Design and Development of
a Smart Vehicle for Inspection of Inservice Water Mains
^{}
^{1}Faculty of Engineering, University
of Regina, Regina, Canada.
@uregina.ca
^{2}School of Engineering, University
of British Columbia, Okanagan Campus, Canada.
@ubc.ca
Abstract
In this
paper the design and development of a crawling robot for inspection of live
water pipes is addressed. The mechanical design of the robot is described in
detail. The governing dynamics equations of the robot moving against water flow
as well as gravity in a straight pipe are derived. Specifically, the
hydrodynamic forces exerted on the robot when moving in a live pressurized pipe
are taken into account. A fuzzylogic based control strategy is adopted to
maintain a constant translational speed in robot’s motion when subjected to
flow disturbances that are numerically modeled using step changes in flow
velocity within a simulation environment. The controller has been synthesized
in realtime within a virtual reality environment.
1. Introduction
Well functioning water networks are essential to the
sustainability of a community. Large transmission and distribution water mains
are often the most sensitive components of these networks since their failure
can be catastrophic. Furthermore, due to the high cost of these pipes, the
system does not usually provide redundancy to enable decommission for
maintenance and rehabilitation. For these reasons, failure of such water mains
often carries severe consequences including loss of service, severe damages and
water contamination. Aging
water mains often suffer from corrosion, tuberculation or excessive leakage.
These problems can affect water quality and decrease hydraulic capacity of the
mains contributing to water loss. In some cases, the main may be structurally
weak and prone to breakage. Consequently, modern urban centers need to
expend a considerable amount of financial resources on their repair and
renewal. However, the financial resources are often insufficient and a backlog
of necessary work accumulates. In North America,
there are approximately 64,000 km water transmission mains, out of which close
to 50% are older than 60 years. The replacement value of these pipes is
estimated at about $100 billion.
Prevention and/or early detection of such
catastrophic failures needs a comprehensive assessment of pipe condition. A
proactive inspection approach is critical to the condition assessment as well
as costeffective repair and renewal of water mains. Regular cyclic inspections
can provide information on the physical conditions of the pipes and on the
rates of material deterioration. Nondestructive/nonintrusive technologies for
evaluating pipe condition are essential tools for the early detection. However,
more research is required to adapt existing technologies to the unique
circumstances of large water mains that cannot be taken off service.
In this context, an underwater robotic vehicle is
designed to carry pipe inspection instruments including Nondestructive Testing
(NDT) sensors used for inspection of inservice water mains of different materials.
The robot can also provide realtime visual information about the interior
surface of the pipe. The visual information and NDT data are synergistically
used to make a more reliable decision about the condition of the pipe.
The onboard sensors would serve two purposes, namely
(1) provide information for navigation and control of the robot, and (2) collect
inspection data that can be postprocessed. The proposed system has the
following features:
·
It remains operational with pipeline in service.
·
It has a very simple structure (i.e., the minimum
number of moving parts/actuators).
·
It is stable enough, throughout its motion, to
maximize the performance of the inspection sensors.
The proposed design for the pipe inspection robot can
suit pipes with inside diameters ranging from 6 to 10 inches. The proposed
system allows for active condition assessment utilizing a variety of NDT
methods to monitor defects such as mechanical damage, tuberculation, general wall loss,
corrosion pitting, graphitization, cracks, reduced thickness of internal
lining, and faulty joints. This can replace the traditional condition assessment
methods, namely passive condition assessment, where only historical data are
used to estimate the remaining service life of a pipe.
2. Review
of previous work
2.1 Conventional Inspection Methods
Statistical methods based on the number of pipe
breaks per kilometer and reactive inspection techniques such as leak detection
have been mainly used in the past for evaluation of water pipe condition. New
testing technologies make it possible to develop more efficient and accurate
approaches to maintain pipeline integrity through direct inspection. These
techniques provide a variety of information about the condition of the pipes
depending on their materials. Examples are the number of wires broken in a
single section of the Prestressed Concrete Cylinder Pipe (PCCP), the depth of
corrosion pitting in a ductile iron pipe, the extent of graphitization in a
castiron pipe, or more generally the presence of leaking water [13].
