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(1)

Abstract—In this paper, a pneumatic worm-like micro robot with active force control (AFC) capability is modelled and simulated in a constrained environment (pipe). A mathematical model that represents the dynamic characteristics of the worm-like micro robot is first presented. Then, the dynamic response of the robot system subjected to different input excitations is investigated. A proportional-integral-derivative (PID) controller is applied to the micro robot system to follow the desired trajectory while an AFC controller is utilized to reject the unwanted disturbances which may be created due to frictional forces or fluid viscosity in the pipe. The control system is tuned so that an accurate trajectory tracking is possible. The performance of the control system under different types of disturbances is evaluated through a rigorous simulation study. The obtained results clearly demonstrate an effective trajectory tracking capability of the worm-like micro robot in spite of the negative effects of the external disturbances.

Index Terms—Active Force Control, Micro Robot, PID Controller, Robust Tracking, In-pipe.

I. INTRODUCTION

Micro robotics is a field that has generated much interest amongst researchers and robot engineers alike due to its potentials operating in adverse working conditions and constrained environments. Examples can be seen in micro robots performing various tasks such as exploration and inspection in industrial pipes that can be associated with petroleum piping installations, chemical plants, heat exchangers, and gas or water supply systems; a much smaller scale robotic system may be applicable to carry out endoscopic procedure in vessels of the human body. An in-pipe inspection micro robot is useful to inspect the state and conditions of the pipe to detect leaks, cracks or modification of cross section in pipe lines. The robot is able to move effectively in the pipe and transport exteroceptive sensors that give different results such as finding or detecting the position/location and type of problem and measurements about the environment.

Some basic research on mobile micro robotic mechanisms for use in pipes have been reported, such as those that are driven by piezoelectric actuators [1, 2, 3], by giant magnetostrictive actuators [4] by pneumatic actuators [5, 6], or by

Manuscript received April 14, 2010.

M. Mailah is with the Universiti Teknologi Malaysia (UTM), 81310 Skudai, Johor, Malaysia (phone: 607-5534562; fax: 607-5566159; e-mail: [email protected]).

Y. Sabzehmeidani is with the Universiti Teknologi Malaysia (UTM), 81310 Skudai, Johor, Malaysia (e-mail: yaser7002@ gmail.com).

M. Hussein is with the Universiti Teknologi Malaysia (UTM), 81310 Skudai, Johor, Malaysia (e-mail: [email protected]).

electromagnetic actuators [7].

However, most of these robots are still in the developmental stage and certain problems still have to be addressed and solved before they become practical. Such micro robots for small pipes have low pulling force and have difficulty negotiating curved pipes or vertical pipes. Besides, commercial charge-coupled device (CCD) cameras are too big to mount on these robots.

Lim et al. invented an inchworm like micro robot by using only one pneumatic line [8]. It is based on drilling different-sized micro holes in two plates among three chambers. The rear clamp, the elongation module, and the front clamp work sequentially as the air flows to each chamber. It enables the robot not only to generate inchworm like locomotion, but also to allow significant reduction of the stiffness of pneumatic lines and the drag force due to one pneumatic line. In order to operate the robot efficiently, the stroke according to the supplied pneumatic pressure is investigated.

In another design, a pneumatic flexible robot prototype for in-pipe inspection was designed and experimented as described in [9]. A dynamic model which takes into account the flexibility, damping and friction was developed. A number of experiments were carried out in order to characterize the robot and provide the input for the numerical model. The model was validated by comparing the experimental and numerical robot gait in time domain. The robot motion for different pipes network geometry is also presented in the research. The works described above mostly focus on the principle of actuation and assume an open loop control configuration that does not include sensory feedback information and control algorithm for critical task applications.

In the proposed research, we incorporate a robust feedback control mechanism into a pneumatically actuated micro robot taking into account the robust tracking performance in a constrained environment in pipe. The strategy used is based on active force control (AFC) technique that has been successfully applied to many dynamical systems [10-13]. Pioneering AFC work applied to robotic manipulator was presented by Hewit and Burdess (1981), in which an efficient disturbance rejection technique was established to facilitate the robust motion control of the dynamical system in the presence of disturbances, parametric uncertainties and changes that are commonly prevalent in the real-world environment [10]. Mailah et al. investigated the usefulness of the AFC method by introducing intelligent mechanisms to approximate the mass or inertia matrix of the dynamic system to trigger the compensation effect of the controller. It was

Modelling and Control of a Worm-Like Micro

Robot with Active Force Control Capability

(2)

recognized that the AFC was rob theory as well as in

AFC method is extended to correct the accuracy, stroke and reach point of

tracking performance

and later simulated with the active force control mode incorporated.

