Intelligent virtualization of crane lifting using laser scanning technology
1. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue 639798, Singapore
2. Interdisciplinary Graduate School (IGS), Nanyang Technological University, 21 Nanyang Link 637371, Singapore
3. Energy Research Institute @ NTU (ERI@N), Nanyang Technological University, Level XF5, 50 Nanyang Drive 637553, Singapore
Abstract
Keywords： Laser scanning ; Point cloud ; Intelligent modeling ; Virtualization of complex environments ; Virtual tower crane ; Automatic lifting path planning ; Rasterization
Content
Parameter  Definitions 

${\alpha}_{BD}$

The rotation angle of the tower body around the
$z$
axis, which is fixed once the tower crane is set up 
${R}_{z}({\alpha}_{BD})$

The rotation matrix around the
$z$
axis for a rotation angle of
${\alpha}_{BD}$

${R}_{z}({\alpha}_{SW})$

The rotation matrix around the
$z$
axis for a rotation angle of
${\alpha}_{SW}$

${T}_{y}({l}_{MV})$

The translation matrix along the
$y$
axis for a moving length of
${l}_{MV}$

${T}_{z}({l}_{HS})$

The translation matrix along the
$z$
axis for a moving length of
${l}_{HS}$

$\stackrel{\u20d7}{AB}$

The vector from point A to point B 
$\stackrel{\u20d7}{BC}$

The vector from point B to point C, its length is the counterjib’s length 
$\stackrel{\u20d7}{BD}$

The vector from point B to point D, its length is the jib’s length 
Scan ID  Number of Points  File Size (MB)  Scanning Time (Min:Sec) 

1  11483663  261.950  10:18 
2  11850648  270.319  10:37 
3  12614167  287.732  11:20 
4  16271827  371.147  10:27 
5  20469452  466.876  13:56 
6  12995088  296.419  12:38 
7  12451583  284.024  10:10 
8  12112391  276.289  10:16 
9  12592680  287.242  10:41 
Rate  Resolution (mm)  Number of points  File size (MB) 

Full  2  120144032  2740.473 
1/2  2  60090038  1716.858 
1/4  3  30027171  885.045 
1/9  4  13341982  471.086 
1/16  5  7513351  265.288 
1/25  6  4804782  169.653 
Sampling rate  File size (MB)  Number of points in the point cloud file  Number of points in the generated depth map  Rasterization time (ms) 

1/9  471.086  1334982  22602  828 
1/16  265.288  7513351  20342  459 
1/25  169.653  4804782  20455  295 
Depth map Resolution (cm) 
Number of points in the point cloud file 
Number of points in the generated depth map 
Rasterization time (ms) 

10  13341982  117898  848 
20  54214  836  
40  22602  828  
100  6569  822 
Input  Value 

Tower crane model  Terex SK41520 
Size of population  100 
Length of string  6 
Crossover rate  0.75 
Mutation rate  0.25 
Start configuration (
${\alpha}_{SW}$
,
${l}_{MV}$
,
${l}_{HS}$
,
${\alpha}_{LD}$
)

(21°, 2714cm, 2113cm, 355°) 
End configuration (
${\alpha}_{SW}$
,
${l}_{MV}$
,
${l}_{HS}$
,
${\alpha}_{LD}$
)

(113°, 6488cm, 2113cm, 113°) 
Termination iteration  200 
Depth map resolution (cm)  GA runtime (ms)  N^{th} Iteration (when convergence begins)  Average success fitness value  Success rate (%) 

10  90358  44  511.46  100% 
20  43289  40  513.79  100% 
40  20312  48  515.15  100% 
100  9941  61  518.90  96% 
Depth map resolution (cm)  GA runtime (ms)  N^{th} Iteration (when convergence begins)  Average success fitness value  Success rate (%) 

10  78991  32  523.38  100 
20  36186  43  521.56  100 
40  18610  43  521.49  100 
100  8742  42  522.96  100 
Resolution of depth map (cm)  GA runtime (ms)  N^{th} Iteration (when convergence begins)  Average success fitness value  Success rate (%) 

10  70431  22  528.52  100 
20  31353  43  529.35  100 
40  16592  48  528.84  100 
100  8664  64  529.89  98 
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