Development and
Implementation of Filter
Algorithms and Controllers
to a Construction Machine Simulator
Tadesse Tafesse Kebede
Masters of Science Thesis in Geodesy No. 3105
TRITAGIT EX 08008
School of Architecture and the Built Environment
Royal Institute of Technology (KTH)
100 44 Stockholm, Sweden
September 2008
TRITAGIT EX 08008
ISSN 16535227
ISRN KTH/GIT/EX08/008SE
i
Title: Development and implementation of filter algorithms and controllers to a
construction machine simulator
Author: Tadesse Tafesse Kebede
Supervisors: PD.Dr.Ing. Volker Schwieger, Dipl.Ing. Alexander Beetz,
Prof. Lars Sjöberg
Abstract:
Different geodetic techniques can be integrated in construction processes to have effective, time
saving and cost minimizing construction through geometric control and guidance of the
construction machines on the designed alignment. This can be achieved by integrating a
tachymeter as kinematic positioning sensor. The institute of application of geodesy to
engineering (IAGB) of University of Stuttgart has developed a modular position guidance toolbox
(a construction machine simulator) that comprises a model truck of scale 1:14, of Leica TPS1201
tachymeter, remote controller and a computer.
Tachymeters can work as kinematic measuring devices by integrating them to a construction
process, in real time, using automatic closedloop control systems with feedbacks. The geometric
deviation between the measured and given trajectories can be minimized to some optimized limit
using different types of controllers. With PID controllers a better accuracy can be achieved,
and with integration of Kalman filter to the control system the controller quality can be
improved.
It is also possible to account for the dynamic effect on the model truck at higher velocities;
however, the accuracy is very small due to some practical working limitations of tachymeter
(such as low scanning rate and dead time) as kinematic position sensor at higher velocities.
Key words:  Vehicle dynamics, construction machine guidance and control, tachymeter, PID
controller, Kalman filter
ii
Acknowledgements:
I would like to express my deep appreciation to my supervisor at University of Stuttgart, IAGB,
PD. Dr.Ing. Volker Schwieger. He has introduced and given me the opportunity to work on this
interesting construction guidance and control in the field of engineering geodesy His guidance
and support through out the project was priceless.
Special thanks also to my supervisor Dipl.Ing. Alexander Beetz for his continual support and for
sharing his knowledge and experiences as an advisor and a friend to me; he spent countless hours
with me through out the experiments in the laboratory and in his office. I would like to give
thanks to my supervisor at Royal Institute of Technology (KTH), Prof. Lars E. Sjöberg. I would
like to say thank you all my lecturers and staff members at KTH, Stockholm.
I also need to express my deepest love and gratitude to my wife Adanech S. Kebede for her love,
care and full support through out my academic carrier; her carrying is invaluable. My thanks also
goes to my brother Getachew Tafesse, his wife Terfatu Tafesse and my wifes mother Simirete
Negash for their moral, material and financial support during my study.
My thanks go to SIDA for the scholarship grant for about ten months, despite of the fact that the
financial support was promised to be a full scholarship grant.
Last but not least, Praised be the Name of The Almighty God who is keeping, guiding and
protecting all my ways. Without Him I could not see this day.
Stuttgart/Stockholm, September 2008 Tadesse T. Kebede
iii
Table of content
Abstract:...........................................................................................................................................i
Acknowledgements........................................................................................................................ii
Table of content............................................................................................................................iii
List of Tables...................................................................................................................................v
List of figures..................................................................................................................................v
1. Introduction............................................................................................................................1
1.1. General........................................................................................................................1
1.2. Geodetic techniques for construction processes......................................................2
1.3. Classification of construction machine guidance systems......................................5
1.4. The modular closed loop system of IAGB................................................................6
1.5. Objective of the thesis................................................................................................8
1.6. Chapter outline...........................................................................................................8
2. Vehicle lateral dynamics......................................................................................................10
2.1. Introduction..............................................................................................................10
2.2. Kinematic model of the vehicle lateral motion......................................................10
2.3. Dynamic model of the vehicle lateral motion.........................................................12
3. Automatic control system....................................................................................................17
3.1. Introduction..............................................................................................................17
3.2. Control systems........................................................................................................17
3.3. Components of a control system.............................................................................19
3.4. Types of controllers..................................................................................................20
3.4.1. Three point controller or onoff controller................................................20
3.4.2. PID controller...............................................................................................21
3.4.2.1. The proportional term...................................................................21
3.4.2.2. The integral term............................................................................21
3.4.2.3. The derivative term........................................................................22
3.4.2.4. How PID affects the system dynamics..........................................22
3.4.2.5. Tuning of PID parameters.............................................................24
iv
4. Automatic guidance system and measuring techniques...................................................26
4.1. Introduction..............................................................................................................26
4.2. Measuring techniques..............................................................................................27
4.2.1. Different geodetic techniques for kinematic measurement system.........28
4.2.2. Comparison of geodetic techniques for kinematic measurements...........29
4.2.3. Tachymeter as kinematic measuring device..............................................31
4.3. Kalman filtering as optimal estimator...................................................................33
5. Implementation of the vehicle model to the model truck.................................................37
5.1. Determination of radii.............................................................................................37
5.2. Determination of vehicle parameters.....................................................................41
5.3. Application of the vehicle parameters....................................................................44
6. Implementation with the model truck................................................................................46
6.1. Components of the automatic guidance system.....................................................46
6.1.1. Hardware components.................................................................................47
6.1.2. The software components............................................................................48
6.2. The experimental setup............................................................................................50
6.3. The mathematical modeling and alignment of controller parameters................54
6.3.1. The vehicle model.........................................................................................55
6.3.2. PID controller alignment.............................................................................56
6.4. Quality of the controllers.........................................................................................57
6.5. Optimization of the automatic control loop...........................................................65
6.5.1. Kalman filter model as optimization method............................................65
6.5.2. Result from Kalman filter...........................................................................66
7. Conclusion and future outlook............................................................................................68
7.1. Conclusion.................................................................................................................68
7.2. Future outlook..........................................................................................................69
References:....................................................................................................................................70
Appendix A. Computation of sideslip angles and cornering coefficients................................73
Appendix B. Model parameters and their definitions..............................................................74
Appendix C. Algorithm of discrete KALMANFilter...............................................................75
v
List of Tables
Table 1.1: Services from geodesy and GIS during different construction phases (Niemeier 2006) 1
Table 1.2: GPS/TPS parameters for construction machine guidance system (Stempfhuber 2006).6
Table 3.1: ZieglerNichols method of parameters alignment (National Instruments, 2001).25
Table 4.1: Some construction guidance systems of construction machines (Retscher 2001)........30
Table 5.1: Cornering coefficients at both wheels (for steering voltage =3.507v)..........................43
Table 5.2: Results of radii after considering the dynamic effect (steering voltage =1.33027V)...44
Table 6.1: Initial controller parameters using ZieglerNichols method of alignment....................57
Table 6.2: Controller parameters after manually adjusted (aligned)..............................................58
Table 6.3: Standard deviations (root mean square, RMS) of different controller types................58
Table 6.4: Standard deviation (RMS) of PID controller................................................................62
Table 6.5: Standard deviation (RMS) of PID controller after some initial values are removed....64