II. A

specifically produces

five phases illustrated by schematic drawings in

(a)

[image:2.612.71.296.220.386.2]

(c)

Figure

part: The rear bladder expands and pushes onto the inner pipe wall, holding the robot fixed (b) Second part: The robot body stretches (c) Third part: The front bladder expands (d) Fourth part: The rear bladder

deflates executing the net gait

B

chambers

with control volumes (CV pneumatic resistance is

Where, the mass

terms of the pneumatic capacitances expressed as:

Where,

and

By

recognized that the AFC was rob theory as well as in

AFC method is extended to correct the accuracy, stroke and reach point of the

tracking performance

and later simulated with the active force control mode incorporated.

. MODELING AND

A. Mechanism of Robot Movement

The proposed study considers that the specifically intended

produces a worm

five phases illustrated by schematic drawings in

(a)

(c)

(e)

Figure 1: Mechanism of micro robot movement, (a) First part: The rear bladder expands and pushes onto the inner pipe wall, holding the robot fixed (b) Second part: The robot body stretches (c) Third part: The front bladder expands (d) Fourth part: The rear bladder

deflates executing the net gait

B. Mathematical Formulation For the given dynamic system chambers and bladders

with control volumes (CV pneumatic resistance is

Where, is defined in terms of the mass rate of flow the input pressure,

mass flow rate of

terms of the pneumatic capacitances expressed as:

Where,

and

By inserting Eq. (1) into Eq. (2), we have recognized that the AFC was rob theory as well as in practice [1

AFC method is extended to correct the accuracy, stroke and the micro robot

tracking performance. The m

and later simulated with the active force control mode

ODELING AND SIMULATION OF

Mechanism of Robot Movement

The proposed study considers that the intended for in-pipe

worm-like locomotion. The gait cycle consists of five phases illustrated by schematic drawings in

(d)

(e)

Mechanism of micro robot movement, (a) First part: The rear bladder expands and pushes onto the inner pipe wall, holding the robot fixed (b) Second part: The robot body stretches (c) Third part: The front bladder expands (d) Fourth part: The rear bladder deflates (e) Fifth part: The robot body deflates executing the net gait

Mathematical Formulation For the given dynamic system

and bladders in a cylindrical space with control volumes (CV1 and CV

pneumatic resistance is given as

is defined in terms of the mass rate of flow input pressure, is the output pressure, and

rate of the fluid. The differential mass flow rate in terms of the pneumatic capacitances

inserting Eq. (1) into Eq. (2), we have

recognized that the AFC was robust and effective both in [12, 13]. In this research, the AFC method is extended to correct the accuracy, stroke and micro robot, all pertaining to robust

micro robot shall be

and later simulated with the active force control mode

IMULATION OF MICRO R

Mechanism of Robot Movement

The proposed study considers that the pipe application

like locomotion. The gait cycle consists of five phases illustrated by schematic drawings in

(b)

(d)

Mechanism of micro robot movement, (a) First part: The rear bladder expands and pushes onto the inner pipe wall, holding the robot fixed (b) Second part: The robot body stretches (c) Third part: The front bladder expands (d) Fourth deflates (e) Fifth part: The robot body

Mathematical Formulation

For the given dynamic system comprising in a cylindrical space

and CV2) as shown in Fig. 2,

given as:

is defined in terms of the mass rate of flow

output pressure, and

The differential mass flow rate in terms of the pneumatic capacitances (C1 and

inserting Eq. (1) into Eq. (2), we have:

ust and effective both in In this research, the AFC method is extended to correct the accuracy, stroke and , all pertaining to robust icro robot shall be modelled and later simulated with the active force control mode

ROBOT SYSTEM

The proposed study considers that the robot is application and that it like locomotion. The gait cycle consists of five phases illustrated by schematic drawings in Fig. 1 [8].

comprising a series of air in a cylindrical space (inside pipe)

own in Fig. 2, the (1) is defined in terms of the mass rate of flow, i

output pressure, and is the The differential mass flow rate in

and C2) can be

(2)

(3) ust and effective both in

In this research, the AFC method is extended to correct the accuracy, stroke and , all pertaining to robust modelled and later simulated with the active force control mode

YSTEM

robot is it like locomotion. The gait cycle consists of

air (inside pipe) the (1) is the The differential mass flow rate in can be (2)

(3)

Using Eq. (1)

Figure

Eq. (3) can also be expressed

Similar to CV CV2 and CV

Figure By using

From Eq. (

!