2.2
Pipeline Inspection Vehicles
Remotely operated or autonomous vehicles moving inside
pipes that can deploy NDT techniques have been studied extensively for the past
two decades. An exhaustive review of the literature is impossible due to the
limited space available. However, various locomotion systems developed and
cited in literature for inpipe operations can be categorized into three main
groups as follows:
Pipe Inspection Gauges (PIG): They
are passive devices widely used for inspection of oil pipes and are designed so
that sealing elements provide a positive interference with the pipe wall. Once
inserted into a line, PIGs are driven through the line by applying pressure in
the direction of required movement. A pressure differential is created across
the PIG, resulting in movement in the direction of the pressure drop. Upon removal,
the information logged using the PIG’s onboard data storage unit is played back
and analyzed. PIGs are normally employed for the inspection of pipelines with
large diameters. Their inspection operations are limited to relatively straight
and uninterrupted pipe lines operating in the highpressure range. Short
inspection runs are costly. Besides, the pipeline must be relatively clean for
precise inspection, [e.g., 4, 5].
Floating
systems/robots: Autonomous Underwater Vehicles (AUV) and Remotely Operated
Vehicles (ROV) are oceanographic locomotion interfaces used for data
acquisition in subsea and deepwater missions. The applicability of existing
floating robots in the confined environments such as pipes will be very
limited. Further modifications will be needed to make them suitable for
inspection of pressurized pipelines, [e.g., 6, 7].
Mobile
robots: significant effort has been put into devising an effective
mechanism to drive a robotic system carrying onboard sensors/testing devices
through different pipe configurations. The sensors on these robots must be
small in physical size, lightweight, and low in power consumption as compared
to the other systems mentioned above. Academic researchers and industrial
corporations have investigated many variations of drive mechanisms such as
wheels, crawlers, wall press, walking, inchworm, screw and pushrods. Some
systems have complex mechanisms and linkages, which in turn require complicated
actuation and control. Wheeled systems claimed the edge over the majority due
to their relative simplicity and ease of navigation and control. Comparatively,
they are able to travel relatively fast and far. However, most of the mobile
robots developed for this purpose have been residential in research labs
because of their lack of ability to move inside pressurized pipes [e.g., 811]. Some popular variants of mobile robots
for pipe inspection are briefly described below.
Wheeled/tractor carriers: These are
the simplest drive mechanisms that are targeted for inspecting empty pipes.
These remotely controlled vehicles are designed to serve as platforms to carry
cameras and navigate through pipes and conduits [12].
Pipe crawlers: These are locomotion platforms
that crawl slowly inside a pipeline. They can move down the pipeline independent
of the product flow and maneuver past the physical barriers that limit
inspection. They can even stop for detailed defect assessment. These robots are
reconfigurable and can fit pipes with a variety of sizes [13, 14].
Helical pipe rovers: The robots developed at
the University Libre de Bruxelles are considered as an example of a helical
pipe rover (they are called HELIPIPES). HELIPIPE family consists of four
different types of robots for inpipe inspection. The robots have two parts
articulated with a universal joint. One part (the stator) is guided along the
pipe by a set of wheels moving parallel to the axis of the pipe, while the
other part (the rotor) is forced to follow a helical motion thanks to tilted
wheels rotating about the axis of the pipe. A single motor (with builtin gear
reducer) is placed between the two parts (i.e., rotor and stator) to generate the
forward motion (no directly actuated wheels needed). All the wheels are mounted
on a suspension to accommodate for slight changes in pipe diameter and also the
curved segments of the pipe. These robots are autonomous and carry their own
batteries and radio links. Their performance is, however, limited to very
smooth and clean pipes [15, 16].
Walking robots: Wallclimbing robots with
pneumatic suction cups and/or electromagnets have been used for inspection of
vertical pipes, conduits, and steel structures [17].
Walking robots are particularly useful for inspection of irregular and rough surfaces
[e.g., 18].
Pipe inspection robots can be configured as
tethered or wireless. They can be controlled remotely, or being totally
autonomous. To the best of our knowledge, all existing pipe rovers are for
inspection purposes only. In general, current mobile robotic systems are not
yet adequate for onthefly repairs in a complex pipe environment.