Table 6.6: standard deviation (RMS) of PID controller with Kalman filter..................................66
Table A.1: Cornering coefficient values computed from the geometry of the dynamic model.....73
List of figures
Figure 1.1: 3D guidance systems for paving machines (Retscher 2001)........................................3
Figure 1.2: Model truck of IAGB as construction machine simulator.............................................7
Figure 1.3: A block diagram of closed loop control system at IAGB (lecture note, IAGB)...........8
Figure 2.1: Single track model (lateral vehicle motion) for smaller velocities..............................11
Figure 2.2: Single track model (lateral vehicle motion) for higher velocities...............................13
Figure 2.3: Orientation of front wheel in a circular motion...........................................................16
Figure 3.1: A physical system........................................................................................................18
Figure 3.2: Simplified control system............................................................................................19
Figure 3.3: Characteristics of a three point controller (Schwieger and Beetz 2007).....................20
vi
Figure 3.4: Block diagram for a PID controller.............................................................................23
Figure 3.5: Response of a typical PID controller (From NI PID theory explained 2006)..........24
Figure 4.1: External and internal control loop during construction process (Möhlenbrink and
Schwieger 2006).....................................................................................................................27
Figure 4.2: General working steps of Kalman filter (Levy 2002)..................................................34
Figure 4.3: Motion of a vehicle in a straight line and a curve........................................................36
Figure 5.1: An example of a circular drive measured by Tachymeter and drawn using MATLAB
for the determination of radius...............................................................................................41
Figure 6.1: Hardware components of the automatic guidance system...........................................47
Figure 6.2: Example of a block diagram of VI..............................................................................49
Figure 6.3: Example of a front panel of VI....................................................................................49
Figure 6.4: Example of a PID virtual instrument as a subVI (National Instruments 2006)...........50
Figure 6.5: The reference trajectory at IAGB testing floor............................................................51
Figure 6.6: User interface at the initialization phase......................................................................53
Figure 6.7: User interface window for visualization of the geometry and control deviation........54
Figure 6.8: A SubVI for radius computation..................................................................................55
Figure 6.9: Block diagram for a closedloop PID controller..........................................................56
Figure 6.10: Behavior of PI controller at straight line...................................................................59
Figure 6.11: Behavior of PI controller at curves............................................................................59
Figure 6.12: Behavior of PI controller...........................................................................................60
Figure 6.13: Behavior of PD controller at straight lines................................................................60
Figure 6.14: Behavior of PD controller at curves..........................................................................61
Figure 6.15: Behavior of PD controller..........................................................................................61
Figure 6.15: STD of a PID controller at the start of the experiment..............................................62
Figure 6.16: Behavior of the PID controller..................................................................................63
Figure 6.17: Behavior of PID controller at straight lines...............................................................63
Figure 6.18: Behavior of PID controller at curves.........................................................................64
Figure 6.19: Kalman filter integrated to the PID control system...................................................65
Figure 6.20: Behavior of PID controller with Kalman filter..........................................................66
Chapter 1 Introduction
1
1. Introduction
1.1. General
One of the main objectives of engineering geodesy, as explained by Niemeier (2006), is a
stronger integration into the construction processes of small or large scale engineering structures.
It is possible to come closer to this target due to the development of powerful new sensors,
adequate communication links and the ability of real time processing of the observations.
In the last years, there are new developments in the construction industry, which, as a result,
brought many changes in the construction process that are involving many types of machines.
The machines are therefore required to be guided so that they can keep the designed (given)
alignment (position and orientation) of the construction. Here, it is important to point out the real
advantages of using modern geodetic techniques to guide the construction machines. The main
target is shortening of the construction time and the reduction of the construction costs due to
adequate geodetic integration. Further advantages are to avoid geometrical conflicts before they
become critical and to improve the final quality of the structure. Niemeier (2006) also outlined
some requirements of construction processes and the geodetic possibilities for navigation,
guidance and control. He listed the deliverables from geodesy and geoinformatics to the
construction process at each step as shown in table 1.1.
Table 1.1: Services from geodesy and GIS during different construction phases (Niemeier 2006)
Chapter 1 Introduction
2
Due to the tremendous progress in sensor developments in geodesy made during the last years
and the advent of modern communications and realtime processing capabilities for geodetic data,
much more rapid geodetic information for the construction processes can be achieved.
1.2. Geodetic techniques for construction processes
Since there is a wide range of construction projects, the methodology, sensors, data structure and
processes may differ to a large extent, but the basic ideas are similar. As an example, given in
Niemeier (2006), the potential and impact of modern geodetic concepts on typical large scale
projects such as compaction control, construction of tunnels and bridges is presented.
In table 1.1 it is listed that there are deliverables from geodesy and geoinformatics to a
construction process during different phases of construction. The geodetic techniques for
construction processes are required mostly at the realization (execution) phase.
Glaeser (2005) categorized the applications of geodetic techniques for automatic guidance and
control of the construction process at realization phase in five general application groups:
o staking out and aligning:  point wise comparison of current positions with stored
(given) positions
o positioning of structural elements:  automatic guiding of elements to a given position
o positioning of machines:  putting into positions to produce a determined geometry
such as drilling or brick laying machines
o guidance of structural elements:  guiding the elements on given trajectories
o guidance of construction machines:  guiding machines that produce some geometry
There are substantial projects and research activities in different construction industries that
integrate the current developments in control engineering with geodetic engineering and geo
informatics.
Different automatic construction machine guidance systems are therefore been developed in the
recent years to achieve the above goals. Those systems cover all aspects of the construction
Chapter 1 Introduction
3
industry, like earth work and embankments, bridge construction, road construction and pavement
works, tunneling, subsurface structures, steel works and additionally tasks for agricultural
machine guidance.
Figure 1.1: 3D guidance systems for paving machines (Retscher 2001)
For compaction, in Niemeier (2006) it is indicated that a sensor head is mounted on top of a
compactor that consists of a realtime differential GPS system, an azimuth sensor and a dualaxis
inclinometer. By numerical coupling of data from different sensors and after some filtering and
smoothing processes the resulting surface observations are available. They are imported into a
GISmodel, where the current change in the surface geometry is computed in realtime. The
guidance or steering information is transmitted to the driver until the required precision is
achieved. A precision of about 2cm is achieved for the compaction process.
In tunneling, the underground control network realization is a process during the complete
construction phase. Geodetic techniques are able to control the construction progress and to give
information if there are possible deviations. Therefore, there is a possibility for correction of the
alignment. Due to modern geodetic sensors and processing techniques, direct guidance
Chapter 1 Introduction
4
information like for tunnel boring machines (TBM) is given by a geodetic system. An automated
total station (laser station) with a specially adopted diode lasers is the main geodetic component.
It focuses to an active target station and an automatic positioning process makes the observations
to the different targets in the back (rear reference object) and aside (survey prisms). Important is
the selfleveling tripod which allows an automatic positioning and orientation of the total station.
For the tunneling a precision of about 5mm is obtained as depicted by Niemeier (2006).
In Glaeser (2005) it is described that computerintegrated construction (CIC) covers, for some
years, many research activities of the automation of building processes. The respective planning
of data from a CAD system as well as the current position of the respective medium is made
available in real time on the construction site. A goal is then to make an execution of construction
possible without preceding mapping of the planning data into the location and to lead back the
resulting information at the same time into the CAD system. Thus an effective building site
controlling becomes possible.
Within road construction and earthwork, geodetic guidance systems are applied in construction
machines such as graders and dozers, to automate excavators and finishing machines.
There are also current scientific investigations mostly in a fully automatic controlling of a
construction machine. At present attainable accuracies of an automatic construction machine
control (relative to the target (given) geometry) lie within the range of up to 2cm with tachymeter
control and 25cm with precise differential GPS control (Glaeser 2006). The accuracy depends
strongly on the speed of the construction machine, the type of the engineering project and the
weather conditions.