For the displacement of

"#" $"

Substituting

% ! &

'

For the above condition, since and rear bladder

displacement is friction) and not change,

Eq. (1), the following expression can

Figure 2: Free body diagram can also be expressed

Similar to CV1 and referring to Fig. 3, the expressions for

and CV3 are given as follows: &

( (

Figure 3: Free body diagram By using Eq. (5), can be written

%

Eq. (8), can be determined

! ( (

displacement of

")" * _'*_*

Substituting Eqs. (8) and (

%

! ( ( _'

+

e above condition, since

and rear bladders is assumed to sufficiently displacement is relatively

and that the lengths of the change, Eq. (12) could be simplif

, the following expression can

ree body diagram related to can also be expressed as:

and referring to Fig. 3, the expressions for are given as follows:

&

ree body diagram related to can be written as:

,

can be determined as: displacement of section, it is given as

* _{- . / 0}

) and (9) into Eq. (6)

'

' 1

e above condition, since the movement of

assumed to sufficiently relatively small enough

that the lengths of the front and rear bladder could be simplified

, the following expression can be written as:

related to CV1 and CV

and referring to Fig. 3, the expressions for

related to CV2 and CV

as:

!1 as:

it is given as:

0

Eq. (6), we have:

!1

! !

the movement of the assumed to sufficiently quick while

small enough (neglecting the front and rear bladder

ied as:

(4) be written as:

(5)

and CV2

(6) and referring to Fig. 3, the expressions for

(7)

(8)

and CV3

1 (9)

(10)

(11)

1 ! &

(3)

+

Using Laplace transformation, the displacemen

2

For testing

tracking the desired locomotion accurately, input sources

functions determine

namely the PID and AFC controllers shall be applied and incorporated into the mi

A

most commonly used control algorithm in industry and has been universally accepted in industrial control

popularity of PID controllers can be attributed partly robust performance in a wide range of operating conditions and partly to their functional simplicity, which allows engineers to operate them in a simple, straightforward manner

controller

The basic idea behind a PID controller is to read a sensor, then compute the desired actuator output by calculating proportional, integral, and derivative responses and summing those three components to com

controller calculation (algorithm) involves three separate parameters;

The

3 45

where

derivative gains, respectively. In this study, the Ziegler

parameters. The final gains

$4

the gains can be seen in Fig. 5 throughout the simulation study.

6

Using Laplace transformation, the displacement can be found as:

27 87 9:;

For testing the

tracking the desired locomotion accurately, input sources in the form of

functions via feedback control techniques determine the system responses.

namely the PID and AFC controllers shall be applied and incorporated into the mi

A. PID control Proportional

most commonly used control algorithm in industry and has been universally accepted in industrial control

popularity of PID controllers can be attributed partly robust performance in a wide range of operating conditions and partly to their functional simplicity, which allows engineers to operate them in a simple, straightforward manner. A schematic diagram of system

[image:3.612.316.540.45.388.2] [image:3.612.78.293.403.472.2]

controller is shown in

Figure

controller calculation (algorithm) involves three separate parameters; the proportional,

The PID control algorithm is

45 $ ₌<

here $ , $₄, and

derivative gains, respectively. In this study, the Ziegler–Nichols

parameters. The final gains

>.?, $₅

the gains can be seen in Fig. 5 throughout the simulation study.

!@ ! !

Using Laplace transformation, the

t can be found as:

ABC C_{C BC}D

EFG_H I_JKGLH_M ;

III. CONTROL

the system effectiveness in producing and tracking the desired locomotion accurately,

in the form of step

via feedback control techniques system responses.

namely the PID and AFC controllers shall be applied and incorporated into the micro robot

PID control

Proportional-Integral-Derivative (PID) control is the most commonly used control algorithm in industry and has been universally accepted in industrial control

popularity of PID controllers can be attributed partly robust performance in a wide range of operating conditions and partly to their functional simplicity, which allows engineers to operate them in a simple, straightforward

chematic diagram of system is shown in Fig. 4.

