MMAN 3210
ENGINEERING EXPERIMENTATION
LABORATORY ASSIGNMENT 3
Yogi K. Gunario
z3246759
Laboratory T 11 A
Tuesday (11 – 1) and Wednesday (3 – 4)
INTRODUCTION
This report will contain 2 sections. Part 1 will focus on evaluating the accuracy of the laser sensor
including the related random errors, whereas part 2 will focus on estimation of the shape of the
scanned objects with using range measurement and regression methods.
EXPERIMENT PART 1
APPROACH
Test Conditions
There are two objects which will be utilised in this experiment, which are a flat board and a
cylindrical bin. For this section, the flat board will be used to evaluate the accuracy of the scan
results.
The data collected from the scans of the flat board at different ranges and angles will be used to
evaluate the quality and accuracy of the measurement. This is possible to be done by examining the
data standard deviation which is caused by random errors. Different ranges of the middle of flat
board from the scanner to be measured are 1 m, 2 m, and 3 m, with various angles for each different
range which are 0o, 30o, and 45o.
Data Extraction Method
The data extraction is done with a laser scanner, with number of scan of 20 and time interval of 0.1 s
between each scans. The scanner will emit laser beams at 361 different angles with a difference of
0.5o between each beam. This will detect object positions in front of the scanner about a plane on
the height of the laser beam emission, covering 180o degrees in the scan. The 180th laser beam will
be used as the range measurement, as this laser is pointing straight towards the object
(perpendicular to laser scan surface). In other words, three-dimensional objects can be interpreted
as two-dimensional objects by the laser scanner and hence it is possible to detect object position
and shape.
The range collected is the range measured by the beam 180; the laser beam pointing to the front of
the scanner. Such example code below shows how to extract the measurement from beam 180 in
order to create plot and histogram as shown in figure 1 and figure 2.
load 1m0d.mat
time_interval = 0:0.1:1.9;
range = X.Scans(:,180);
plot(time_interval,range,'.')
hist(range)
The code above represents an example of data extraction by loading data set 1m0d.mat. Setting the
time interval from 0 to 1.9 s with time interval of 0.1 s (this gives 20 scan attempts), and the range
taken from beam 180, plots and histograms for such time interval and range as shown in figure 1 and
figure 2 can be created.
Standard Deviation
Standard deviation is a magnitude of how much the data values spread from the mean value of all
data points, which is also the square root of the data variance. Standard deviation can be
mathematically expressed as
∞
𝑁
1
𝜎 = √𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = √ ∫ (𝑥𝑖 − 𝑥̅ )2 𝑝(𝑥)𝑑𝑥 = √
∑(𝑥𝑖 − 𝑥̅ )2
𝑛−1
𝑖=1
−∞
Meanwhile such functions can be used to find standard deviation and mean value in Matlab
STD = std(R)
MEAN = mean(R), where R is the collection of data points
By comparing the standard deviation to the mean value, it is possible to evaluate the quality and
accuracy of the measurement done by laser scanner.
It is expected that the error is dependent against the test. The hypothesis is that the error will
increase as the range and angle of inclination of the object are increased while being measured.
There are various reasons why the error might be dependent against different tests.
 Any small error represents in the laser scanner will cultivate into larger error as the range of
object is increased.
 Discrepancies caused by noise interference contributes to error
 Human error does not allow the object to be placed perfectly at the desired range and
inclination angle.