In Glaeser (2006) it is also indicated that the European Union project CIRC (computer integrated
road construction) has set a goal of conversion of the ideas of the CIC (computer integrated
construction) in road construction. In the CIRC two prototypic systems, the guidance of
compactor (CIRCOM) and paving machines (CIRPAV) have been developed. CIRCOM uses
precise differential GPS (PDGPS) for positioning and makes a 2D controlling of the compactors
Chapter 1 Introduction
5
with a standard deviation of 510cm. CIRPAV contains a laser guide system besides the PDGPS
and makes height controlling of the paving machine with an accuracy of 1cm.
The precise positioning of moving objects is one of the main research areas today in engineering
geodesy. The beginning of the polar tracking systems already lie in the 80's and were usually
based on motorized theodolites with imageprocessing systems for target acquisition. Substantial
focuses of the research range from highly exact navigation  to integration of navigational and
geodetic methods made at University of Stuttgart. The system MOPS (modular optical
positioning system) at University of Stuttgart is one important representative of the first optical
measuring systems with automatic target acquisition on theodolite basis. This has the effect of
increasing the quality of the kinematic positioning of slowly moving objects for dynamic
applications of construction machine control (Glaeser 2006).
Today precise tachymeters become more useful and successful for threedimensional positioning
of moving objects, such as compaction controls in road and tunnel construction. Nowadays the
integration of precise tachymeters into building construction processes has much importance. By
connecting the tachymeter to a computer, and by combining with individual measuring programs,
integrated controlling functions get possible.
1.3. Classification of construction machine guidance systems
Construction guidance and control systems can be classified into the following general groups
(Stempfhuber 2006)
o 1D guidance and control systems:  for height, machine left or right control applications.
Control is made manually by the machine driver. It may be with or without slope
(example rotating laser scanners).
o 3D guidance and control systems:  includes both position and height guidance and
control in 3D such as 3D guidance and control of excavators (example GPS, total
stations)
o semiautomatic control systems:  this is a guidan ce only system with precise position
information. The height is the only automatically controlled component, the position
Chapter 1 Introduction
6
information can be obtained from RTK GPS or total stations. The steering control is done
manually by the machine driver. Common applications are control of asphalt moulds,
trimmer heads, dozers (earth works) or motor grader blades.
o fullautomatic control systems: they control the machine fully; both in height and
position such as guidance and control of paving machines including slipform pavers,
curb and gutter machines.
Stempfhuber (2006) also gives some parameters of GPS/TPS as a construction machine guidance
and control system for different types of construction processes. Table 1.2 gives some
information on semiautomated and fullautomated machine guidance systems with their
maximum speed limits. It also shows the accuracies achieved in height and position guidance and
control.
Table 1.2: GPS/TPS parameters for construction machine guidance system (Stempfhuber 2006)
1.4. The modular closed loop system of IAGB
As it is described in the above sections the research in geodetic techniques for navigation,
guidance and control of construction processes is playing some important role in the construction
industry. This is due to the fact that the position and orientation of the moving object (the
construction machine) is to be guided and controlled; and this is now become more possible with
the advent of different precise measuring sensors.
Chapter 1 Introduction
7
The institute for applications of geodesy to engineering (IAGB) of University of Stuttgart is also
playing an important role in this typical field of research. The institute has undergone a research
in the last years about modular closedloop system for geometric guidance and control of
construction machines. It has developed a simulator for the experimental testing which allows to
implement and test different types of control algorithms and vehicle modeling.
For the realization of the simulator, a model truck shown in figure 1.2 is also developed to
represent the construction machine that has to be guided. A tachymeter (Leica TPS1201) is used
as a positioning sensor for an automatic tracking. A reflecting prism (360
o
reflector GRZ101
prism) of very high accuracy (accuracy of 1.5mm) is attached on the model truck. The tachymeter
automatically tracks the prism and determines the coordinates of the position of the model truck
while it is moving in some given (predetermined) trajectory. The tachymeter is controlled by a
computer.
Figure 1.2: Model truck of IAGB as construction machine simulator
The coordinates of the model truck are sent to the computer and the values are compared with the
coordinates of the given (predetermined) trajectory; the difference between the two values which
is the control deviation is used to calculate the regulating variable of the control system.
The realization of the guidance and control system and the tachymeter controlling, database
communication, remote controlling of the model truck and the tachymeter is implemented in the
graphical programming environment LabView
®
.
A Kalman filter is also integrated to the control system to influence the dynamic behavior of the
system so that the current position of the model truck can be estimated on a better way from the
position information received from the sensor. Using this control system accuracy of about 1cm
Chapter 1 Introduction
8
without Kalman filter and about 4mm with integration of Kalman filter is obtained (Schwieger
and Beetz 2007).
Figure 1.3: A block diagram of closed loop control system at IAGB (lecture note, IAGB)
1.5. Objective of the thesis
As described in the above section, IAGB has developed a construction machine simulator in
which a threepoint controller is used as a controller. The controller works together with a
Kalman filter. An accuracy of 1cm without Kalman filter and 4mm with Kalman filter is
achieved.
The objective of this thesis is to improve the vehicle model so that it accounts for dynamic effects
on the model truck. In this thesis, new controllers such as PI, PD and PIDcontrollers will also
be aligned and integrated into the closedloop system so that an optimized accuracy with regard
to the previous research result will be obtained.
1.6. Chapter outline
This thesis comprises of seven chapters. In the first chapter some relationship between
engineering geodesy and the construction processes is shown. Some geodetic techniques for
Geometry information
controller
Controlled
system
tachymeter
Kalman filter
control variable
y(t)
Control deviation
e(t)
Regulating
variable
u(t)
Filtered control
variable
y
filt
(t)
Reference
signal
w(t)
disturbance
z(t)
Chapter 1 Introduction
9
guidance and control of different types of construction processes are described. The chapter also
gives brief description about the experience of IAGB and the objective of the thesis. Chapter two
is dedicated to the vehicle lateral modeling; both kinematic and dynamic vehicle lateral modeling
are discussed. Chapter three gives information about the control system theory and its application
in dynamic systems where the output of a physical system should be compared with the reference
or input value to obtain the maximum possible accuracy. Different types of controllers and their
method of adjustment are also shown in brief.
In chapter four, automatic guidance and control systems for construction machines are discussed.
One can also find some notes on different types of measuring systems in kinematic mode, but
more emphasis is given to the application of tachymeter as kinematic measuring device in
construction machines guidance and control process. For kinematic measurements some states
are time variant and the signals may contain unwanted noises. Therefore, there is a need of
filtering to avoid those noises. The chapter gives information about Kalman filter which is one of
the most widely used filtering methods in engineering geodesy.
Chapter five is about the implementation of chapter two for the model truck of IAGB to consider
the dynamic effect at higher velocities. In this chapter some dynamic parameters of the vehicle
are computed from the geometry of the vehicle lateral dynamics models and these parameters are
also checked by applying them to the model vehicle.
Chapter six will give information deeply on the alignment of PI, PD and PID controllers for
the automatic guidance module (Position Guidance Toolbox) of IAGB. Their quality is also
analyzed with respect to the accuracy limit required for this specific construction machine
guidance and control system. One can also get information about the integration of the controllers
with the Kalman filter so that noises and systematic errors can be removed as discussed in
chapter four.
The last chapter gives remarks on the overall work regarding vehicle modeling and the quality of
the controller. It gives also some remarks on what is to be done in the future regarding this
specific construction machine guidance system.