Figure 4: Schematic diagram of system

controller calculation (algorithm) involves three separate proportional, i

control algorithm is given as follows:

$5N

and $₅ are the proportional, integral and derivative gains, respectively. In this study, the method is employed to tune the PID parameters. The final gains were determined as

>0. The resultant tracking control based on the gains can be seen in Fig. 5

throughout the simulation study.

! ,

Using Laplace transformation, the transfer function based on

D

H

M AC BCC C DO

ONTROL SCHEMES

effectiveness in producing and tracking the desired locomotion accurately, we applied

step, square and sin via feedback control techniques

system responses. Two types of controllers, namely the PID and AFC controllers shall be applied and

cro robot system.

Derivative (PID) control is the most commonly used control algorithm in industry and has been universally accepted in industrial control

popularity of PID controllers can be attributed partly robust performance in a wide range of operating conditions and partly to their functional simplicity, which allows engineers to operate them in a simple, straightforward chematic diagram of system employing a PID

Schematic diagram of system

The basic idea behind a PID controller is to read a sensor, then compute the desired actuator output by calculating proportional, integral, and derivative responses and summing those three components to compute the output. The PID controller calculation (algorithm) involves three separate

integral and derivative given as follows:

are the proportional, integral and derivative gains, respectively. In this study, the method is employed to tune the PID

were determined as

The resultant tracking control based on and these gains shall be used throughout the simulation study.

'

(13) transfer function based on

DO (14)

effectiveness in producing and we applied three

sinusoidal input via feedback control techniques in order to

Two types of controllers, namely the PID and AFC controllers shall be applied and

Derivative (PID) control is the most commonly used control algorithm in industry and has been universally accepted in industrial control [14]. The popularity of PID controllers can be attributed partly to their robust performance in a wide range of operating conditions and partly to their functional simplicity, which allows engineers to operate them in a simple, straightforward employing a PID

Schematic diagram of system

The basic idea behind a PID controller is to read a sensor, then compute the desired actuator output by calculating proportional, integral, and derivative responses and summing pute the output. The PID controller calculation (algorithm) involves three separate derivative terms given as follows:

(15) are the proportional, integral and derivative gains, respectively. In this study, the method is employed to tune the PID were determined as $ P? The resultant tracking control based on

hese gains shall be used (13) transfer function based on

(14)

effectiveness in producing and three input in order to Two types of controllers, namely the PID and AFC controllers shall be applied and

Derivative (PID) control is the most commonly used control algorithm in industry and has . The to their robust performance in a wide range of operating conditions and partly to their functional simplicity, which allows engineers to operate them in a simple, straightforward employing a PID

The basic idea behind a PID controller is to read a sensor, then compute the desired actuator output by calculating proportional, integral, and derivative responses and summing pute the output. The PID controller calculation (algorithm) involves three separate terms. (15) are the proportional, integral and derivative gains, respectively. In this study, the method is employed to tune the PID

P?, The resultant tracking control based on hese gains shall be used

Figure 5:

B. Active Force Control

The research on active force control (AFC) is initiated by Johnson (1971) and later Davison (1976) based on the principle of invariance and the classic

of motion

to design a feedback controller that will ensure the system setpoint remains unchanged even in the presence of the disturbances or adverse operating and loading conditions provided that the actual disturbances can be modelled effectively. Hewit and Burdess (1981) proposed a more complete package of the system such that the nature of disturbances is oblivious to the system and that it is readily applied to multi

Thus, an effective

robust motion control of dynamical systems in the presence of disturbances

commonly

et al. extended the usefulness of the method by intro intelligent mechanisms to approximate the mass or inertia matrix of the dynamic system to trigger the compensation effect of the controller

technique that relies on the appropriate estimation of the inertial or mass

measurements of the acceleration and force signals induced by the system

For theoretical simulation, it is normal that perfect modelling of the sensors is assumed and

totally neglected.

