left|{d}_{2i,j}\right|\vee \left|{d}_{3i,j}\right|\vee \left|{d}_{4i,j}\right|\right\}=\frac{w}{2}$$

- For the corner connection of axes (see Figure 12, State 1):$$\{\begin{array}{c}\left\{{P}_{1i}\left[x;y\right]\vee {P}_{2i}\left[x;y\right]\right\}=\left[{x}_{c};{y}_{c}\right]\\ \left\{{P}_{3i}\left[x;y\right]\vee {P}_{4i}\left[x;y\right]\right\}=\left[{x}_{c};{y}_{c}\right]\end{array}.$$
- For the T-connection (see Figure 12, State 2):$$\left\{{P}_{1i}\left[x;y\right]\vee {P}_{2i}\left[x;y\right]\right\}\vee \left\{{P}_{3i}\left[x;y\right]\vee {P}_{4i}\left[x;y\right]\right\}=\left[{x}_{c};{y}_{c}\right]$$

## 5. Experimental Verification and Practical Demonstration of Research

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BIM | Building Information Modeling |

BREP | Boundary Representation |

IFC | Industry Foundation Classes |

KRL | Kuka Robotic Language |

KUKA | a German-based manufacturer of industrial robots |

PHP | Hypertext Preprocessor (or Personal HomePage a popular general-purpose scripting language) |

TCP | Tool Centre Point |

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**Figure 8.**Connection of axes with the method of connecting discontinuous axes with an orthogonal layout.

**Figure 15.**Sample of PHP code for searching the intersections of the axes, viewed in the Notepad++ editor.

Intermediate Steps | Visualization of Conversion |
---|---|

Reading from IFC file and searching for wall object | 159 IFCSHAPEREPRESENTATION(#102,‘Body’,‘SweptSolid’,(#149)); 162 IFCPRODUCTDEFINITIONSHAPE($,$,(#141,#159)); 166 IFCWALLSTANDARDCASE(‘1JhL2KuR9Fthk9hVMuZzBg’, #41, ‘Non-bearing wall: Porotherm 8:318893’,$,‘Non-bearing wall:Porotherm 8:318625’,#135,#162,‘318893’); 175 IFCMATERIAL(‘Brick wall’); 180 IFCSTYLEDITEM($,(#178),$); 182 IFCSTYLEDREPRESENTATION(#97,‘Style’,‘Material’,(#180)); |

Parsing object and searching for other properties | 166: IFCWALLSTANDARDCASE, #41, $, #135, #162 135: IFCLOCALPLACEMENT, #122, #134 134: IFCAXIS2PLACEMENT3D, #132, #19, #17 132: IFCCARTESIANPOINT, −8320.17111815646, 16161.2332918, 0. 17: IFCDIRECTION, 0., −1., 0. 162: IFCPRODUCTDEFINITIONSHAPE, $, $, #141, #159 159: IFCSHAPEREPRESENTATION, #102, #149 149: IFCEXTRUDEDAREASOLID, #147, #148, #19, 2750. 147: IFCRECTANGLEPROFILEDEF, .AREA., $, #146, 9500., 79.999 |

Translated and rotated co-ordinates for each wall object | Type of object: non-bearing wall IFC Raw: 166 Geometry of object (length/width/height in mm): 9500/80/2750 Co-ordinate axis: middle Rotation (degree): 270 Co-ordinates of object start: −8320;16161 Co-ordinates of object end: −8320;6661 |

ID | IFC | Length, [mm] | Width, [mm] | Height, [mm] | Axis | Axis Rotation, [grad] | Axis Beginning, [X;Y] | Axis End, [X;Y] |
---|---|---|---|---|---|---|---|---|

1 | 560 | 9500 | 440 | 2750 | middle | 90 | 220;440 | 220;9940 |

2 | 527 | 9940 | 440 | 2750 | middle | 180 | 9940;220 | 0;220 |

3 | 494 | 9940 | 440 | 2750 | middle | 270 | 10160;9940 | 10160;0 |

4 | 445 | 10380 | 440 | 2750 | middle | 0 | 0;10160 | 10380;10160 |

5 | 405 | 1250 | 80 | 2750 | middle | 0 | 4060;8340 | 5310;8340 |

6 | 371 | 2380 | 80 | 2750 | middle | 0 | 4060;3150 | 6440;3150 |

7 | 337 | 5810 | 80 | 2750 | middle | 270 | 6480;6250 | 6480;440 |

8 | 303 | 3420 | 80 | 2750 | middle | 180 | 9940;4340 | 6520;4340 |

9 | 269 | 5880 | 80 | 2750 | middle | 0 | 4060;6290 | 9940;6290 |

10 | 235 | 1970 | 80 | 2750 | middle | 270 | 5270;8300 | 5270;6330 |

11 | 166 | 9500 | 80 | 2750 | middle | 270 | 4020;9940 | 4020;440 |

ID | Length, [mm] | Width, [mm] | Height, [mm] | Axis Rotation, [grad] | New Length, [mm] | Axis Start, [X;Y] | Axis End, [X;Y] | New Axis Start, [X;Y] | New Axis End, [X;Y] |
---|---|---|---|---|---|---|---|---|---|

1 | 10380 | 440 | 2750 | 0 | 9940 | 0;10160 | 10380;10160 | 220;10160 | 10160;10160 |

2 | 9940 | 440 | 2750 | 270 | 9940 | 10160;9940 | 10160;0 | 10160;10160 | 10160;220 |