Chapter 2 Vehicle lateral dynamics
10
2. Vehicle lateral dynamics
2.1. Introduction
A vehicle can be modeled in such a way that the two front and rear wheels are considered as one
single front and one single rear wheel. This type of modeling is known as a single track (or
bicycle) models. Using this model, it is possible to have both kinematic and dynamic vehicle
model. The modeling is highly dependant on the forces acting on the vehicle and the magnitude
of the velocity of the vehicle.
The modeling is for the vehicle motion in curves. When a vehicle is moving in a circular motion
the vehicle tires will produce a lateral force directed towards some center of rotation called
moment pole. The magnitude of the lateral force is influenced by the mass of the vehicle, the
magnitude of the velocity, the road behavior (the embankment angle), and other factors.
The objective of this chapter is to use a dynamic model of vehicle system to support the
automatic guidance and control system for the construction machine. This dynamic model
consists of a single track model of the vehicle. In this chapter some theories are given how to
estimate the cornering stiffness of the model truck.
2.2. Kinematic model of the vehicle lateral motion
A kinematic model provides a mathematical description of the vehicle motion without
considering the forces that affect the motion. The equation of motion is purely based on the
geometry of the system.
In Rajamani (2006) an assumption is given that the velocity vector at each wheel is in the
direction of the wheel. The angle between the velocity vector v
v
and the longitudinal axis of the
vehicle at the front wheel is called the steering angle δ
v
at the front wheel.
Chapter 2 Vehicle lateral dynamics
11
The angle between the velocity v at the centre of gravity (CG) of the vehicle and the longitudinal
axis of the vehicle is called the slip angle b of the vehicle. This assumption holds true for vehicle
motion at small velocities (for example <5m/s) and the lateral forces generated by the wheels are
therefore very small.
Figure 2.1 below shows a kinematic bicycle vehicle model,
90°
X
A
o
R
16°
o
28°
v
CG
v
v
l
l
29°
16°
o
h
h
v
A
Figure 2.1: Single track model (lateral vehicle motion) for smaller velocities
where
A
is the steering angle at the front wheel,
l is the distance between the front and the rear wheels,
l
h
is the distance between the rear wheel and CG,
R is the radius of curvature of the curve driven by the vehicle,
v is the velocity of the vehicle,
o
is the slip angle of the vehicle.
The vehicle will have a heading angle yyyy with the global horizontal axis X and the course angle
will then be g=y+b
g=y+bg=y+b
g=y+b.
Chapter 2 Vehicle lateral dynamics
12
From the geometry in figure 2.1, the relationship between the vehicle dimension and the steering
angle can be given as:
)(
tan
22
h
A
lR
l
=
(2.1)
The vehicle model in equation 2.1 is a simple vehicle model. It considers slow vehicle velocity
and ignores the effect of the lateral forces on the vehicle. In this case, the lateral force induced at
the wheels is negligible and hence the sideslip is ignored.
This model is implemented on the model truck in the previous research works of the automatic
guidance and control system for construction machines of the IAGB.
For small steering angles:
R
l
A
=
(2.2)
and the vehicle slip angle is:
l
l
R
l
h
A
h
o
×==
(2.3)
The angular velocity of the vehicle is given as
R
V
=
.
(2.4)
2.3. Dynamic model of the vehicle lateral motion
The assumption made for the orientation of the velocity in section 2.2 will be no longer true at
higher vehicle velocities. The velocity vectors make some angles with respect to the orientation
of the wheels, as shown in figure 2.2 below. In this case, lateral forces F
v
and F
h
at the front
wheel and the rear wheel, respectively, will be developed towards the moment pole.
Due to the lateral forces at the tires, the vehicle will start to slip while it is turning in curves, and
hence a sideslip angle will occur at each tire. The sideslip angles will affect the movement of the
vehicle on some given trajectory by creating some form of stiffness known in vehicle engineering
as cornering stiffness or cornering coefficient.
Chapter 2 Vehicle lateral dynamics
13
Fv
Fh
v
h
h
o
14°
l
l
v
v
CG
v
40°
R
21°
38°
R
R
h
v
v
h


+
h

h
90
O
81°
16°
h
11°
v
moment pole
o
Figure 2.2: Single track model (lateral vehicle motion) for higher velocities
The sideslip angle can be defined as the angle between the orientation of the velocity vector of
the wheel and the orientation of the tire. For small sideslip angles, the lateral tire forces are
directly proportional to the sideslip angles developed at the tires. This proportionality constant is
also called the cornering coefficient or cornering stiffness of the vehicle. The cornering
coefficients are therefore constant values for a given vehicle.
The lateral force for the front wheels can be given as:
vvv
CF
×
=
, (2.5)
and the lateral force at the rear wheels:
hhh
CF
×
=
, (2.6)
where:
F
v
and F
h
are the lateral forces at the front and rear wheel, respectively
δ is the steering angle at the front wheel
Chapter 2 Vehicle lateral dynamics
14
C
v
and C
h
are the cornering stiffness at the front and rear wheel, respectively
a
v
and a
h
are the sideslip angles at the front and rear wheel, respectively.
The total lateral force due to the rotational acceleration at the center of gravity of the vehicle is
shared between the front and rear wheels as a ratio of their distances from the CG:
R
v
l
l
mF
h
v
2
.×=
(2.7)
and
R
v
l
l
mF
v
h
2
.×=
(2.8)
The sideslip angles can then be given as:
R
v
l
l
C
m
C
F
h
v
v
v
v
2
.×==
, (2.9)
and
R
v
l
l
C
m
C
F
v
hh
h
h
2
.×==
, (2.10)
where, m is the mass of the vehicle and l
v
and
l
h
are the distances from the front and rear wheels
to the center of gravity of the vehicle, respectively.
Considering the angles at both wheels formed by the velocity vectors and the orientation of the
wheels with the longitudinal axis, the following relationship can be obtained:
v
l
h
v
×
=
×
(2.11)
v
l
h
h
×
+=
×
. (2.12)
from the geometry in figure 2.2 above and using sine rule for small angles we can get:
)(
hv
l
R
=
(2.13)
Chapter 2 Vehicle lateral dynamics
15
or
hv
R
l
+=
(2.14)
where
R
v
CCl
lClC
l
m
hv
vvhh
hv
2
)(
×
××
××
×=
(2.15)
One can also have
+
h
h
R
l
(2.16)
or
+
ho
(2.17)
Equation 2.14 can be considered as a simple vehicle lateral dynamic model. It takes the effect of
the lateral forces and the velocity into account in terms of the sideslip angles at the front and rear
wheels.
Vehicle model integration in a control loop
Once the radius of curvature at which the vehicle is moving is obtained from equation 2.13 it can
be integrated in an automatic guidance of a construction machine. The theories behind a control
system and automatic guidance system will be dealt in chapter three and four. Here we will have
a brief look at how a vehicle model is implemented in an automatic guidance and control system.
The driving variables for the model truck discussed in section 1.4 are the front wheel steering
angle δ
v
, the change in orientation α, the radius of the curvature R, and the length of the truck l
and l
h
.
Consider figure 2.3 below and assume that the truck is moving in a curve from position P
k1
to
position P
k
:
Chapter 2 Vehicle lateral dynamics
16
51°
34
°
17°
k1
k
Pk ( yk, xk)
Pk1
(yk1, xk1)
R
17°
X
Y
Figure 2.3: Orientation of front wheel in a circular motion
The orientation (azimuth) of the front wheel can be obtained from:
=
1
1
1
tan
kk
kk
yy
xx
(2.18)
For small distance between two consecutive positions the change in orientation between two
positions can be given as:
R
tv
=
.
