development of sewer pipe measurement system by vehicle

J-STAGE Advance Publication date: 8 January, 2016Paper No.14-00546

© 2016 The Japan Society of Mechanical Engineers[DOI: 10.1299/mej.14-00546]

Vol.3, No.1, 2016Bulletin of the JSME

Mechanical Engineering Journal

0123456789

Development of sewer pipe measurement system by vehicle equipped with low-priced MEMS sensor

Fujio IKEDA*, Shigehiro TOYAMA*, Toshio KUMOTA** and Takashi YANAGISAWA** * National Institute of Technology, Nagaoka College

888 Nishikatakai-machi, Nagaoka-shi, Niigata 940-8532, Japan

E-mail: [email protected]

**Kumota Incorporated Company

6-13 Gakko-cho, Myoko-shi, Niigata 944-0837, Japan

Abstract The total length of sewer pipelines in Japan is over 440,000 kilometers. Until now, experienced inspectors have conducted visual inspections by watching in-pipe animation images that are obtained from an autonomous vehicle equipped with a CCD camera. Their inspection methods have difficulties of quantitative evaluation with high accuracy because the viewpoints depend on the judging skills of the inspectors. In this study, we developed vehicles equipped with an inertial navigation system (INS) consisting of a gyro sensor and accelerometer in order to measure unevenness of the sewer pipe accurately and quantitatively. We also aim to achieve a simple measurement scheme at comparatively low cost. To accomplish these missions, two vehicles were designed and manufactured. The first vehicle is designed for the function of driving and pulls a second vehicle. The second vehicle’s only function is measurement; it is towed and does not move independently. We use the MEMS sensor devices installed on the second vehicle to suit our particular needs of low price and small size. However, these low-priced gyro sensors are notorious for their inaccuracy (experiencing such problems as drift error). We apply the extended Kalman filter (EKF) algorithm to reduce the estimation errors. We use quaternions as state variables of the posture for the 3D coordinate system. The experimental study shows that the suggested algorithms effectively remove the errors and can lead to systematic measurement schemes to accurately determine the unevenness of the sewer pipes.

Key words : Measurement vehicle, Sewer pipe, Quaternion, Extended Kalman filter, Gyro sensor, Accelerometer

1. Introduction

Sewer pipes are one of the most important urban infrastructure facilities. They discharge sewage, rainwater and

wastewater, conserving water quality and controlling flood damage to improve the housing environment and quality of public life. The sewerage systems in Japan have been developed rapidly from the period of high economic growth in the 1970s; as of the end of fiscal year 2012, the total length of sewer pipelines is over 450,000 kilometers (MLIT, 2015). As the years go by, cracks and distortions (such as those shown in Fig. 1(a)) emerge in sewer pipes because of pressures such as the load of moving vehicles on the ground above. This leads to serious risk of accidents due to road collapses (such as shown in Fig. 1(b)). Therefore, it is indispensable to routinely investigate the sewer pipelines in order to identify abnormal states in their early stages. About 90% of the buried pipes in Japan have narrow diameters of 200mm to 600mm, too narrow for actual human inspection. It is well known that pipe inspectors operate a vehicle equipped with CCD cameras to observe the state of the pipes from the inside (Muramatsu et al., 2005; Ogawa, 2009; Ohta et al., 1995). Since the skills and opinions of the inspectors vary widely, it is difficult to maintain a consistent appraisal of how serious the damage is, and it also places a heavy burden on the inspectors. Therefore, quantitative measurement methods have been desired. In recent years, quantitative ways to measure the cross-sectional shapes of pipes were proposed and put into partial use in local governments (Kantool Inc., 2008; Kawasue et al., 2008; Tanaka,

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Received 24 December 2014

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Ikeda, Toyama, Kumota and Yanagisawa, Mechanical Engineering Journal, Vol.3, No.1 (2016)


2001). One proposed method was to shoot a laser light—with a light-emitting device mounted on a moving vehicle—at a plate that is placed at the other end of the pipeline (Kumota Inc., 2015). The position of the laser light is received and recorded on a photo-detector plate mounted on the vehicle. This method has certain drawbacks. For example, manholes have to be set up at both ends of the target pipe, and some pipes may be so distorted that the light from the emitter cannot reach the light on the plate at the other end. Moreover, setting up the equipment itself takes plenty of time, and the initial cost of the system is comparatively expensive.