Development of the locomotion unit of a robot capable
of inspecting inservice pressurized pipes remains a very challenging and novel
research topic. Moreover, precise control of such a pipe inspection robot when
subjected to flow disturbances necessitates development of nonlinear control
strategies. This study addresses the mechanical design of a pipe crawling robot
capable of moving inside pressurized pipes and a fuzzylogic based control
strategy to maintain a constant speed for the robot when moving inside live
pipes.
3. The Proposed Design of the Pipe Crawler
3.1 Design Factors
Major factors considered in the design of the
proposed pipe inspection robot are reviewed in this section. The principle
objective put into practice in our design is to build a vehicle to serve as a
highly stable platform capable of conducting precise sensing/scanning
actions. The stability of the platform
in terms of having smooth motion with regulated cruise speed is necessary for
accommodating sensor readings at a high bandwidth. Precise positioning of the
vehicle is particularly important for using precision probes to inspect and
evaluate the condition of the inner surface of the pipes. The main design
requirements of the robot are as follows:
1.
The vehicle should be capable of completing inspection
without decommissioning the pipeline.
2. The
vehicle has to be pressure tolerant up to 20 atmospheres.
a. Freshwater
transmission lines are operated at pressures of up to 16 atmospheres, therefore
with a reasonable margin of safety we require the vehicle to be able to operate
at 20 atmospheres, which corresponds to the hydrostatic pressure experienced at
200 m of depth in open water.
3. The
sensor payload of the vehicle has to be flexible and user interchangeable.
a. The
primary use of this vehicle is to carry a number of NDT sensors that are in
various states of development. It is therefore necessary for the user to be
able to swap and replace sensors within hours.
4. Autonomy
of the inspection process.
a. The
length of the survey (several kilometers) makes a tethered vehicle impractical.
b. Very
detailed inspection should be done autonomously.
5. The
robot should be designed in a way that it will not deteriorate the sanitation
of the drinkable water when used in distribution water pipes.
6. The
vehicle should be capable of traveling with any inclined pipe angle. The
vehicle shall have the ability to travel vertically, negotiate multiple elbows,
and potential obstacles protruding into the pipe up to 1/3 of the pipe
diameter.
7. Travel
speeds should be a minimum of 3 centimeters per second, with 30 centimeters per
second as the desirable speed.
8. Finally,
the vehicle should be able to stop and position itself at a specific location
within the pipe using its onboard internal sensors, such as optical encoders.
3.2 The Proposed
Vehicle Configuration
In our proposed
system, we use a low drag cylindrical shape hull as a platform for carrying
inspection/navigation sensors and NDT devices. The symmetric shape of the hull
can maintain a laminar boundary layer around the hull’s outer surface. The
lowdrag property of the main body enables the system to show superior
stability against current in the pipe without loosing too much energy which is
necessary in minimizing the size of the onboard battery pack required to
travel long distances.
The
hull consists of the following modules:
·
Nose Module – This module accommodates a
viewport for a digital still or a video camera.
·
Rechargeable Battery
Module – It provides power for propulsion, system hardware, and sensors during
mission. The module contains LithiumIon rechargeable batteries with a total
capacity of 1kWh. The battery module has a builtin charger and can be charged
separately from the vehicle as well as in the vehicle.
·
Actuator, Control and Communication Module – it
accommodates the vehicle’s actuator along with the control and communication electronics.
Control instrumentation includes a 3axis magnetoinductive compass,
inclinometers, a temperature sensor, and an optical encoder. Communication is
done via Bluetooth wireless module for short distances. For distances longer
that 30 meters, the controller switches to autonomous operation. The actuator consists
of a geared DC motor.
The main hull houses the actuator and the battery
pack. The electronics responsible for power conversion, communication to the
wireless transceiver, sensor integration, and various electric motor controls
is housed in the second module connected to the main hull via a universal joint
(see Figure 1a1b). Further details on the design of the proposed robot can be
found in [19].
(a) (b)
Figure 1: The pipe inspecting robot. (a) active and passive
wheels, (b) the actuation and control modules.
There is one set of driving wheels located at one end
of the hull, pushing against the pipe inner wall. These wheels are springloaded
(see Figure 1). The driving wheels are approximately 4 centimeters in diameter
with aluminum hubs and rubber tires. The tires have treads to provide additional
traction. Larger compliant tires are appropriate for bumps and uneven internal
surfaces. The driving wheels are actuated
by a central geared DC motor which provides forward propulsion for the robot.