subjected to a number of disturbances remains stable and Performance of

wave and (c Active Force Control

of motion [15, 16]. It has been demonstrated

to design a feedback controller that will ensure the system setpoint remains unchanged even in the presence of the disturbances or adverse operating and loading conditions provided that the actual disturbances can be modelled y. Hewit and Burdess (1981) proposed a more complete package of the system such that the nature of disturbances is oblivious to the system and that it is readily applied to multi-degree of freedom dynamic systems Thus, an effective method

robust motion control of dynamical systems in the presence of disturbances, parametric

commonly prevalent in the real

extended the usefulness of the method by intro intelligent mechanisms to approximate the mass or inertia matrix of the dynamic system to trigger the compensation effect of the controller

technique that relies on the appropriate estimation of the inertial or mass parameters of the dynamic system and the measurements of the acceleration and force signals induced by the system if practical implementation is ever considered. For theoretical simulation, it is normal that perfect modelling of the sensors is assumed and

totally neglected. In AFC, it is shown that the system subjected to a number of disturbances remains stable and

(a)

(b)

(c) Performance of PID controller

c) square input Active Force Control

. It has been demonstrated

to design a feedback controller that will ensure the system setpoint remains unchanged even in the presence of the disturbances or adverse operating and loading conditions provided that the actual disturbances can be modelled y. Hewit and Burdess (1981) proposed a more complete package of the system such that the nature of disturbances is oblivious to the system and that it is readily

degree of freedom dynamic systems method has been es

robust motion control of dynamical systems in the presence , parametric uncertainties

in the real-world environment. extended the usefulness of the method by intro intelligent mechanisms to approximate the mass or inertia matrix of the dynamic system to trigger the compensation

[11, 12, 17]. The AFC method technique that relies on the appropriate estimation of the

parameters of the dynamic system and the measurements of the acceleration and force signals induced if practical implementation is ever considered. For theoretical simulation, it is normal that perfect modelling of the sensors is assumed and that noises in the sensors are In AFC, it is shown that the system subjected to a number of disturbances remains stable and

PID controller for (a) step, input functions

The research on active force control (AFC) is initiated by Johnson (1971) and later Davison (1976) based on the principle of invariance and the classic Newton’s second law . It has been demonstrated that it is possible to design a feedback controller that will ensure the system setpoint remains unchanged even in the presence of the disturbances or adverse operating and loading conditions provided that the actual disturbances can be modelled y. Hewit and Burdess (1981) proposed a more complete package of the system such that the nature of disturbances is oblivious to the system and that it is readily

degree of freedom dynamic systems has been established to facilitate robust motion control of dynamical systems in the presence

uncertainties and changes world environment. extended the usefulness of the method by intro intelligent mechanisms to approximate the mass or inertia matrix of the dynamic system to trigger the compensation

The AFC method technique that relies on the appropriate estimation of the

parameters of the dynamic system and the measurements of the acceleration and force signals induced if practical implementation is ever considered. For theoretical simulation, it is normal that perfect modelling that noises in the sensors are In AFC, it is shown that the system subjected to a number of disturbances remains stable and for (a) step, (b) sine

(4)

robust via the compensating action of the control strategy. A more detailed description on the mathematical trea related to the derivation of important equations and stability criterion, can be found in

concept of AFC applied to presented with reference to Fig.

The notations used in

The

following expression:

F can be readily measured by means of a using an accelerometer.

perfect model [11]

give the ultimate AFC signal command to be embedded with an outer control loop. This creates a two degree

controller that could provide excellent overall system performance provided that the measurement and estimated parameters were appropriately acquired. The outer control loop can be a proportional

controller, resolved mo

intelligent controller or others deemed suitable. It is apparent that a

cause the output to disturbances

G

A

open loop system, by first generating the world coordinate error vector, which would then be processed through a controller function,

that maybe represented by Eq (15).

burden in AFC is the multiplication of the estimated inertia parameter

component Mailah

demonstrated the effectiveness of the AFC scheme applied to rigid robot arms.

robust intelligent AFC method that is capable of controlling a vehicle suspension system

introduced

Desired Position

robust via the compensating action of the control strategy. A more detailed description on the mathematical trea related to the derivation of important equations and stability criterion, can be found in

[image:4.612.72.299.112.210.2]

concept of AFC applied to presented with reference to Fig.