As one reasonable solution, we developed the vehicles equipped with an inertial navigation system (INS) using a gyro sensor and an accelerometer to measures unevenness of the sewer pipe. To detect the distance of the moving vehicle, one-wheel axle is equipped with a rotary encoder. Highly accurate sensors that have few bias errors are commercially available. These include inertial measurement units (IMU) (Crossbow Ltd., 2014), fiber optical gyroscopes (FOG), and ring laser gyroscopes (RLG). They are very expensive and a little too large to install on the small vehicle, though. Therefore, we used low-priced and small-sized MEMS sensor devices (ATR-Promotions, 2014) for the INS system to suit our objectives. However, they are less accurate than the expensive sensors. In particular, the most serious problem is the large drift error of the MEMS gyro (Rogers, 2003), which increases with the passage of measurement time. In order to solve the problem, we applied the extended Kalman filter algorithm, introduced in Suzuki et al. (2008) and Tawara et al. (2012), which integrated the MEMS sensor devices to estimate the posture of UAVs and reduce these estimation errors. We also used quaternions (Sabatini, 2006) for the vehicle’s three-dimensional coordinates. The experimental study shows that the integrated algorithms obtain the unevenness effectively and precisely.

2. Design and production of vehicles

In the early design stage of the measurement vehicle, we intended that all of the actuators, batteries, and sensors

(and their processing system) would be installed on one autonomous vehicle. However, it was difficult to satisfy this requirement and still fit inside a small pipe diameter of around 200mm. Therefore, we determined to design and manufacture two vehicles. One vehicle is optimized for driving and contains the actuators and batteries, and the other specializes in measurement and is towed (i.e., it has no independent power supply). The prototypes of both vehicles are manufactured to operate in the diameter range of 200mm to 300mm. Moreover, the vehicles can be converted to operate in pipes of 600mm by mounting an attachment. 2.1 Outline of measuring procedures

The measurement vehicle is drawn by the traction vehicle with a wire, as shown in Fig. 2. The traction vehicle drives forward and pulls the measurement vehicle with the wire kept at a fixed length. Separating the measurement devices and actuator devices has some advantages: The influence of the noise that arises from the vibration and magnetic field from the power supply is removed. This

decreases measurement errors.

Fig. 1(a) One sample picture of deteriorated sewer pipes

after several decades of use. There are cracks in

some places inside the pipe.

Fig. 1(b) The cracks of a sewer pipe thicken and spread,

which eventually causes a more serious

problem of road collapse.

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2



Enough power required for a drive and batteries can be mounted. Sufficient movement performance is thus achieved in a small vehicle body.

It is easy to change spare parts and measurement specifications. On the other hand, the following concerns may be considered: It is necessary to offer the function of wire roll-up in case of an emergency. The measurement vehicle does not have a drive function. It cannot move backward and forward on its own in case

of an emergency.

2.2 Design and manufacture of traction vehicle The draft designs and overview of the manufactured traction vehicle are shown in Fig. 3. It possesses two types of

pantograph arm mechanisms and is shaped like a horn. Wheels are mounted on the pantograph-type arms and tensioned with springs to fit tight on the inner side of a pipe, regardless of its diameter. This enables the vehicle to move stably even when there are unusual states, such as piled deposits or multiple breakage points. The horn-type arm is hooked at the finishing side of the manhole and prevents the traction vehicle from moving backward. We employed a Mabuchi RS540SH motor with a gear-to-gear ratio of 300 for the traction vehicle. A 6V1.5Ah lead–acid battery is used for these common power supplies. The specifications of the traction vehicle are shown in Tab. 1(a).

2.3 Design and manufacture of measurement vehicle The design policies of the measurement vehicle are as follows.

It is to avoid running onto deposit mounds to keep the noise level low. The sensor position must always keep the same profile across the pipe.

(a) In the case of the diameter of 200mm.

(b) In the case of the diameter of 300mm. (c) Overview of the traction vehicle.

Fig. 3 Draft designs and a photograph of the manufactured traction vehicle.

Traction vehicleMeasurement vehicle

sensor box

Fig. 2 Outline of measurement procedure. The measurement robot is drawn by the traction robot with a wire.

connecting wire

3

2



The draft designs and overview of the manufactured measurement vehicle are shown in Fig. 4. In order to cope with the first design policy, the vehicle has three legs (each with two wheels), with a leg mounted on every second face of a central hexagonal main body. These legs accomplish the rolling movement. Each leg is foldable and uses a slider and

(a) In the case of the diameter of 200mm.

(b) In the case of the diameter of 300mm.

