Measuring Runout Value of Sliding Door Using Combination Method

of Laser and Machine Vision

Qi Chen

, Liming Wu

, Ya’nan Zhao

, Chao Xu

and Yonggen Xu

1School of Electromechanical Engineering,Guangdong University of Technology, Guangzhou, China

2Zhongshan OPK Hardware products Co., Ltd, Zhongshan Xiaolan, China

Keywords: Measuring runout value of sliding door, Laser measurement, Machine vision measurement, nonlinear

optimization.

Abstract: In order to solve the problem of low automation in the original measurement of sliding door run out value, a

method of using a servo motor to replace the manual sliding door is proposed at first, then give an analysis

about the error source of laser measurement when the run out value is large, and a measurement method of

the run out value of the sliding door based on machine vision is designed. The method estimate the ROI of

every frame by calculating of the motor speed at first, then use image processing to process the run out

video, and the position of the marker is finally gotten. The measurement results of the laser displacement

sensor are used to optimize the visual measurement results, and Gauss-Newton is used to solve the nonlinear

least squares problem. Experimental results show that this method can effectively improve the overall

accuracy in visual measurement.

1 INTRODUCTION

The damping system of the pulley is an important

part of the sliding door. Because the ordinary sliding

door does not have a damping system installed, the

door will have a strong collision with the door frame

at the moment of closing, which not only destroys

the structure of the door frame, but also creates

environmental noise and affects people's quality of

life. Instead, elegant sliding doors are installed with

the damping system on the door rail, which can

effectively avoid this problem. The door will

experience a buffering time of 2-5s before fully

closing. However, the performance of the damping

system will also directly affect the user's sliding

door experience. When the sliding door contacts

with the damping system, it will be affected by the

force which make it generate a run out in the vertical

direction, and the value of run out is not only

affected by the installation quality of the sliding

door fittings but also the speed of door movement

and the structure of the damper pulley system. If the

value of jump is too large, not only will it reduce the

comfort when using the sliding door and increase the

noise of the sliding door, but it will also cause the

door to fall off from the track.

Obviously, the measurement of the run out value

of the sliding door has become a key step in the

testing of the damping system. Analysis of the run

out curve can not only verify the product's

conformity, but also can reflect the defects in the

structural design of the damping system. In this

paper, according to the existing test methods, the

servo motor is used instead of the manual sliding

door, after analysing the inevitable error of the laser

measurement method in the test process , a vision-

based runout measurement method is proposed, and

the laser sensor is used for correcting the result

which can reduces the overall measurement error.

2 SLIDING DOOR TEST FRAME

The sliding door run out test is tested on the test

frame. The traditional test frame consists of a door

frame, a track, a sliding door, and a damping system.

After being installed with the matching damping

system, when the sliding door is closed to a certain

distance, it will be subject to a buffering effect of

damping, so that the sliding door will automatically

and slowly close in the closing direction. Due to the

different mechanical structures of the dampers, some

dampers will cause the door to jump slightly in the

vertical direction while allowing the sliding door to

close slowly. The value of run out is also related to

the weight of the door itself. The smaller the weight,

the greater the run out value.

The traditional testing framework itself does not

have the power to move the door. It requires people

to push the door manually. The manual method of

sliding the door is closer to the actual use, but the

long-time test can easily cause fatigue to the

operator (Xu Xianzhe, 2015). That will cause the

intensity and speed of pushing the door cannot be

accurately grasped. And the manual push door test

method has uncertainty in the direction of the push

door. If the force of the push door is not horizontal,

it will generate extra displacement in the vertical

direction.

In order to solve this problem, the sliding door

frame was reconstructed and servo motor with

conveyor belt was used to control the movement of

the door. In this method, the position, speed,

acceleration and test times of the door movement

could be set to achieve automatic testing, which

greatly reduced the workload of testers. Use this

method to push the sliding door can only produce a

horizontal speed and ensuring that the moving door

is in the horizontal direction before the run out

occurs.

3 ANALYSIS THE ERROR OF

LASER MEASUREMENT

The run out value of the sliding door refers to the

moving distance of the door in the vertical direction

during the movement. The jumping usually occurs at

the moment of contact with the damping system, and

the whole process is about 200 ms. The traditional

method is to use the laser sensor to measure the

displacement in real time. The laser sensor has the

advantages of high precision, fast response and non-

contact measurement, and the measurement

frequency can reach 50-100 Hz(Sun Bin,2015). The

method is to install the laser sensor on the sliding

door when the door is not moving, and record the

distance from the sensor to the door frame at this

time. This distance is defined as the base reference

value. In the test process, the actual run out value is

equal to the measured value minus the base

reference value:

(1)

Note that the sensor observation value is , C1

is the base reference value of the sensor before the

start of the test, and is the theoretical jump

distance.