3 | 9940 | 440 | 2750 | 180 | 9940 | 9940;220 | 0;220 | 10160;220 | 220;220 |

4 | 9500 | 440 | 2750 | 90 | 9940 | 220;440 | 220;9940 | 220;220 | 220;10160 |

5 | 9500 | 80 | 2750 | 270 | 9500 | 4020;9940 | 4020;440 | 4020;9940 | 4020;440 |

6 | 1970 | 80 | 2750 | 270 | 2050 | 5270;8300 | 5270;6330 | 5270;8340 | 5270;6290 |

7 | 5880 | 80 | 2750 | 0 | 5920 | 4060;6290 | 9940;6290 | 4020;6290 | 9940;6290 |

8 | 3420 | 80 | 2750 | 180 | 3460 | 9940;4340 | 6520;4340 | 9940;4340 | 6480;4340 |

9 | 5810 | 80 | 2750 | 270 | 5850 | 6480;6250 | 6480;440 | 6480;6290 | 6480;440 |

10 | 2380 | 80 | 2750 | 0 | 2460 | 4060;3150 | 6440;3150 | 4020;3150 | 6480;3150 |

11 | 1250 | 80 | 2750 | 0 | 1250 | 4060;8340 | 5310;8340 | 4020;8340 | 5270;8340 |

Order | Wall | Description | Length, [mm] | Width, [mm] | Height, [mm] | Position of Center, [X;Y;Z] | Layer | Rotation | Weight, [kg] |
---|---|---|---|---|---|---|---|---|---|

1 | Bearing | Porotherm 44 Profi K | 250 | 440 | 250 | 220;9815;125 | 1 | 180 | 21.1 |

2 | Bearing | Porotherm 44 Profi | 250 | 440 | 250 | 220;9565;125 | 1 | 180 | 20.4 |

3 | Bearing | Porotherm 44 Profi R | 187 | 440 | 250 | 93.5;10160;125 | 1 | 90 | 15.4 |

4 | Bearing | Porotherm 44 Pro 1/2 | 125 | 440 | 250 | 249.5;10160;125 | 1 | 90 | 11.0 |

… | … | … | … | … | … | … | … | … | … |

2230 | Non-bearing | Porotherm 8 Profi | 500 | 80 | 250 | 4020;2360;2625 | 11 | 180 | 9.4 |

2231 | Non-bearing | Porotherm 8 Profi | 500 | 80 | 250 | 4020;1860;2625 | 11 | 180 | 9.4 |

2232 | Non-bearing | Porotherm 8 Profi | 500 | 80 | 250 | 4020;1360;2625 | 11 | 180 | 9.4 |

2233 | Non-bearing | Porotherm 8 Profi | 500 | 80 | 250 | 4020;860;2625 | 11 | 180 | 9.4 |

2234 | Non-bearing | Porotherm 8 Profi | 170 | 80 | 250 | 4020;525;2625 | 11 | 180 | 3.2 |

Location | Initial Co-Ordinates, [X;Y;Z] in mm | Initial Amount of Examined Points | Number of Admissible Points |
---|---|---|---|

1 | 2500;2500;1375 | 2209 | 176 |

2 | 2500;7500;1375 | 2162 | 176 |

3 | 7500;7500;1375 | 2116 | 137 |

4 | 7500;2500;1375 | 2162 | 148 |

**Table 6.**Computing the movement route of robotic unit TCP (Tool Centre Point) for admissible points in the first location.

Point | Co-ordinates, [X;Y;Z] in mm | Total Distance of TCP Movement, [mm] |
---|---|---|

1 | 1500;2000;1375 | 1,230,399 |

2 | 1500;2100;1375 | 1,240,776 |

3 | 1500;2200;1375 | 1,252,321 |

… | … | … |

174 | 3000;2700;1375 | 1,338,326 |

175 | 3000;2800;1375 | 1,401,561 |

176 | 3000;2900;1375 | 1,420,925 |

Location | Optimal Position, [X;Y;Z] in mm | Minimum Movement Route of TCP, [m] | Maximum Movement Route of TCP, [m] | Initial Movement Route of TCP, [m] | Total Reduction of Route Distance |
---|---|---|---|---|---|

1 | 2200;1600;1375 | 1192 | 1467 | 1306 | 9.56% |

2 | 2200;8700;1375 | 1392 | 1584 | 1504 | 8.05% |

3 | 8300;8100;1375 | 1585 | 1675 | 1643 | 3.65% |

4 | 8200;1900;1375 | 1564 | 1703 | 1629 | 4.16% |

Total: | 5733 | 6429 | 6082 | 6.09% |

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**MDPI and ACS Style**

Usmanov, V.; Illetško, J.; Šulc, R.
Digital Plan of Brickwork Layout for Robotic Bricklaying Technology. *Sustainability* **2021**, *13*, 3905.
https://doi.org/10.3390/su13073905

**AMA Style**

Usmanov V, Illetško J, Šulc R.
Digital Plan of Brickwork Layout for Robotic Bricklaying Technology. *Sustainability*. 2021; 13(7):3905.
https://doi.org/10.3390/su13073905

**Chicago/Turabian Style**

Usmanov, Vjačeslav, Jan Illetško, and Rostislav Šulc.
2021. "Digital Plan of Brickwork Layout for Robotic Bricklaying Technology" *Sustainability* 13, no. 7: 3905.
https://doi.org/10.3390/su13073905