Fig. 4 Draft designs and a photograph of the manufactured measurement vehicle.

(c) Overview of the measurement vehicle.

Weights

Bearings

Fig. 5 Enlarge view of the surroundings of the sensor box

around the center of the measurement vehicle.

Table 2 Specification of the MEMS sensor TSND121.

Items Specifications Unit

Weight 22 g

Size 37 46 12 mm

Range of gyro sensor 250 deg/s

Range of accelerometer 2 G

Chassis Value Unit

Dimensions ( ) mm

Weight 2.35 kg

Mechanical

Locomotive speed (Max) 220 mm/s

Traction speed (Rated) 83 mm/s

Traction weight (Max) 40 kg

Table 1(a) Specification of the traction vehicle.

Table 1(b) Specification of the measurement vehicle.

Chassis Value Unit

Length of body 175 mm

Length of legs 104 mm

Weight (No load) 1.10 kg

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spring mechanism to fit tight to the inner side of a pipe, regardless of its diameter. The MEMS sensor is put into a box that is mounted around the center of the main body. The sensor box rotates smoothly by bearings, and a weight under the box keeps it horizontal regardless of vehicle posture. The enlarged view of the sensor box area is shown in Fig. 5. In this paper, we adopt TSND121 (ATR-Promotions, 2014) as a small and low-cost MEMS sensor. The specifications of the measurement vehicle and the MEMS sensor are shown in Tab. 1(b) and 2, respectively.

3. Coordinate system and measurement method 3.1 Coordinate system

The three-dimensional coordinate system is defined to represent the posture of the vehicle in the sewer pipe as shown in Fig. 6. The first coordinate system is an inertial frame of reference represented by the R-frame, which satisfies Newton’s first law, and its origin is set at the center of the pipe at the starting point. The Xr axis is defined to be parallel to the longitudinal direction of the pipe, the Zr axis is in the upward direction, and the Yr axis indicates leftward direction in the horizontal plane (which follows the right-hand rule). The second coordinate system is a body frame represented by the B-frame, and its origin is fixed at the center of gravity of the measurement vehicle. The Xb axis is in the forward direction of the measurement vehicle, the Z r axis is in the upward direction, and the Y r axis is in the leftward direction.

3.2 Posture representation by quaternions

Quaternions are introduced to represent the conversion of these two coordinate systems for the R-frame and B-frame. Quaternions, also called Euler parameters (Tajima, 2006), provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions. In mathematics, quaternions are a number system that extends the complex numbers and is applied to mechanics in three-dimensional space. The system was first described by Irish mathematician William Rowan Hamilton in 1843. Now, it has found its way into applications in computer graphics, robotics, navigation, flight dynamics, and so on (Sabatini, 2006; Suzuki et al., 2008; Tawara et al., 2012). Compared to Euler angles, quaternions are easy to operate in algorithm and avoid the problem of a singular point known as gimbal lock. The quaternion is defined as follows:

kji 3210 . (1) Quaternions consist of one real part and three imaginary parts, where i, j, and k are the imaginary units that satisfy

1222 kji , (2) jkiijkkij ,, . (3)

As a matter of convenience in algorithm, quaternions are often represented by a vector notation such as

R-frame

Xr-axisYr-axis

Zr-axis B-frame

Xb-axis

Zb-axis

Yb-axis

moving direction

starting point

Fig. 6 The coordinate system composed of an inertial frame of reference (R-frame) and a body frame (B-frame).

5

2



T3210 . (4)

This notation can be used to define the sum, the difference, and the product of quaternions a and b as follows:

Tbabababa 33221100 ba , (5)

Tbabababa 33221100 ba , (6)

3

2

1

0

0123

1032

2301

3210

b

b

b

b

aaaa

aaaa

aaaa

aaaa

baZba )( . (7)

According to Euler's rotation theorem, any sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation (also called simple rotation (Tajima, 2006)) by a given angle about a fixed axis (called a Euler axis) that is described as follows:

Tzyx , (8)

1222 zyx . (9)

The quaternion , which represent the same posture of the single rotation, is defined and described by using λ and as follows:

2

2

2

2

2

2

3

2

1

0

sin

sin

sin

cos

sin

cos

z

y

x

. (10)

This quaternion to represent the single rotation is easily found to be the unit vector (called unit quaternion) described as