. (2.19)
where v is the velocity of the vehicle and t the time the vehicle takes to travel between two
consecutive positions. The velocity can be calculated from the coordinates as
( ) ( )
t
yyxx
v
kkkk
+
=
2
1
2
1
(2.20)
Chapter 3 Automatic control system
17
3. Automatic control system
3.1. Introduction
Control systems, nowadays, are used in different types of engineering fields, where a real system
is required to follow some given or predefined state. Problems such as coordination of
manipulators, motion planning, construction machine guidance and coordination of mobile robots
require a central controller. Motion control is therefore one of the technological foundations for
construction machine guidance and control system and it is a fundamental concern for having
efficient, cost and time saving construction.
To be able to control a motion process, the precise position of the controlled system (physical
system) needs to be measured. Then a feedback comparison of the target (or the given) and
current positions is a natural step in implementing a motion control system. This comparison
generates an error signal called control deviation that may be used to correct the system. If the
error is smaller than some allowable limit for the specific task, the system performance can be
considered as accurate.
3.2. Control systems
When working with applications where control of a physical system output due to changes in
reference value or input is required, implementation of a control algorithm is necessary to reduce
the change between the reference (input) signal and the control (output) variables.
Control system analysis is concerned with the study of the behavior of dynamic systems as
defined in Anand (1974). The analysis relies upon the fundamentals of system theory where the
relationship between the reference signal and the output (control variable) assumes a causeeffect
relationship, as represented in figure 3.1,
Chapter 3 Automatic control system
18
y( t )
w ( t)
P hysi cal
S yst em
Figure 3.1: A physical system
where w (t) is the reference signal (input) of the system and y (t) is the output or control variable
of the system. When the control variable is compared with the reference signal using the
difference between the two signals, then the control system is considered as having a feedback.
Control engineering is defined in Wikipedia as the engineering discipline that focuses on
mathematical modeling of systems of a diverse nature, analyzing their dynamic behavior, and
using control theory to create a controller that will cause the systems to behave in a desired
manner.
It is then concerned with the task to affect a temporally changing process in such a way that the
process runs in a given or predetermined way. Substantial tools of control engineering are the
automatic control loop.
Control theory is also given as an interdisciplina ry branch of engineering and mathematics that
deals with the behavior of dynamical systems. The desired output of a system is called the
reference. When one or more output variables of a system need to follow a certain reference over
time, a controller manipulates the inputs to a system to obtain the desired effect on the output of
the system.
The basic requirement that a control system should be able to fulfill is stability. This means that a
controlled system should remain stable in all circumstances. The quality of the control can be
measured by analyzing the accuracy, speed and robustness of a control system. For this thesis, the
quality of the controller will be analyzed by considering the accuracy obtained from the control
system and stability of the overall system.
Chapter 3 Automatic control system
19
3.3. Components of a control system
A closedloop control system consists of:
o reference signal:  reference input that gives the desired control variable (usually called a
set point or input)
o controller: which takes the control deviation as an input to compute a regulating variable
o controlled system :  a physical system or a plant to be controlled
o measuring device:  this allows the current state of the system to be assessed and to
generate an appropriate control deviation
o control variable:  the controlled output actually generated by the closed loop system
o feedback
o plant model:  having a sufficiently accurate model (such as the model truck) helps us
how to build an optimal controller
control
variable
y(t)
reference
signal
w(t)
Measuring device
Physical
system
controller
u
e
Figure 3.2: Simplified control system
The control system in figure 3.2 is a principal simplified structure of closedloop control system
in which the current trajectory is wanted to follow the reference signal as precisely as possible. In
this case, the output y (t) is the current state of the physical system. The input value w (t) is the
desired reference signal or the given trajectory with which the controlled variable is to be
compared. The measuring device provides the output to the system. The deviation of the
measured variable (output) from the reference signal is known as the control deviation and given
as:
e (t) = w (t) y (t) (3.1)
Chapter 3 Automatic control system
20
The control deviation is fed to the controller as an input signal for the controller. Then the
controller will determine the regulating variable u (t) or the control signal based on the control
deviation and depending on the dynamic property of the physical system. The variable from the
controller regulates and controls the overall system so that the deviation of the current position
from the reference signal will ideally be zero. In other words, w (t) = y (t). This type of control
system is known as a feedback control system.
3.4. Types of controllers
There are different types of controllers that are used in control systems application, among which
three point controllers and PID controllers are widely used in the field.
3.4.1. Three point controller or onoff controller
In three point controller, the regulation of the offsets on the correcting variable takes place in
three stages. In the zerorange of the error, no correcting value is required. When a limiting value
of the control deviation
g
e
±
is exceeded, then a firmly defined correcting variable of
g
u
±
is
used for the adjustment. With this method, the automatic controller will use the limiting values to
minimize the control deviation between the reference signal and the control variable.
+ u g
 u g
e (t)
u (t)
Figure 3.3: Characteristics of a three point controller (Schwieger and Beetz 2007)
Chapter 3 Automatic control system
21
3.4.2. PID controller
A PID controller is capable of manipulating the process inputs based on the history and the rate
of change of the signal. This process gives a more accurate and stable control for the physical
system that is to be controlled. Many feedback controllers use a proportionalderivativeintegral
algorithm to manipulate the control deviation and apply a regulating effort to the process.
The basic idea in a PID controller is that the controller reads the system state by a sensor. Then it
subtracts the control variable (output signal) from a reference signal or input to generate the
control deviation. The control deviation in the controller is managed in three ways, handling the
present control deviation through the proportional term (P), recovering from the past using the
integral term (I), and the rate of change of the control deviation through the derivative term (D).
3.4.2.1. The proportional term
The proportional term (P) adjusts the control variable in proportional to the control deviation of
the control system. It is the one which contributes much to the control variable (output) change.
The proportional regulating variable can be adjusted by multiplying the magnitude of the control
deviation by a constant called proportional gain K
P.
)()( te
K
tu
P
=
(3.2)
3.4.2.2. The integral term
The integral term (I) sums up a regulating variable from the previous control deviation. It gives
an additional response to the system regulating variable. The integral response will continue until
the system output value equals the given value and these results in no stationary control deviation
when the reference is stable. The most common use of the I term is together with the P term
called a PI controller.
The PI controller considers only the present and past control deviations. The integral term when
added to the proportional eliminates the accumulated control deviation from the past. The
Chapter 3 Automatic control system
22
regulating variable of a PI controller is given in equation 3.3 where K
I
is the integral gain and T
I
is the integral time.
∫
+= dtte
K
te
K
tu
IP
)()()(
+=
∫
dtte
T
te
K
I
P
)(
1
)( (3.3)
3.4.2.3. The derivative term
The derivative term (D) accounts for the rate of change of the control deviation and adds to the
regulating variable. It is proportional to the rate of change of the control deviation. It improves
the response to a sudden change in the controller. Increasing the derivative parameter will cause
the control system to react more strongly to changes in the control deviation and will increase the
speed of the overall control system response. The derivative response is highly sensitive to noise
in the process reference signal, and, therefore, most practical control systems use very small
derivative terms. In a system where the controller response is too slow, the derivative response
can make the control system unstable. The magnitude of the derivative term of the controller is
called derivative gain K
D
. The D term is typically used with the P or PI as a PD or PID controller
respectively.
The PD controller considers the proportional and the derivative terms of the regulating variable.