This measurement method can accurately

measure the run out value of the moving door

without considering the tilt angle of the jump.

However, when the door is jumping, it must be one

end jumping and the other end is in the original

posture. This will cause the tilt angle is not equal to

0 at the jumping moment, as shown in the figure:

Figure 1: Tilted laser sensor.

When there is a certain tilt angle between the

sensor and the test frame, the observation value of

the laser sensor is no longer the shortest distance AC

from the test frame. Instead, the result is tilted by .

Obviously, the actual run out value should be:

(2)

is the actual run-out distance. Since the laser

sensor cannot measure the tilt angle , the

measurement error of the laser method is:

(3)

As can be seen from equation, the measurement

error of the laser measurement method is affected by

the run out observation value and the magnitude of

the tilt angle, and when the run out value and the tilt

angle are small, high-precision measurement results

can be obtained. With the increase of the tilt angle,

the error will be gradually enlarged. In this regard,

there is an urgent need to design a measurement

method capable of observing from a global

perspective so that the accuracy of the observation

results will not be affected by the position of the

sliding door.

4 DETECTION BASED ON

MACHINE VISION

The advantage of machine vision-based run out

detection is that the camera sensor can observe the

run out value from a global perspective. The position

of the sensor during the observation process is not

affected by the movement of the sliding door.

The camera is mounted on the top right of the

test frame where the jump occurs. A square red

marker with a side of 10 mm is pasted on the sliding

door and let the edge of the marker is parallel to the

sliding door frame.

Figure2: Test Frame with Camera and Marker.

4.1 Camera Calibration

Camera calibration is a key step in the process of

obtaining three-dimensional information using the

two-dimensional plane image information of the

object (Xu Chao,2017). The camera calibration is to

obtain the camera's own structural parameters and

camera pose. In the visual inspection system, the

accuracy of the calibration directly affects the

accuracy of the measurement results. Different

inspection requirements require different calibration

methods.

Realizing the three-dimensional point in the real

world and the two-dimensional transformation in the

image requires the use of four coordinate systems:

world coordinate system, camera coordinate system,

image coordinate system and pixel coordinate

system (Li Xin,2017). The world coordinates are the

reference coordinates of the spatial position. The

camera coordinates are based on the lens optical

center and the optical axis direction is the z-axis.

The formula from the world coordinate to the

camera coordinate is:

（4）

R is a 3x3 rotation matrix, which represents the

rotation of the camera coordinates to world

coordinates, and t is a 3x1 translation vector.

The image coordinate system refers to the two-

dimensional coordinate system established on the

image with the camera optical center as the origin,

and the unit of the coordinate axis is the physical

size of the actual pixel. The pixel coordinates are the

coordinate system established with the upper left

corner of the image as the origin of coordinates. The

unit of the pixel coordinate axis is the pixel. The

conversion from the image coordinate system to the

pixel coordinate system can be expressed as:

（5）

To detect the amount of run out value, we only

need to calculate the proportional relationship

between the unit pixel and the actual length. This

paper selects the checkerboard calibration board as

the reference object, first determines the physical

dimension d (unit: mm)of the calibration board, and

calculates the number of pixels n(unit: pixel) of the

checker boxin the image is acquired, then the

proportional coefficient (Gong Cong,2014):

(6)

In order to improve the camera calibration

accuracy and eliminate the impact of the camera lens

distortion, the calibration board needs to be

photographed at different angles, and then take the

average of these calibration results as the final

calibration result. In this paper, the resolution of the

camera is 1024*960, 9*9, checkerboard calibration

board with 4mm grid length is used for calibration,

and 9 pictures of different angles are taken on the

calibration board. The measurement results are as

follows:

Table 1:Camera calibration results.

times Pixel number

1 128.0212

2 129.0043

3 128

4 129

5 128.0089

6 129.0012

7 129.0318

8 128.0724

9 128.0416

The average value is 128.4646 and the

proportional coefficient k=0.0311 mm/pixel.

4.2 Runout Displacement

Measurement

After the test video is recorded, images are extracted

frame by frame for processing. The first is the image

preprocessing. In order to reduce the image

processing time, the image needs to be extracted

from the region of interest (Qiu Zhicheng, 2012).

Because the servo motor is used to control the

sliding door, the approximate position of the marker

at a certain moment can be calculated according to

the speed, and then converts it to image coordinates

and intercepts the image. As shown in the figure, the

color of the marker and the color of the door are

significantly different. After the grayscale

transformation and binarization of the image, the

background is filtered from the image, and use the

canny edge detection to extract the edges of the

marker.

Figure 3: Visual Measurement Process.