123

22

21

20 T . (11)

3.3 State vectors setting for measurement model

We consider position, posture, and velocity of the measurement vehicle, in two different frames (R-frame and B-frame) of the coordinate systems in Fig. 6. We denote the notations xr as an arbitrary vector from the viewpoint of the R-frame and xb as the one from the viewpoint of the B-frame. The position r and velocity v of the measurement vehicle’s center of gravity are described as follows:

r

z

ry

rx

r

r

rrr ,

r

z

ry

rx

v

v

vrv ,

0

0

0

bz

by

bx

r

r

rbr ,

0

0x

bz

by

bx v

v

v

vbv . (12)

In this paper, we set the vehicle’s speed as constant xv , and its correct value is supposed to be detected by a rotary

encoder. Then, the relationship between two frames is represented by brr vvr )C( , (13)

where )C( is the conversion matrix of coordinate systems from the B-frame to R-frame, and the expression is

described by using quaternions as follows:

2222

2222

2222

22

22

22

)

321010322031

103232103021

203130213210

C( , (14)

This conversion matrix is easily found to be the orthonormal matrix written as T)) 1 C(C(

. The time derivative

of the quaternion which expresses the posture of the vehicle is formed by using the product of the quaternions of Eq. (7) written as

6

2



bZ

0)

2

1(

dt

d, (15)

where Tbz

by

bx b is the tri-axial angular rate vector of the measurement vehicle, with the values as

measured by the gyro sensor. The gravity vectors are also described by the relationship between two frames as br gg )C( (16)

where Tg 00rg is the gravity vector in an inertial frame and Tbz

by

bx gggbg is the

acceleration vector measured by the accelerometer. 3.4 Constitution of state space measurement model

To obtain the correct state values of unevenness of the pipe, accurate posture and position information for the moving vehicle is required. However, drift errors included in the measurement data of the low-precision MEMS gyro sensors reduce the accuracy. The Kalman filter (Adachi, 2012) is known to be suitable for estimating the correct state variables of a system from observed states including errors and noise. Therefore, we applied the extended Kalman filter (EKF) algorithm to the nonlinear system of our measurement model. The angular rate and the acceleration used in Eq. (15) and (16) are obtained by gyro sensor and accelerometer, respectively. They are affected by drift errors and measurement noise.

First, the model of the angular rate vector is supposed to be described by bbb

gyro , (17)

where Tbgyroz

bgyroy

bgyrox b

gyro and Tbz

by

bx b are measured variables of

angular rates by the gyro sensor and their drift errors, respectively. Equation (15) is rewritten as follows:

Tdt

d 11

2

10)

2

1

bbgyro

Z( , (18)

where the second term of the right-hand side is one idea to satisfy the unit quaternion condition in Eq. (11) which is

disrupted by increasing integration error. The drift error dynamics b are known to be simply modeled by the first-order Markov process that Rogers (2003) described by

wbb dt

d, (19)

where is the drift parameter matrix, and w is white noise written as follows:

z

y

x

00

00

00

,

z

y

x

w

w

w

w . (20)

These parameters are estimated by the static test for analyzing characteristics of the gyro sensor (Allan, 1987). Second, the model of the gravity vector is supposed to be described by

noisebb

acc ggg , (21)

where Tbaccz

baccy

baccx gggb

accg and Tzyx ggg noiseg are measured variables of acceleration

by the accelerometer and their measurement noise, respectively. Equation (16) is rewritten as follows:

noiserb

acc ggg T)C( . (22)

We define the state vector as Tbx , and the output vector asb

accgy . Then the state equation and the

output equation are described as follows:

dxhy

Bwxfx

)(

)(dt

d, (23)

where )(,,)( xhBxf , and d are given by

7

2



b

bbgyro

Zxf

Tτ

11

2

10)(

2

1)( ,

33

340

IB ,

gT

2222

2

2

)()(

3210

1032

2031rgxh

C , noisegd . (24)

3.5 Estimation algorithm by extended Kalman filter

To make the estimation model for applying the Kalman filter algorithm, the discrete time system model is rebuilt from the continuous time model in Eq. (23). We obtain the discrete time model by using Euler (first-order) approximation with sampling time T which is described as follows:

kkkk

kkkk1k

dxhy

wBxfx

)(

)(, (25)

where subscript k indicate the number of sampling and the functions are defined as T )()( kkkk xfxxf , and T BBk . The process noise kw , and the observation noise kd are assumed to be zero mean multivariate Gaussian distribution with covariance matrices Q and R , respectively. Since Eq. (25) represents the nonlinear models for the state, we apply EKF algorithm which is one of the commonly used estimation methods for nonlinear system models. The algorithm works in a two-step process consisting of prediction and filtering (updating) as follows: Prediction step:

kT

kkT

1-kkk-

1-kkk-

QBBFPFP

xfx

)ˆ(ˆ, (26)