 Object has limited ability to reflect laser beam
RESULTS
1 m 0 deg
0
1
Time (s)
2 m 30 deg
1
Time (s)
1 m 45 deg
Range
0
1
Time (s)
2 m 45 deg
0
1
Time (s)
2
2.14
2.12
2
0
1
Time (s)
3 m 45 deg
2
0
1
Time (s)
2
3.25
Range
2
1
Time (s)
3 m 30 deg
3.2
3.18
2
2.16
Range
4
0
3.22
2.18
2.16
2
3.08
3.07
2
2.2
0
Range
2.08
2.07
2
Range
Range
1
Time (s)
1 m 30 deg
Range
Range
Range
0
1.14
1.135
1.13
1.125
0
3.09
2.09
1.1
1.05
3 m 0 deg
2 m 0 deg
1.15
0
1
Time (s)
2
3.245
3.24
Figure 1 – Multiple scan for flat board for laser beam 180, range versus time
1 m 0 Deg
2 m 0 deg
3 m 0 deg
20
20
10
10
10
5
0
1.05
1.1
1.15
0
2.07
2.08
1 m 30 deg
2.09
0
3.07
2 m 30 deg
20
20
20
10
10
10
0
1.1251.131.1351.14
0
2.16
2.18
1 m 45 deg
2.2
0
3.18
2 m 45 deg
20
20
10
10
10
0
10
0
2.12
2.14
3.09
3.2
3.22
3 m 45 deg
20
0
-10
3.08
3 m 30 deg
2.16
0
3.24
3.245
3.25
Figure 2 – Histograms of extracted measurement, number of data points versus data point value
(Board at angle of 0 degrees)
4
Figure 3 – Example of flat surface locations –
Locations at incidence angle of 0 degree and at
different ranges; 1, 2, and 3 m
Random Readings
Board
3.5
Distance reading (m)
3
2.5
2
1.5
1
0.5
0
-2
-1.5
-1
-0.5
0
0.5
Horizontal position (m)
1
1.5
2
Figure 3 shows an example of locating flat surface
from data points available from scan. In the figure,
the flat surfaces at different ranges are shown in the
graph by green dots, whereas the red dots show
random surrounding objects. By observation from
such graph, the locations of the flat surfaces can be
clearly seen.
INVESTIGATION
Table 1 below shows the error standard deviation for different range and angle of inclination of the
measured flat board
Object
scanned
Flat board
Angle of
inclination
(degrees)
0
0
0
30
30
30
45
Distance (m)
Mean
𝑥̅ (m)
Error (m)
1
2
3
1
2
3
1
1.0710
2.0810
3.0850
1.1210
2.1745
3.1905
1.1000
0.0710
0.0810
0.0850
0.1210
0.1745
0.1905
0.1000
Standard
Deviation
σ (m)
0.0055
0.0031
0.0051
0.0031
0.0051
0.0022
1.2231e-007
45
45
2
2.1325
3
3.2405
Table 1 – error standard deviation
0.1325
0.2405
0.0044
0.0022
Based on table 1, the error in measurement generally increases as the angle of inclination and
distance are increased. The error is represented by the difference between the mean and the
distance. By looking at the error column, there is a general trend of increase in error by increasing
distance and angle of inclination. However, there is no certain trend of change in the standard
deviation for any change of distance and angle of inclination, as shown in the table above.
Furthermore, there is no strong evidence to proof that the increase in error is dependent to the
increase in distance and angle of inclination. The error might be caused by some other factors.
To increase experiment quality by reducing the effects of any possible error factors, there are some
possible methods can be applied. Firstly, the number of scanning repetition and data sets can be
increased to obtain more reliable measurement. Secondly, the experiment can be held in an
environment with minimal disturbances (including noise, vibration, etc.). Lastly, providing a new
laser scanner with better quality will increase the quality of data measurement.
EXPERIMENT PART 2
APPROACH
In this section, the positions and estimated shape of the flat board and cylindrical bin will be
evaluated by the laser sensor. However, due to random errors, uncertainties, and limited ability of
the laser scanning, the position and shape of both objects cannot be fully estimated by only using
the data points available from the scanning result. Therefore, line regression must be done to
estimate their position and shape, including possible dimensions. Figure 3, 4 and 5 below shows the
linear regression for the required estimations.