Then use the Hough transformation to detect line

segment to locate the coordinates of the four edges

of the marker, and note that the endpoint in the

upper right corner is

and the endpoint in the

upper left corner is

. Before the start of the

test, the reference value

is measured

using this method. In the following frames, - can

be used to obtain the vertical pixel of the jumping

gate, and and coordinates can be used to find

the runout tilt angle α. As we can see from the

formula:

(7)

You can calculate the actual runout value of the

sliding door.

Figure 4: ROI and Binary image.

Figure 5: Canny and Hough Change.

5 OPTIMIZE MEASUREMENT

RESULTS

Among the above two measurement methods, the

displacement measurement accuracy of the laser

displacement sensor is higher, reaching 0.01mm,

repeatability 15um, and the error mainly comes from

the tilt angle α in the test process, and the laser

sensor tilt angle αcannot be measured by itself. In

the detection of runout using machine vision, we can

get both the runout value and the tilt angle by using

the points

and and the reference

coordinates

. However, because of

camera noise in the actual measurement process, our

measurement results will inevitably have errors, that

is, the coordinates of A and B may actually have a

certain offset:

(8)

(9)

Here, a, b, c, d are the offsets of the new

coordinate point on the original coordinate point.

The angle and the new runout value calculated from

the new coordinate are:

（10）

(11)

Substituting the obtained into Equation 1：

(12)

It is not difficult to know that both S

and

indicate the actual run out value. Ideally there

are：

(13)

(14)

(15)

Due to the presence of noise, a, b, c, d are not

always equal to zero. The above formula cannot be

established, defining the error function：

(16)

(17)

Here N is the total number of video frames. It

can be seen that this is a non-linear optimization

problem that can be linearized by performing a first-

order Taylor expansion:

(18)

Substitute the linearized f(x) into (17).Then

calculates the derivative of and let it equals to

zero.

(19)

x is a 4x1 vector [a,b,c,d]T, the Gauss-Newton

method is used to find the optimal offset. The

solution is(Li Bo,2015):

(1) Given a preliminary test value

(2) Calculate iteration step size

(3) Update iterative value =

(4) The result of the calculation. If e is small

enough, is output, otherwise, step 2 is returned.

This article uses a small weight sliding door to

test, the purpose is to make the tilt angle and runout

value more obvious. After testing 10 times, 50 sets

of laser sensor data synchronized with time stamp

and 50 frames were obtained. After using Google

ceres library for optimization, after 8 iterations, the

value of the error function was decreased from

0.1118 to 0.0421. The optimal values of a, b, c, and

d are 1.2622, -3.6903, -1.2622, and -3.9108.

6 CONCLUSIONS

Aiming at the problem that the method of laser

measurement has obvious errors when the runout

value and tilt angle are large, a detection method

based on machine vision is proposed. The

measurement result of the laser sensor is used to

correct the visual measurement result and a

nonlinear optimization problemis constructed, then

use Gaussian Newton method to solve the

optimization variables. The experimental results

show that, given the initial value of 0,0,0,0, the

Gauss Newton method can iterate the optimal offset

with fewer iterations, and the optimization error

decreases from 0.1118 to 0.0421, which effectively

improve the overall accuracy in visual measurement.

ACKNOWLEDGEMENTS

This work was supported by the Science and

Technology Planning Project of Guangdong

Province (no.2017A090905047), Science and

Technology Planning Project of

Guangzhou(no.201806010128) and A New

Generation of Intelligent Large-Scale Carton

Printing Equipment Package Development and

Industrialization. Thanks for the helps.

REFERENCES

1. Sun Bin, Lin Bing, 2015. A quantitative error

compensation model of the inclination angle of the

laser displacement sensor. Chinese Journal of

Scientific Instrument 36(05):996-1004.

2. Xu Xianze, Liang Chu, 2015. Design of circular

runout detecting system of automobile transmission

shaft based on ARM. Engineering Journal of Wuhan

University 48(2):234-238.

3. Xu Chao, Zhang Yifan, Han Xiaoming, Deng Jianjun,

2017. Machine Vision Based Vibration Displacement

Measurement of Large Flexible Structures.Journal of

Vibration, Measurement and Diagnosis37(04):781-

786+846.

4. Li Xin, Wu Liming, WangGuitang,Xiong Feng, Chen

Yujun, 2017. Image Mosaic Method for Large Size

Component Vision Measurement Based on

Homography Matrix. Computer Measurement and

Control 25(11):26-29+33.

5. Qiu Zhicheng, Zhang Xiangtong, 2012. Vision-Based

Vibration Measurement and Control of Flexible

Structure.Journal of Vibration, Measurement and

Diagnosis 32(01):11-16+157-158.

6. Gong Cong, 2014. The Method and Realization of

High-Precision Size Measurement Based on Machine

Vision.Guangdong University of Technology.

7. Li Bo,Chen Yan, Zhou Xiangjun, 2015.Accurate

recognition of work-pieces based on Gauss-Newton

image registration.Optics and Precision Engineering.