Filtering (updating) step:

k-

kkk

k-

kkkk-

k

kT

k-

kkT

k-

k

PHKIP

xhyKxx

RHPHHPK

)ˆ(ˆˆ

1

, (27)

where k-x̂ and k

-P are the predicted (a priori) estimate of the state variables and the error covariance matrix, kx̂ and kP are their updated (a posteriori), and kK is Kalman gain. kF and kH imply linear approximation of the functions of kf and kh at each sampling time, and are described by the following Jacobian matrices

k-

k- xx

kk

xx

kk x

hH

x

fF

ˆˆ

,

. (28)

4. Experiment 4.1 Experimental set up

Experiments were carried out to confirm the performance of the low-cost MEMS sensor and to verify the improvement of accuracy of estimated data applied by the EKF algorithm. In this paper, we used an experimental pipe

Fig. 7 Experimental pipe made from acrylics is 300mm in diameter and 3m long.

300mm 3000 mm

ball caster

acrylics pipe

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2



having a diameter of 300mm and a total length of 3m, made of acrylic (shown in Fig. 7). The pipe is supported on ball casters attached on the corner of rectangular wooden supports, so that the pipe can be intentionally rotated in a rolling motion at any point in time. This arrangement was to simulate the phenomenon of rotation of the vehicle while moving in the pipe. The positional information was known beforehand by measuring several points of the pipe in 3D coordinates by using surveying devices.

The measurement accuracy of the currently-used method (Kumota Inc., 2015) is the displacement error of less than 10 millimeters. It can clearly determine the soundness levels of evaluation for sewage pipes in the stock management (MLIT, 2015). Therefore, we aim to satisfy the measurement accuracy on error level of less than 10 millimeters in our proposal method. The experimental procedures are as follows. First, several measurement tests at various vehicle speeds were carried out by the measurement method shown in Fig. 2. Second, the estimation of the EKF algorithm was executed offline by a computer after measurement. In order to quantitatively evaluate the quality of measurement data, we compared the estimated data measured by the MEMS gyro with the high-performance sensor NAV440 that is produced by Crossbow Japan Ltd., and which is famous for high performance with few drift errors. The overview of this sensor is shown in Fig.8, and its specifications are listed in Tab.3. To validate the performance of the

Table 3 Specification of NAV440.

Items Specifications Unit

Weight 620 g

Size 76 95 76 mm

Range of gyro sensor 200 deg/s

Range of accelerometer 4 G Fig. 8 Overview of the high performance sensor NAV440.

Fig. 9 Experimental result of the quaternion variables in the case of traveling at constant speed without roll motion

0 5 10 15 20 25 300.95

1

1.05

1.1

Time [sec]

NAV440MEMS Raw dataEstimated by EKF

0 5 10 15 20 25 30-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

Time [sec]


0 5 10 15 20 25 30-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

Time [sec]

NAV440 MEMS Raw dataEstimated by EKF

0 5 10 15 20 25 30-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

Time [sec]


0 o

f qu

ater

nion

3 o

f qu

ater

nion

2 o

f qu

ater

nion

1 o

f qu

ater

nion

9

2



algorithm, it is preferable to mount both the sensors on our measurement vehicle at the same time. However, measurement tests were executed independently at different time for each sensor, because NAV440 is too large to mount on our manufactured sensor box unit, and the box unit was taken away in the case of experiment for NAV440 to be mounted in our measurement vehicle. 4.2 Movement along the pipe without rolling motion

Here we show one of the results in the case of moving along at constant speed [mm/s]70xv , with a measurement time of around 30 seconds. Figure 9 shows the quaternion variables, while Fig. 10 and Fig. 11 are the posture of Euler angles and positions, respectively, that are transformed from the quaternions. The solid line represents the result of the high-performance sensor NAV440, the dashed line represents the raw data of the low-cost MEMS sensor TSND121, and the dotted line represents the estimated values of EKF applied for the MEMS sensor data. From Fig. 9, we could find that the estimated values by EKF are almost the same as NAV440, and Eq. (10) is also satisfied. These quaternion variables are transformed into posture of Euler angles (roll, pitch and yaw angles) shown in Fig. 10, so that we could easily figure out the physical movement of the vehicle. The reference values of Euler angles are supposed to be kept almost zero, though the actual posture could not be measured. The data in these figures show that the MEMS sensor has large drift errors of more than 10 degrees in 30 seconds for all Euler angles. On the other hand, the response of the estimated value applying EKF algorithm has drastically improved the performance, which is almost the same as the NAV440, although the pitch angle error is a little bit larger than the NAV440. Figure 11 shows the time course of position ry