3.4.2.4. How PID affects the system dynamics
The PID controller works in a closedloop system using the mathematical model shown in
equations 3.4 and 3.5. The variable e (t) represents the control deviation. It is the difference
between the given reference signal (input value) w (t) and the current control variable (output
value) y (t). The control deviation e (t) will be sent to the PID controller, and the controller
computes both the derivative and the integral of the control deviation. The regulating variable u(t)
of the controller is now equal to the proportional gain (K
P
) times the magnitude of the control
deviation plus the integral gain (K
I
) times the integral of the control deviation plus the derivative
gain (K
D
) times the derivative of the control deviation.
Chapter 3 Automatic control system
23
∫
++=
dt
tde
Kdtte
K
te
K
tu
D
IP
)(
)()()(
(3.4)
++=
∫
dt
tde
Tdtte
T
te
K
D
I
P
)(
)(
1
)( (3.5)
The regulating variable u (t) will be sent to the controlled system (plant), and the new control
variable y (t) will be obtained. The new y (t) will be sent back to the sensor again to find a new
control deviation e (t). The controller takes the new controller deviation and computes the
derivative and integral again. This process goes on and on until the limiting regulating variable or
the required accuracy is reached.
y(t)
w(t)
measuring
device
physical
system
KP(e)
proportional
integral
derivative
KD(de dt)
KI ( e)
e(t)
u(t)
PID controller
+
+
+

+
Figure 3.4: Block diagram for a PID controller
As explained by the National Instruments control process design (2006), the control design
process starts by defining the performance requirements of the control system. Performance of a
control system is often measured by applying a step function as the reference signal (input
variable), and then measuring the control variable (output) of the process.
Consider the step response of a control system shown in figure 3.5 below. The figure has some
waveform characteristics such as rise time, percent overshoot, settling time and steady state error.
Chapter 3 Automatic control system
24
Figure 3.5: Response of a typical PID controller (From NI PID theory explained 2006)
Rise time can be defined as the time the system or the plant output takes to go from 10% to 90%
of the steadystate value, or the reference signal. Percent overshoot is the amount that the control
variable overshoots the final value, expressed in percentage of the final value. Settling time is the
time required for the control variable to settle to within a certain percentage (commonly 5%) of
the steadystate variable. Steadystate error is the final difference between the control variable
which is the steadystate variable and reference signal.
These are parameters to describe the quality of the controller. The steady state error is the
limiting control deviation or the required accuracy from the control system.
3.4.2.5. Tuning of PID parameters
Tuning a control loop is the adjustment of its control parameters to the optimum values for the
desired control response. Typical steps in tuning a PID controller are: determining the system
characteristics that needs to be improved, and then using K
P
to decrease the rise time, using K
D
to
reduce the overshoot and the settling time, and using K
I
to eliminate the steady state error.
In National Instruments PID toolkit user manual, PID theory explained, two of the different
methods of tuning of PID parameters are explained. They are the guess and check method and
the ZieglerNichols method.
Chapter 3 Automatic control system
25
In guess and check or manual process of tuning method, the first step is to set all the three gains
to zero. The proportional gain is then adjusted until the system is responding to input changes
without excessive overshoot or until the system starts to have an oscillation. After that the
integral gain is increased until the long term control deviations disappear. The differential gain
will be increased finally to make the system respond faster.
Ziegler Nichols method of tuning is similar to the first method; however, in this method some
empirical adjustments are given in tabular form. Tuning is started by first setting all the three
terms to zero. Then the P term is increased gradually until the system starts to oscillate. The value
of P at this oscillation is said to be the critical gain K
C.
The critical gain and the period of the oscillation P
C
are recorded and used to adjust the P, I and D
values according to table 3.1 below. T
I
and T
D
denote the time constants of the integral and
derivative terms respectively.
Table 3.1: ZieglerNichols method of parameters alignment (National Instruments, 2001)
The first method is relatively easy if there is a good understanding of the significance of each
parameter and if there is a good knowledge of how the physical system responds towards the
controller parameters. The second method gives initial values of the PID controller parameters
empirically.
In this thesis the ZieglerNichols method will be applied as tuning. Once the initial controller
parameters are obtained from table 3.1, they are integrated in the PIDcontroller of the automatic
guidance module of the model truck.
controller K
P
T
I
T
D
P 0.50 * K
C
 
PI 0.45 * K
C
0.85 * P
C

PD 0.65 * K
C
 0.12 * P
C
PID 0.65 * K
C
0. 50 * P
C
0.12 * P
C
Chapter 4 Automatic guidance system and measuring techniques
26
4. Automatic guidance system and measuring techniques
4.1. Introduction
In automatic control loops in the construction process, one of the important things is the
geometrical information about the ongoing construction. For the better quality required, the
geometrical information is needed for control; thus the integration of the geodetic measuring
systems into a building processes control system is one of the topics in engineering geodesy
research.
In the construction process, as explained by Möhlenbrink and Schwieger (2006), the building
process comprises many steps, from the definition of the intended purpose of the construction to
the execution, and in each step there is a need for the geoinformation (see section 1.1 and table
1.1). The goal is the provision of information in realtime to navigate the construction processes
with the help of the latest available geometric data. The basis for the solution will be an
integrative description of the process, the data and the quality. The overall task in the process is
considered as an external and internal control process.
The technical control or guidance of a construction machine such as pavers or finishing machines
is held during the execution process and is called internal automatic control process. The need for
automatic guidance system arises in the execution process of the construction (as explained in
section 1.2). The deviations (control deviations) from planning (given value or reference
variable) are specified and the data is passed on in real time to the controller of the construction
machine.
Figure 4.1 below shows both the external and internal control loops in engineering construction
processes. Here we are interested in the internal control process which is known as automatic
guidance and control of construction machine.
Chapter 4 Automatic guidance system and measuring techniques
27
The necessary positioning can be determined by different geodetic measuring systems such as
global positioning system (GPS) receivers or precise tachymeter.
Figure 4.1: External and internal control loop during construction process (Möhlenbrink and
Schwieger 2006)
4.2. Measuring techniques
Position is defined in Hormuz (2006) as a set of c oordinates related to a welldefined coordinate
reference frame and the process of determining pos ition is called positioning. Route guidance
refers to guidance of an object or a physical system along a predefined route or given trajectory.
Navigation deals with moving objects (or some physical systems) and it involves the
determination of trajectory of the object and its guidance. It requires processing of kinematic
observations in (near) real time, and the accuracy is dependant on the sensors, measuring
instruments and processing algorithms applied in dataprocessing (Hormuz 2006).
Chapter 4 Automatic guidance system and measuring techniques
28
4.2.1. Different geodetic techniques for kinematic measurement system
In section 1.2 it is described that different geodetic techniques are so far used for guidance and
control of different construction processes. The activities range from small to large scale
constructions such as road and bridge construction, tunneling, pavement works and the likes. The
activities range from height control (1D) to 3D guidance and control systems as a semiautomatic
or fullautomatic control system. The classification of construction machine guidance systems is
given in section 1.3.
Different construction processes and hence the motion of the construction machines have a
kinematic behavior. Therefore, the process contains surveying of moving objects which is
considered as a kinematic surveying.
Construction machines can be equipped with automatic guidance systems to automatically keep
their position and orientation within a small control deviation from the given trajectory. These
systems are multisensor systems where sensors for absolute and relative positioning are
combined and integrated.