The onboard electronics will be responsible for producing, filtering and
controlling the power delivered to the motor for safe operation. Friction
between the passive straight wheels attached to the hull’s back end and the
pipe’s wall, prevents the hull from spinning while the main actuator is providing
smooth forward motion in the pipe.
Figure 2 shows a simplified representation of the
robot’s driving mechanism. One should
note that, (1) only a pair of driving wheels are considered, and (2) the passive
straight back wheels are not shown in this figure for simplicity. As can be
seen from Figures 1 and 2, the driving wheels are positioned at a small angle with
respect to the vertical plane of the hull. The wheels are pushed against the inside
wall of the pipe and driven along the circumference of the pipe. In this way, they
generate a screwtype motion and move
along the pipe. This mechanism, as schematically illustrated in Figure 2, is
analogous to a large screw being turned inside the pipe and consequently moving
forward. When a reverse driving torque is applied to the wheels, the robot runs
backward in the pipe.
Figure 2. The drive mechanism
of the robot based on the principle of screw.
This design
provides simplicity and compactness with minimal blockage of live pipes. Our
proposed robot can negotiate pipes composed of straight and curved segments.
3.3 Onboard
Sensors
Three
different types of sensors are incorporated into the design, namely (1)
navigation, (2) communication, and (3) inspection sensors. However, some
sensors potentially can be employed for both navigation and inspection. An
optical encoder reading motor’s shaft displacement was used for localizing the
robot inside the pipe. A vision sensor (i.e., a pinhole camera) along with an Omnidirectional
Stereo Laser Scanner (OSLS) were employed for navigation/inspection purposes.
Unbounded position errors due to slippage in wheels is inevitable, therefore
the OSLS can be superior over optical encoders to precisely measure lateral
translational motion of the robot, namely, sway and two rotational
motions, namely pitch and heave, [20]. A sensor fusion strategy
would be required to integrate orthogonal information coming from different
sensing units as the robot moves. It is also noteworthy that some temperature
sensors were used in each module to continuously monitor the temperature build
up in each watertight unit.
4. Motion analysis
In this section the kinematics and kinetics of the
proposed robot moving inside a vertical straight pipe is investigated. The
development of the mathematical model of the robot leads to a full
understanding of all of the key elements of the system needed before devising a
controller. For simplicity, the dynamics equations are derived based on the
assumption that (1) there is only one pair of driving wheels, (2) the angle of
the driving wheels cannot change on fly, and (2) the wheels apply a fixed
amount of normal force to the pipes’ wall preventing the slippage (i.e., no
onfly extension in arms applied as the robot moves). One should note that
assumption (1) can be relaxed without loose of generality.
The vehicle model and coordinate systems used in this study are
shown in Figure 3. It is assumed that one DC motor drives the hub and
accordingly the wheels attached to the hull (or main body), as the prime
actuator. From Figure 3, frames i, B, and W represent the
inertial fixed frame, the body frame attached to the main body of the robot,
and the wheel frame attached to the wheel’s center of rotation, respectively.
Figure 3: The simplified model of the robot, with one pair of
driving wheels, showing three reference frames.
In the presented dynamics model of the robot the following
parameters are used:
 The main body of the robot
(aka, the hull) is assumed as an axially symmetric rigid body with mass M
and axial moments of inertia I_{B}.
 The
wheels are considered perfectly rigid disks that roll without slippage
with mass m and polar moment of inertia of I_{W}_{Z}.
We also assume a simple friction model at the singlepoint contact between
each wheel and the pipe’s wall.
 Due to
the symmetric shape of the robot, the total hydrodynamics drag force is
assumed to be applied at the hull’s center of gravity.
 Although
rolling resistance will be present, but it will not be considered here.
Instead, the frictional moment associated with the wheels’ bearings would
be assumed to consist of this rolling resistance.
 It is
assumed that the only energy dissipation is due to friction in wheels and
their bearings.
 The
robot moves on a surface with no irregularities.
 The
distance between the wheel’s center of rotation and the COG of the hull is
considered constant, namely b = constant.