r in Yr -axis (leftward direction) and rzr in Zr-axis (upward direction) of the vehicle. These position

variables are calculated by numerical integration of Eq. (13). The dotted lines represent reference values that are constantly zero, and this means that the pipe is placed horizontally on the ground and Xr -axis (forward direction) is set along the pipeline. From these figures, the estimated value applying EKF algorithm has good performance within an

Fig. 10 Experimental result of the Euler angles in the case of traveling at constant speed without rolling motion

0 10 20 30-15

-10

-5

0

5

Time [sec]

Rol

l an

gle

[deg

]


0 10 20 30-15

-10

-5

0

5

Time [sec]Pi

tch

angl

e [d

eg]


0 10 20 30-15

-10

-5

0

5

Time [sec]

Yaw

ang

le [

deg]


Fig. 11 Experimental result of the position Yr and Zr in the case of traveling at constant speed without rolling motion

0 5 10 15 20 25 30-0.3

-0.2

-0.1

0

0.1

Time [sec]

Posi

tion

of Y

r [m

]

NAV440MEMS Raw dataEstimated by EKFReference value

0 5 10 15 20 25 30-0.1

0

0.1

0.2

0.3

Time [sec]

Posi

tion

of Z

r [m

]


10

2



error of 0.01m, which has almost the same quality as the high-performance sensor NAV440. This result also suggests that the measurement accuracy is satisfied in practical use.

4.3 Movement along the pipe with rolling motion

Here, we show the case when the pipe is intentionally rolled around [deg]60 while the vehicle is moving along the pipe at constant speed [mm/s]70xv . The rolling motion of the pipe is considered to be substantially equivalent to the phenomenon of rotation of the vehicle while moving in the pipe. Figures 12 and 13 are the posture of Euler angles and positions, respectively. From these figures, the raw data from the MEMS sensor show large drift errors in a similar way to the previous result. Pitch and yaw angles of MEMS data are affected by rolling motions and this low-frequency influence could not be removed from the estimated data, even with the EKF algorithm. However, from Figure 13, the position variables are not violated by these affects, and the estimated value applying the EKF algorithm acquires almost the same performance as the high-performance sensor NAV440.

5. Conclusion

In this paper, we designed and manufactured two vehicles to measure the state variables of unevenness within

sewer pipes. The first vehicle is designed for the function of driving, in order to pull a second vehicle. The second vehicle is designed strictly for measurement; it is towed and cannot move alone. The vehicles are manufactured to operate within a diameter range of 200mm to 300mm. To measure its own posture and acquire information on its position within a pipe, the measurement vehicle is equipped with a low-cost MEMS sensor device consisting of gyro sensor and accelerometer. Then, the extended Kalman filter (EKF) algorithm is applied to reduce the drift errors in the data from the MEMS sensor. The experimental study shows that the suggested algorithms effectively remove the errors at normal and rotational situations. The results indicate that we achieved the systematic measurement schemes to obtain

Fig. 12 Experimental result of the Euler angles in the case of traveling at constant speed with rolling motion

0 10 20

-50

0

50

Time [sec]

Rol

l an

gle

[deg

]

0 10 20-15

-10

-5

0

5

Time [sec]


0 10 20-15

-10

-5

0

5

Time [sec]

Yaw

ang

le [

deg]


Pitc

h an

gle

[deg

]

Fig. 13 Experimental result of the position Yr and Zr in the case of traveling at constant speed with rolling motion

0 5 10 15 20 25-0.3

-0.2

-0.1

0

0.1

Time [sec]

Posi

tion

of Y

r [m

]


0 5 10 15 20 25-0.1

0

0.1

0.2

0.3

Time [sec]

Posi

tion

of Z

r [m

]


11

2


© 2016 The Japan Society of Mechanical Engineers[DOI: 10.1299/mej.14-00546]12

the precise data of unevenness for small-sized sewer pipes.

Acknowledgement This work was partially supported by a Grant-in-Aid for trial manufacture from the Small and Medium Enterprise

Agency.

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development of sewer pipe measurement system by vehicle

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