The positioning and trajectory determination of moving objects can be realized by different types
of geodetic measuring devices such as tracking total stations, precise differential GPS (PDGPS),
highly precise tachymeter, or laser scanning. For some moving objects, determination of
trajectories can also be carried out by inertial navigation systems (INS). The trajectory
determination of the moving objects will then be the aim of the survey. Tracking total stations or
highly precise tachymeters represent a valuable alternative for kinematic positioning.
In most construction machines, a GPS antenna or a reflector prism is mounted (when GPS or
tachymeter or robotic total stations are used as measuring instruments) at the center of gravity of
the machine to determine the position of the machine. These reflectors are then used as active
targets and advanced tracking sensors (ATS). ATS with robotic total stations (RTS) is used as a
sensor for almost unlimited number of applications for guiding and controlling construction
machines as well as for surveying purposes.
Chapter 4 Automatic guidance system and measuring techniques
29
Advanced tracking sensors (ATS) in Trimble data sheet (2004) is defined as an automatically
lock on active targets while the RTS measures and transmits the targets position continuously to
a computer. The computer then determines the desired position and orientation of the target.
For kinematic positioning, the measurements are integrated with different sensors and are
connected to a computer that controls the overall process. The selection of the sensors is,
therefore, dependant on the required accuracy of the process.
The kinematic surveying parameters to be considered (such as the position, orientation and
velocity of the moving objects) are functions of time. The motion of the objects is described by
kinematic model or dynamic model, as explained in chapter two for vehicle lateral motion.
4.2.2. Comparison of geodetic techniques for kinematic measurements
Different types of geodetic techniques for guidance and control of construction machines are used
as measuring sensors for construction machine guidance and control systems. Retscher (2001)
listed some of them as shown in table 4.1 below. The working environment of the devices is
listed with the accuracies achieved so far.
String lines or stakes can be used for guidance of road and slipform paving machines as 3D guidance
system. GPS and robotic total stations can also be used as 3D guidance and control systems for guidance
of dozers and other construction machines. The application of rotating laser scanners is limited to 1D
guidance and control of construction machines.
Chapter 4 Automatic guidance system and measuring techniques
30
Table 4.1: Some construction guidance systems of construction machines (Retscher 2001)
string lines or
stakes
rotating Laser
systems
robotic total
stations
GPS
dimensions 3D 1D (height only) 3D 3D
reference stations
per construction
site
many
tachymeter
stations for
setting out
one or more; site
dependent
one per machine
one
setups per
construction site
not applicable
multiple times per
site
multiple times
per site
one
number of
machines
supported by
reference station
not applicable
unlimited in one
plane
one per total
station
unlimited
maximum range
sensors work in
closerange
up to 300m
depending on line of
site
up to 700m
depending on
line of site
several
kilometers
usability under
bad visibility
conditions
not affected
reduced
reduced
not affected
accuracy mm level mm level mm cm level cm level
major applications
guidance of road
and slipform
paving machines
precise height control
for graders; guidance
of road and slip form
paving machines
guidance of
graders,
excavators,
scrapers or
dozers
guidance of
dozers,
precise
farming
Chapter 4 Automatic guidance system and measuring techniques
31
4.2.3. Tachymeter as kinematic measuring device
In the above sections it is stated that there are different measuring device as kinematic position
sensor applied in construction machine guidance and control. Their application is also discussed
in table 4.1. They can be applicable in different types of construction process in 3D with the
exception that rotating laser scanning better works in height control. They can work also in
different distance ranges depending on the line of site, but GPS can work in several km range
independent of the line of site. An accuracy in cm level for GPS and in mm level for tachymeter
and rotating laser scanning can be reached.
Nowadays, tachymeter is also used as a kinematic measuring device in different construction
sites. The tachymeter must provide the polar coordinates of the moving object in one hand (the
vertical and horizontal angles of the target) and the slope distance to the target with respect to the
position of the tachymeter on the other hand. For this purpose, it is required that a reflector prism
has to be attached on the moving object.
A tachymeter for kinematic survey is typically placed near the required trajectory and tied up to
the reference frame. A prism is placed on the moving object and tracked by the tachymeter. The
position of the prism is then carried out automatically.
The working principle of the tachymeter as kinematic measuring device is presented deeply in
Glaeser (2006) and is beyond the scope of this paper. It is shown that the accuracy of the
tachymeter is highly dependant on the accuracy of the reflector prism, the distance between the
tachymeter and the target object, and the speed of the moving object. The reflector must also be
with in the visual field of the tachymeter.
As stated by the Leica TPS 1200 series, a tachymeter uses an electronic distance measurement
(EDM) or a phase shift measurement technique for distance measurements. The tachymeter
operates in both reflector and reflectorless modes. The EDM transmits an invisible beam of
modulated frequency of 100MHz. to the reflector. The reflector or the prism reflects the beam
back. The reflected beam is detected by a sensitive photo receiver and is digitized. The distance is
Chapter 4 Automatic guidance system and measuring techniques
32
then calculated by standard phase measurement techniques using modern signal processing
techniques. The processing incorporates the advantages of high measurement quality and
reliability under different weather conditions (measuring in rain or snow), and the detection of
multiple targets within the measurement beam.
The automatic target recognition (ATR/LOCK) of the Leica TPS 1200 series actively follows the
reflector as it moves on the trajectory. It has additional on board software that predicts the
trajectory of the reflector movement. This helps the tachymeter to continue to track the reflector
although there are obstructions and short interruptions. If the interruption is too long, then the
operator must utilize the Power Search function to find and aim at the reflector.
Leica describes Power Search as fast and reliable prism search using a sender/ receiver couple
to detect prisms by means of digital signal processing algorithms. It is a function that helps the
tachymeter to detect the reflector within short time no matter how far it moves. When it is
activated the tachymeter rotates and sends out a laser fan. At the time the fan hits the prism the
tachymeter stops rotating and ATR will take over. It is more advantageous when operation is
using a remote controller.
Leica TPS1200 series tachymeter manual also describes that the tracking of moving objects is
possible with speeds of 5m/s at 20m and 25m/s at 100m distance and with a rotating speed
around the axles of up to 45°/sec. Thus tracking of moving objects with most modern
tachymeters can be possible as a kinematic measuring device. It can also be used as a kinematic
measuring device in the application of construction machine guidance systems. The accuracy of
the tachymeter is given as 2mm + 2ppm in static mode and 5mm + 2ppm in tracking mode.
However, in Glaeser (2005) it is indicated that the tachymeter has also some disadvantages of a
low scanning rate of maximum 10Hz and a time delay of up to several hundreds of milliseconds.
These characteristics will affect the control system negatively. These factors limit the practical
use of the tachymeter for guidance of moving construction machines that are having small
velocities (12 cm/s) otherwise it will cause the vehicle behavior unstable.
Chapter 4 Automatic guidance system and measuring techniques
33
4.3. Kalman filtering as optimal estimator
When geodetic measurements and data processing involve continuous and real time navigation,
as in the case of kinematic positioning with GPS and tachymeter measurements for the purpose
of construction machine guidance, the system becomes a timedependent dynamical system (Fan
1997). In this case, the received signals (measurements) may contain some noise and need to be
filtered. Filtering can then be considered as optimally estimating the required parameters by
filtering out the effects of noise from the received signals (measurements).
One of the most widely applied filtering methods for linear dynamical systems is the Kalman
filtering, and it is also widely used in geodesy, surveying and photogrammetry. Levy (2002)
states that the purpose of a Kalman filter is to optimally estimate statistically the values of the
state of a dynamic system. The estimation consists of filtering the measurements contaminated by
noise in the sense that it minimizes the mean square estimation error.