4.1
Kinematics
It can be easily shown that the translational
velocity of the hull’s COG, _{}can be related to the wheel’s inclination angle, _{} wheel’s radius of
rotation, r, and the rotational speed of the wheel, _{} as follows:
_{} (1)
Correspondingly, the rotational speed of the hull, _{} can be related to that
in wheels as follows:
_{}, (2)
where b denotes the
distance between wheel’s center of rotation and that for the hull (see Figure 3).
_{}
4.2
Dynamics
The dynamic equations of motion of the robotic
vehicle can be derived following the standard Lagrangian approach. In this
approach, first the Lagrangian L has to be calculated as follows:
_{ }_{(3) }
where T and V denote the kinetic energy and the potential
energy due to gravitational forces, respectively. The total kinetic energy of
the robotic vehicle can be represented by:
_{ }(4)
where T_{Hull}
and T_{Angled_wheel} denote kinetic energies of the hull and the
wheels, respectively. In Eqn. (4), the kinetic energy of the passive straight
wheels is disregarded. The T_{Hull}
can be readily calculated as:
_{} (5)
_{ }
The T_{Angled_wheel} can be calculated
as follows:
_{, (6)}
_{ }
Where I_{WZ} denotes the polar moment of inertia of the
wheel about its axis of rotation, I_{WX} represents the moment of inertia of the wheel
about its diameter. Also, in Eqn. (6), _{}and _{}represent the short form of _{}and _{}, respectively. Considering equations (2), (5) and (6), the
total kinetic energy of the system can be written as:
_{ } (7)
where,
_{} (8)
The potential
energy of the robot due to the gravity when moving in a vertical pipe can be
calculated as:
_{ } (9)
Where g represents the gravitational acceleration.
The Lagrange’s equations are expressed as follows:
_{ }(10)
Where _{}denotes the generalized coordinates, and _{} denotes the
generalized active forces associated with the generalized coordinates, _{}. Considering the angle of rotation of the wheel, θ
as the only generalized coordinate in the Lagrange formulation, one can write:
_{ }(11)
The generalized forces Q applied on the robot moving
inside the pipe can be given as:
_{} (12)
Where the right hand side of the above equation represents
the nonpotential generalized torques such as motor’s torque, T_{m}
and the resisting torques due to the dry friction between the wheels and their
axles, T_{f} , and the resisting torque due to
hydrodynamic drag force posed on the system via the flow inside the pipe, T_{D}
all projected onto the generalized coordinate, q.
Friction plays a significant role in creating the
motion of the robot. The robot wheels roll due
to the translational friction between the wheels and the internal
surface of the pipe. Insufficient friction at the pointofcontact between the
wheels and the pipe’s wall leads to wheel slippage. The slippage constraint of a wheel is expressed as (using Coulomb’s
friction law):
_{ }(13)
Where µ denotes the friction coefficient, and F_{N}
denotes the the normal force applied on the internal surface of the pipe by the
robot’s wheels. Therefore, the resisting
torque due to the internal friction can be obtained from the following
equation:
_{ }(14)
Where d represents
the diameter of the wheel’s hub.
The hydrodynamic drag force induced by the flow
on the robot, projected onto the generalized coordinate q, can be expressed as follows:
_{ }(15)
In Eqn. (15), r denotes the density
of the water, A is the effective cross sectional area of the robot, v
denotes the effective velocity of the flow inside the pipe, and C_{d}
represents the drag coefficient. By substituting Eqns. (14) and (15) in Eqn. (12), the
generalized force Q will be computed as:
_{ }(16)
By using Eqn.
(16) and substituting T and V from Eqns. (7) and (9) into
Eqn. (11), the following closed form
solution in form of a nonlinear 2^{nd}order differential equation for
the wheels’ motion (and correspondingly the robot’s motion) can be obtained:
_{}, (17)
_{ }
Where h in Eqn. (17) is the same as that given in Eqn. (8). From Eqn. (17), one
can realize that the motion of the robot can be controlled by changing
parameters such as the wheel’s inclination angle, d the normal force exerted on the pipe’s wall
via the wheels, F_{N}, and the torque applied to the wheels’
actuators, T_{m}. The
only control input that can vary on fly in our design is the motor’s torque,
namely T_{m}. How to manipulate this torque in order to maintain
a constant speed of motion when the robot is subjected to flow disturbances
(i.e., variation in the flow speed, v) will be discussed in Section
5.