Figure 6: A schematic diagram The notations used in

G(s) : Ga(s) :

Gc(s) :

KAFC :

H(s) : F : F* : m : a :

he estimated disturbance following expression:

F*₌

can be readily measured by means of a using an accelerometer.

perfect model, crude approximation [11]. F* is then passed through a

controller, resolved mo

intelligent controller or others deemed suitable. It is apparent that a suitable choice of

cause the output to disturbances such that:

Ga(s)H(s) = 1

A set of outer

open loop system, by first generating the world coordinate error vector, which would then be processed through a controller function,

burden in AFC is the multiplication of the estimated inertia parameter with the angular acceleration of the

component before being fed into the AFC feedforward loop. Mailah et al. [18]

demonstrated the effectiveness of the AFC scheme applied to rigid robot arms.

robust intelligent AFC method that is capable of controlling a vehicle suspension system

introduced disturbances. Gc(s) Desired Position Controller +

-robust via the compensating action of the control strategy. A more detailed description on the mathematical trea related to the derivation of important equations and stability criterion, can be found in [10]

concept of AFC applied to a dynamic rotational system is presented with reference to Fig.

A schematic diagram The notations used in Fig. 6 are as follows:

Dynamic system transfer function Actuator transfer function

Outer loop controller AFC constant Weighting function Applied force Estimated force Estimated mass Linear acceleration estimated disturbance is following expression:

= F – m a

can be readily measured by means of a

using an accelerometer. m may be obtained by assuming a crude approximation

passed through a

controller, resolved motion acceleration controller (RMAC), intelligent controller or others deemed suitable. It is apparent

suitable choice of H(s) needs to be obtained that cause the output to be made invariant with respect to the

such that: outer control loop control

open loop system, by first generating the world coordinate error vector, which would then be processed through a controller function, Gc(s), typically a classic P

burden in AFC is the multiplication of the estimated inertia with the angular acceleration of the

before being fed into the AFC feedforward loop. ], Mailah [11] and Pitowarno

demonstrated the effectiveness of the AFC scheme applied to rigid robot arms. Gigih et al.

robust intelligent AFC method that is capable of controlling a vehicle suspension system and

disturbances. Ga(s) KAFC F Actuator H(s) + +

robust via the compensating action of the control strategy. A more detailed description on the mathematical trea related to the derivation of important equations and stability

[10]. For brevity, the underlying a dynamic rotational system is presented with reference to Fig. 6.

A schematic diagram of an AFC scheme are as follows:

ynamic system transfer function Actuator transfer function Outer loop controller AFC constant Weighting function force force mass acceleration

is obtained by considering the

can be readily measured by means of a force

may be obtained by assuming a crude approximation or intelligent methods

passed through a weighting function give the ultimate AFC signal command to be embedded with an outer control loop. This creates a two degree

controller that could provide excellent overall system performance provided that the measurement and estimated parameters were appropriately acquired. The outer control loop can be a proportional-integral-derivative (PID) tion acceleration controller (RMAC), intelligent controller or others deemed suitable. It is apparent

needs to be obtained that be made invariant with respect to the

control is applied to the above open loop system, by first generating the world coordinate error vector, which would then be processed through a

typically a classic P

that maybe represented by Eq (15). The main computational burden in AFC is the multiplication of the estimated inertia

with the angular acceleration of the

before being fed into the AFC feedforward loop. and Pitowarno

demonstrated the effectiveness of the AFC scheme applied to . [20] have equally shown a robust intelligent AFC method that is capable of controlling a and effectively suppressing the

G(s) Disturbances m F + + + -Force Sensor Accelero meter Dynamic System Estimated Mass F*

robust via the compensating action of the control strategy. A more detailed description on the mathematical treatment related to the derivation of important equations and stability . For brevity, the underlying a dynamic rotational system is

of an AFC scheme

ynamic system transfer function

obtained by considering the

(16 force sensor and a may be obtained by assuming a

or intelligent methods function H(s) to give the ultimate AFC signal command to be embedded with an outer control loop. This creates a two degree-of-freedom controller that could provide excellent overall system performance provided that the measurement and estimated parameters were appropriately acquired. The outer control derivative (PID) tion acceleration controller (RMAC), intelligent controller or others deemed suitable. It is apparent needs to be obtained that can be made invariant with respect to the (2) is applied to the above open loop system, by first generating the world coordinate error vector, which would then be processed through a typically a classic PID controller

The main computational burden in AFC is the multiplication of the estimated inertia

with the angular acceleration of the dynamic before being fed into the AFC feedforward loop. and Pitowarno et al. [19] have demonstrated the effectiveness of the AFC scheme applied to have equally shown a robust intelligent AFC method that is capable of controlling a ffectively suppressing the