To provide current estimation of the system variables such as position coordinates, the filter uses
a statistical approach to weight each and every new measurement in relation to the past
information gathered. In addition, it determines up to date uncertainties of the estimates for real
time quality assessments.
The Kalman filter is a multiple inputoutput of filtering process that the optimal estimation takes
place in real time. Because the measurement is a vector of scalar random variables, the state
uncertainty estimate is a variancecovariance matrix. The diagonal is the variance of the random
variable. In other words it is the description of uncertainty of the reference signal (Levy 2002).
In Levy (2002) it is also indicated that, starting with an initial p redicted state estimate and its
associated covariance obtained from past information, the filter calculates the weights to be used
when combining this estimate with the first measurement vector to obtain an updated best
estimation as shown in Figure 4.2 below. The filte r then calculates an updated estimation using
the new measurement. The new estimation of covariance must be changed so that it reflects the
Chapter 4 Automatic guidance system and measuring techniques
34
new information and reduces uncertainty. The updated estimation and the associated covariance
will form the outputs of the Kalman filter.
Figure 4.2: General working steps of Kalman filter (Levy 2002)
Finally, in order to prepare for the next measurement, the filter must project the updated
estimation and associated covariance to the next measurement time. The actual system vector is
assumed to change with time. Output of data will complete the cycle of Kalman filter.
Hence, the Kalman filter algorithm generally involves four main steps; i.e. gain computation,
state estimate update, covariance update and prediction. The working steps of the filter are shown
in figure 4.2 above. At each step, the state estimate is updated by combining new measurements
with the predicted state estimate from the previous measurements.
Integration of Kalman filter in the IAGB construction machine simulator
Kalman filter is integrated in the simulator of IAGB, as shown in Schwieger and Beetz (2007), so
that the controller is able to account for some noises or unwanted large overshoots in the system.
The steps described above are implemented in the automatic guidance system of IAGB. The
detailed algorithm is stated in appendix C, in which a discrete Kalman filter is used.
It has been shown in chapter two the basic dynamic parameters for the model truck from which
the control deviation e(t) and the regulating variable u(t) are to be determined. Those dynamic
Chapter 4 Automatic guidance system and measuring techniques
35
variables are used to enhance the Kalman filter integrated in the automatic guidance and control
system of the model truck.
Consider figure 4.3 below, the discrete Kalman filter equations can be applied to the model truck
using the following equations. The predicted coordinates of the model truck
k
y and
k
x at epoch k
in the curves can be obtained from the estimated coordinates at epoch k1 as given in Schwieger
and Beetz (2007) as follows:
(4.1)
The predicted coordinates at the straight lines can be obtained as
(4.2)
The azimuth or the orientation of the front wheel and the velocity of the vehicle is updated each
time according to equations 4.3 and 4.4 below:
+=
1kk
(4.3)
1
=
kk
vv
(4.4)
The change in orientation or the change in azimuth between epochs k and k1 can also be
calculated using equation 2.19 or as:
for
0
v
(4.5)
for
0
=
v
(4.6)
The radius of curvature R is computed from equation 2.1. The azimuth or orientation of the front
wheel and the velocity at each position can be computed from the coordinates of the points
measured by the tachymeter using equations 2.18 and 2.20 respectively.
.sincos)cos1(sin
,sinsin)cos1(cos
1
1
kkkkkk
kkkkkk
RRxx
RRyy
××+××=
×
×
+
×
×
+
=
tvxx
tvyy
kkk
kkk
××+=
×
×
+
=
cos
,sin
1
1
0
=
×
=
R
tv
Chapter 4 Automatic guidance system and measuring techniques
36
.
Y
X
1
6°
R
17°
34°
51°
Pk1 ( y k1, x k1)
Pk ( y k, x k)
k
k1
Figure 4.3: Motion of a vehicle in a straight line and a curve
Chapter 5 Implementation of the vehicle model to the model truck
37
5. Implementation of the vehicle model to the model truck
The first task in this research is to determine the vehicle dynamic parameters of the model truck.
In doing so, the dynamic vehicle model and hence the effect of the lateral forces on the vehicle
circular motion stated in equation 2.14 may be taken into account.
Here the parameters that are to be determined are the values of the cornering coefficients at the
front and the rear wheels. Different methods are so far used to determine the vehicle parameters
by the automotive engineers, amongst which are:
a. Using GPS antennas fixed on the center of gravity of the vehicle and measuring
the position and yaw angle of the vehicle
b. Using optimal ground sensors attached to the wheels of the vehicle
The first method requires access to GPS signals and cannot be applied inside a building
especially in a laboratory condition, while the second method is very expensive.
Since the experiment is made in laboratory inside a building, tachymeter of Leica TPS1201 is
used as measuring device instead of GPS sensors. A reflector with very high accuracy is fixed
between the front and rear wheels of the model truck. The cornering coefficients are tried to be
computed using the geometrical relationship stated in chapter two.
The measurement is done using the graphical programming environment LabView®, in which
the program for the remote controllers of the tachymeter and the model truck are implemented.
5.1. Determination of radii
For the experiment, the point of reference for the vehicle position is put into the center of
reflector. The reflector, as point of reference for the positioning by means of tachymeter, is
between front and rear wheels on the vehicle longitudinal axis as a single track model is assumed.
Chapter 5 Implementation of the vehicle model to the model truck
38
The first step here is to drive different circles keeping the front wheel steering angle (voltage)
constant and varying the velocity of the drives. The position of the reflector, hence the position of
the vehicle, is measured by the tachymeter and stored in MySQL data base in the computer. A
minimum of three circles are driven for each velocity case.
After the circles are driven, the next step is to estimate the radius of each circle. The estimation is
made by using the method of determining radius with the help of three points. Condition
adjustment with unknowns is used as a least square adjustment. This method in geodetic
literatures is also known as GaussHelmert model (Fan 1997).
Once the radii of the circles for different velocities are obtained, the vehicle cornering
coefficients can be determined by applying different equations of the vehicle dynamic model
given in chapter two.
The mathematical model for the circles is given as
222
)()(
mimi
yyxxr +=
(5.1)
where r is the radius for the circles
x
i
, y
i
. the position of the i
th
point measured by the tachymeter
x
m
, y
m
is the coordinate of the circle centre
The equation can be rearranged as,
222
)()()( ryyxxwxf
mimi
+==
(5.2)
The GaussHelmert model can be written in the following way:
),(
o
XlfcwvBXA ==+ (5.3)
Where A is the design matrix, B is the coefficient matrix, w is the misclosure matrix and c is a
constant. Here one can understand that l are the observations or measurements (x, and y) from
the tachymeter and X the unknown parameters (x
o
m
, y
o
m
and r
o
).
The normal equation of condition adjustment with unknowns is given in Fan (1997) as:
Chapter 5 Implementation of the vehicle model to the model truck
39
=
0
0
1
w
X
A
A BBP
T
T
(5.4)
From which, the unknowns
and
X
can be solved as:
wNAANAX
TT 111
)(
= (5.5)
)XA(wNλ
1
=
(5.6)
where:
T
BBPN
1
=
(5.7)
and, P is the weight matrix for the measurements, x
i
and y
i
. For this experiment an equal weight
of unity is assumed for both x and y coordinates of each point and hence the weight matrix is
considered as an identity matrix; that is, P = I.
X
and
are least square estimates of the
correction to unknown parameters and the Lagrange multiplier respectively.
The optimal estimate can be computed as:
1 T
BPv
=
(5.8)
This value is used to compute the a posteriori variance factor using the equation below:
t
vPv
o
2
2
=
(5.9)
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