4.3 Motor
Dynamics
Motor
dynamics has been considered in our model which is briefly discussed in this
section. The mechanical torque generated by a Permanent Magnet DC (PMDC) motor
can be related to its input voltage and current through the following equation,
[21]:
_{ } (18)
where K_{t} is the
motor’s torque constant and i_{a} denotes the armature current.
For a PMDC one can also write:
_{ (19)}
Where L_{a}
denotes the armature’s inductance, R_{a} denotes the armature
copper resistance, and e_{b} denotes the Back ElectroMotor Force
(BEMF). The input voltage (i.e., the control variable) is denoted by e_{a}
in Eqn. (19). The BEMF is related to the rotational speed of the motor’s shaft
as:
_{ }(20)
where K_{b} represents the BEMF
constant. By incorporating Eqns. (1820)
into Eqn. (17), one can take the motor’s dynamics into account when controlling
the robot’s speed subjected to flow disturbances
The above
mathematical model was created and implemented in a MATLAB/Simulink
environment. An overview of the system’s model in Simulink is presented in
Figure 4. The motion of the robot was also presented in a virtual reality
environment. A snapshot of the implemented graphical simulation is also shown
in Figure 5.
Figure
4: The system’s model in MATLAB/SIMULINK
Figure 5: Visualization of the robot moving inside a pipe.
A user can control the motion of the robot by
either changing the normal force F_{N} and/or the wheels’
inclination angle, d offline, or by changing the input voltage
provided to the DC motor on fly. A realtime interactive interface was
implemented in MATLAB/Simulink, by making use of the realtime workshop toolbox
from Mathworks, [22], for verification of the design in a humanintheloop
control fashion. The performance of the humancontrolled system in real time
can be further used to optimize the performance of a standalone and autonomous
controller such as a FuzzyLogic based controller offline. A standalone
fuzzylogic controller was utilized for speed control of the robot at this
stage.
5. FuzzyLogic Control of the Proposed Pipe
Crawling Robot
A control strategy based on FuzzyLogic was
adopted. The controller strives to reject flow disturbances by maintaining a
constant speed for the robot. A disturbance, in the form of step changes in
flow velocity, is generated randomly as the robot moves in a simulated
environment. The controller tracks the response of the system to its
userdefined velocity setpoint and sends a correction command in terms of the
input voltage provided to the DC motor actuators. The overall control scheme is
shown in the Figure 6.
Figure 6: The fuzzylogic based control scheme
modeled in Simulink.
Fuzzy logic controllers incorporate heuristic control
knowledge in the form of ifthen rules,
and are a convenient choice when a precise linear dynamic model of the system
to be controlled cannot be easily obtained. They have also shown a good degree
of robustness in face of large variability and uncertainty in the system
parameters, [23].
5.1
Description of the Proposed Control Logic
There are two main approaches to fuzzy control,
namely the Mamdani method and the modelbased fuzzy control, [24, 25]. We have
adopted Mamdani’s in our studies. Central to the design of a Mamdani fuzzy
control are: (1) fuzzification of crisp variables using membership functions
along with application of implication and aggregation methods, (2) defining an
ifthen rulebase, and (3) the
defuzzification. In our proposed fuzzy
control the inputs are the error between robot’s linear velocity inside the
pipe and its desired value, and its rate of change. Triangular membership
functions were utilized for fuzzification and defuzzification phases. The fuzzy
logic controller adjusts the control variable, namely the input voltage
provided to the wheels’ actuators in order to maintain a constant speed in the
robot when subjected to flow disturbances. Table I shows the rule base and
fuzzy implication for the error in the system and its rate of change. The error
and its rate of change could assume the following values: Positive (P),
Positive Large (PL), Zero (Z), Negative (N), and Negative Large (NL). The
control values are tabulated in Table I.
The controller is designed using five membership
functions for each input variable (i.e., error in linear speed and its rate of
change) and that for the control variable.
Table I: Fuzzy rule
base.
The fuzzy rules were extracted through the
implementation of a realtime humanintheloop virtual reality simulation
environment, [26]. It was then conjectured that the simple rule base provided
in Table I would suffice to reject flow disturbances in form of step changes in
flow velocity within a userset design objective.