(Board at angle of 0 degrees)
4
Random Readings
Board
Polynomial fit
3.5
Distance reading (m)
3
2.5
2
1.5
1
0.5
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
Horizontal position (m)
0.6
0.8
1
Figure 3 – Board at 0oinclination angle, at different ranges
(Board at angle of 30 degrees)
(Board at angle of 45 degrees)
4
4
Random Readings
Board
Polynomial fit
3.5
3
Distance reading (m)
Distance reading (m)
3
2.5
2
1.5
2.5
2
1.5
1
1
0.5
0.5
0
-1
Random Readings
Board
Polynomial fit
3.5
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
Horizontal position (m)
0.6
Figure 4 – Board at inclination angle 30o
at different positions
0.8
1
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
Horizontal position (m)
0.6
Figure 5 – Board at inclination angle 45o
at different positions
For flat board, linear regression is done so that its position and dimensions can be estimated. This
can be done by applying a polynomial function to create a line of best fit for the data points which
represent the position and dimensions of the flat board. However, there are random objects being
scanned during the experiment. It is desired to separate these random data points from the flat
board data points.
Code taken from Matlab below shows the method to separate the points on the flat board from all
random data points. This will allow the flat board to be recognised by computer, so that estimations
can be done. The code minimises the data points for which to be taken for the linear regression.
k = 1; % define k to be 1 for for loop
for u=1:length(x)
if (x(u) > -0.8 && x(u) < 0.8) % minimise range of x
x1(k) = x(u);
y1(k) = y(u);
k = k + 1; % increment k
end
end
k = 1; % define k to be 1 again for new loop
for u=1:length(y1)
if (y1(u) > 0.4 && y1(u) < 4) % minimise range of y
x_board(k) = x1(u);
y_board(k) = y1(u);
k = k + 1; % increment k
end
num = k-1; % total number of points for board
end
The minimisation of point selection is done after board location inspection from the result shown in
figure 3, 4, and 5. As shown above, all boards at different ranges are located within the x-coordinate
of -0.8 and 0.8, and y-coordinate of 0.4 and 4. Variables x1 and y1 store the data points which is
already within the minimised x-coordinate range. Variables x_board and y_board store minimised
data points about y-coordinate by using x1 and y1 which have already been minimised in xcoordinate before. Hence, x_board and y_board carry vectors of data points for the flat board within
the desired range.
0.8
1
RESULTS
Table 2 represents the result for end-points and coefficients for linear regression applied to flat
board at different distances and incidence angles.
Object
scanned
Angle of
Distance
Left end-point
Right end-point Coefficient A
inclination
(m)
coordinate [X,Y]
coordinate [X,Y]
(degrees)
Flat board
0
1
-0.4785, 1.0748
0.4842 ,1.0876
-0.9329
0
2
-0.3995, 2.0550
0.5622 ,2.0980
-0.4800
0
3
-0.2433, 3.0914
0.7135 ,3.0907
-0.3242
30
1
-0.4290 ,0.8605
0.4103 ,1.3422
-0.8922
30
2
-0.4041 ,1.9010
0.4276 ,2.4251
-0.4612
30
3
-0.4643 ,2.9315
0.3904 ,3.4263
-0.3143
45
1
-0.3576 ,0.7173
0.3102 ,1.3990
-0.9144
45
2
-0.3143 ,1.7825
0.3289 ,2.4984
-0.4710
45
3
-0.4250 ,2.8434
0.2833 ,3.5994
-0.3103
Table 2 – Coefficients and end points for flat board at different situations
INVESTIGATION
Cylindrical Bin Readings
Random Readings
Bin
Circle Fit by Pratt
Center of Circle (Cylindrical bin)
4
3.5
Distance reading (m)
3
2.5
2
1.5
1
0.5
0
-1
-0.5
0
0.5
Horizontal position (m)
1
Coefficient B
-0.0129
-4.5503e-005
7.4786e-006
-0.4763
-0.2702
-0.1794
-0.9058
-0.5250
-0.3017
Object
scanned
Cylindrical Bin
Range (m)
Angle of
Estimated Centre Coordinate
inclination
[X,Y]
(degrees)
0.5
0.0831 ,0.7585
1
0.1077 ,1.2635
2
0.0830 ,2.2489
2.5
0.0677 ,2.8820
Table 3 – Estimated Circle Centre and Radius at different locations
Estimated Circle Radius
(m)
0.2438
0.2536
0.2205
0.2550