The membership functions assigned to the error in
system are shown in Figure 7. Similar membership functions were implemented for
the rate of change of the error in the system as well. The range of error is
limited to ±
0.8 m/sec. Correspondingly, the rate of change in error has been limited to ± 5
m/sec^{2}. The normalized membership functions associated with the
control variable (motor voltage) is represented in Figure 8. As can be seen from Figure 8, the control
variable can become Negative Large (NL), Negative (N), Zero (Z), Positive (P),
and Positive Large (PL).
Figure 7: Error’s membership functions.
Figure 8: Control variable’s membership functions.
6.
Simulation Results
Computer simulations were conducted to show the
robustness of the FLbased controller in rejecting flow disturbances. The
desired linear speed of the robot was set at 0.15 m/sec. A flow disturbance in
form of step changes in flow velocity were synthesized (see Figure 9). As can
be seen from Figure 9, there is no flow for the first 10 seconds of simulation.
There is a step increase in flow velocity from 0 to 2 m/sec at t = 10 seconds
and a step decrease from 2 m/sec to 1 m/sec at time t = 20 seconds. Figures (1011)
show the variation of the error signal and its rate of change versus time. The
rise time of the controller is ~1.1 seconds with a settling time of ~2 seconds
when the system being subjected to step changes in flow velocity. The rate of
change of the error signal decays to zero within a reasonable time as well.
Figure 12 shows the robot’s linear speed versus time. The controller can reject
flow disturbances quite fast with reasonable under/overshoot. Figure 13 shows
the 3D error surface of the FLbased controller. Manufacturer’s specification
of a Pittman servo motor were utilized in the simulations, [27].
Figure 9: Flow
disturbance in form of step changes in flow velocity.
Figure 10: Time
response of error.
Figure 11: Rate of change of the error.
Robot’s linear speed inside the pipe


Figure 12: Time response of the robot’s linear speed.
Figure
13: The 3D error surface of the FLbased controller.
7. Conclusions and future work
This paper addressed the preliminary design of a
robotic system for active condition assessment of inservice water pipes. The
robot has a very simple driving mechanism. By utilization of angled wheels on
the robot one can generate a screwtype motion. The robot can move against
gravity. Besides, the proposed robot will be able to better negotiate curved
sections of the pipe as opposed to that in existing robots with straight
wheels.
A FuzzyLogic (FL) based controller was developed and
its performance was depicted in a representative computer simulation. The
FLbased control strategy can meet the design requirements, namely fast and
precise control of the robot’s linear speed when subjected to flow disturbances
(i.e., pressure fluctuation inside the pipe, flow velocity, etc.). The FLbased
control strategy was simulated in realtime utilizing a comprehensive dynamics
model of the robot.
Future work has three folds as follows: (1) using an
AdaptiveNetworkBased Fuzzy Inference Systems (ANFIS) to tune the FLbased
controller parameters/rules to optimize its performance. In this context, a
dynamic realtime humanintheloop simulation has been developed where
a human (expert) could physically control the motion of the robot through
visual feedback in real time. The proposed fuzzylogic controller will be then
further optimized to match the expert’s performance adaptively depending on
application domain, (2) design and fabrication of a real prototype with
extending arms to fit a variety of pipes with different sizes, and (3)
developing a HardwareIntheLoop (HIL) simulation system, as depicted
in Figure 14, to control the motion of the robot when located in an empty pipe
(or duct) in a dry lab. A motorized flow simulator will be employed to simulate
the effect of hydrodynamic forces exerted on the robot as it were moving inside
a live pipe. The flow simulator and the robot will be connected via force
sensors.
Figure 14: The proposed HIL simulation
system.
Appendix A: Dynamics Model of the Proposed Pipe
Inspecting Robot (the kinetic energy of the robot’s wheels).
In order to derive the dynamics model of our proposed
system, three coordinate frames, as shown in Figure 3, are taken into
consideration which are as follows:
 Inertial
reference system  This is the earthfixed coordinate system defined by a
righthanded, orthogonal X_{i}, Y_{i},
Z_{i} coordinate frame. The Z_{i }axis
is parallel to the pipe’s centerline and is pointed upward. The X_{i}
and Y_{i} directions and the location of the origin can be
selected arbitrarily (within the requirement of orthogonality). The
inertial frame is denoted by letter i.
 Bodyfixed
coordinate frame  This is the bodyfixed coordinate system that is
defined by a righthanded, orthogonal coordinate system attached to the
robot’s hull. Its origin lies on the hull’s centre of gravity. The Z_{B}
axis is set parallel to the Z_{i} and is pointed upward.
The X_{B} and Y_{B} axes
remain perpendicular to the Z_{B} axis within the
requirement of orthogonality. The bodyfixed frame is denoted by letter B.
 Wheelfixed
coordinate frame  This is the righthanded orthogonal reference frame
fixed to the wheel with its origin located on the intersection point
between the Y_{B} axis and the wheel center. The Z_{W}
axis is perpendicular to the wheel’s plane pointing towards the vehicle’s direction of
motion. It makes an angle of δ with respect to the the Z_{B}
axis. The X_{W} and Y_{W} axes
remain perpendicular to the Z_{W} axis within the
requirement of orthogonality. The
wheelfixed frame is denoted by letter W.
One should note that the
extension of robot’s arms is not considered in the dynamics model for
simplicity. Transformations from the wheel and bodyfixed coordinate frames to
the inertial reference frame are described here. The general orientation of the
wheelfixed frame (hereinafter called wheel frame) represented in the inertial
frame can be utilized through a number of successive rotations called Euler
Angles. The relative rotation between the wheel frame and inertial frame can be
represented as follows:
_{ } (A1)
where
_{ }(A2)
_{ } (A3)
In Eqns. (A1A3), f,
q,
and d
denote the rotational angle of the robot’s body with respect to the inertial
frame, the rotational angle of the wheel with respect to the body frame, and
the inclination angle of the wheels, respectively. One should note that the
following notation is used in long equations; _{}, and _{}
Total
kinetic energy of each robot’s wheel can be calculated as follows:
_{ }(A4)
where _{}, _{}, m, and ^{i}I_{W} denote the
linear velocity of the origin of the wheel frame represented in the inertial
frame, the angular velocity of the wheel frame represented in the inertial
frame, the wheel’s mass, and the wheel’s inertial tensor represented in the
inertial frame, respectively. These
terms are described below in more detail.
One can write:
_{}, (A5)
where _{}denotes the velocity of the origin of the body frame
represented in the inertial frame, _{}denotes the relative velocity of the wheel frame and body
frame represented in the inertial frame, _{} denotes the angular
velocity of the body frame represented in the inertial frame, and _{}denotes the vector connecting the origin of the body frame to
the origin of the wheel frame represented in the inertial frame. One can
readily conclude:
_{} (A6)
and:
_{} (A7)
With
the assumption that the robot’s arms are fixed, namely b = 0 (see Figure
6), one can conclude: _{} = 0^{T}.
One can also write:
_{} (A8)
After substituting Eqns. (A6A8) into Eqn. A5, one
gets:
_{} (A9)
Correspondingly, the angular velocity of the wheel
frame represented in the inertial frame can be calculated as follows:
_{}, (A10)
where _{}denotes the relative angular velocity between the wheel frame
and that for the body frame represented in the inertial frame. One can write:
_{} (A11)
By substituting Eqns. A7 and
A11 in A10 one can write:
_{} (A12)
With the assumption that the wheel assembly has
a symmetric mass distribution about its axis of rotation and with the
assumption of small wheel’s inclination angle, d, its inertia tensor expressed in the inertial
frame can be calculated as follows:
_{ } (A13)
Where the diagonal of
the inertia matrix given in Eqn. (A13) denotes the moment of inertia of the
wheel around the X, Y, and Z axes of the wheel frame, respectively. One should
note that_{}.
By substituting Eqns. (A9), (A12),
and (A13) in Eqn. (A4), one can derive:
_{ } (A14)
One should note
that the kinematics constraint of _{}, applicable under no slippage condition on robot wheels, was
utilized to derive Eqn. (A14) as well. Eqn. (A14) can be further simplified for
small inclination angles of the wheels, d in which case one can
assume; sin(δ) @ 0 and cos(δ) @ 1 as follows:
_{ }(A15)
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