1/s2 Actual Position

AFC

a

robust via the compensating action of the control strategy. A tment related to the derivation of important equations and stability . For brevity, the underlying a dynamic rotational system is

obtained by considering the

6) a may be obtained by assuming a or intelligent methods to give the ultimate AFC signal command to be embedded with freedom controller that could provide excellent overall system performance provided that the measurement and estimated parameters were appropriately acquired. The outer control derivative (PID) tion acceleration controller (RMAC), intelligent controller or others deemed suitable. It is apparent can be made invariant with respect to the (2) is applied to the above open loop system, by first generating the world coordinate error vector, which would then be processed through a ller The main computational burden in AFC is the multiplication of the estimated inertial dynamic before being fed into the AFC feedforward loop. have demonstrated the effectiveness of the AFC scheme applied to have equally shown a robust intelligent AFC method that is capable of controlling a ffectively suppressing the

A useful point to note is that, the constant can effectively serve as a

scheme (AFC by simply setting the between value of effect of percentage this study.

IV For th MATLAB robot are Parameter ! $! #!

The applied disturbance considered in the study is a harmonic force that emulates a constant vibratory excitation with a magnitude of 40 N and frequency, 10

the following function, 40 sin 10

[image:4.612.322.534.207.343.2]

disturbance shall act as a test for the robustness of the system performance via observation of the response obtained.

Figure 7:

For simulating th

PID plus AFC, a number of input that are related to

functions. The responses to these inputs are shown in Figs. and 9.

Actual Position

A useful point to note is that, the constant effectively serve as a

scheme (AFC – OFF) or PID plus AFC method (AFC by simply setting the K

between value of KAFC can also be experimented to show the

effect of percentage KAFC

this study.

IV. SIMULATION

For the proposed simulation study of the MATLAB and Simulink was used

[image:4.612.326.534.438.553.2]

are shown in Table

Table I: Parameters of micro robot arameter Value

?7P ?70Q

! ?7.

! ?7> RS

! ?7?0_{T >?}

The applied disturbance considered in the study is a harmonic force that emulates a constant vibratory excitation with a magnitude of 40 N and frequency, 10

the following function, 40 sin 10

disturbance shall act as a test for the robustness of the system performance via observation of the response obtained.

The applied harmonic

For simulating the proposed control schemes, i.e., PID and PID plus AFC, a number of input

related to step, sinusoidal and

functions. The responses to these inputs are shown in Figs. A useful point to note is that, the constant

effectively serve as a mode switch between the PID only OFF) or PID plus AFC method (AFC

KAFC to 0 or 1 respectively.

can also be experimented to show the

AFC which however is not covered in

IMULATION RESULTS AND

e proposed simulation study of the Simulink was used. The

shown in Table I.

arameters of micro robot alue Parameter

P 0Q U . 2 ++ S V + m

The applied disturbance considered in the study is a harmonic force that emulates a constant vibratory excitation with a magnitude of 40 N and frequency, 10 rad/s

the following function, 40 sin 10t as shown in Fig. disturbance shall act as a test for the robustness of the system performance via observation of the response obtained.

harmonic disturbance considered in the study

e proposed control schemes, i.e., PID and PID plus AFC, a number of input sources

, sinusoidal and

functions. The responses to these inputs are shown in Figs.

(a)

A useful point to note is that, the constant KAFC in Fig. 6

switch between the PID only OFF) or PID plus AFC method (AFC

to 0 or 1 respectively. can also be experimented to show the

which however is not covered in

ESULTS AND DISCUSSION

e proposed simulation study of the

The parameters of micro

arameters of micro robot arameter Value

>??? ₊WX ?7?YZQ

>? + /??[ \ ] ^_ +_[\ ?7>Q WX

The applied disturbance considered in the study is a harmonic force that emulates a constant vibratory excitation with a rad/s, i.e., according to as shown in Fig. disturbance shall act as a test for the robustness of the system performance via observation of the response obtained.

disturbance considered in the

e proposed control schemes, i.e., PID and sources were considered , sinusoidal and square wave functions. The responses to these inputs are shown in Figs.

in Fig. 6 switch between the PID only OFF) or PID plus AFC method (AFC – ON) to 0 or 1 respectively. The in can also be experimented to show the which however is not covered in

ISCUSSION

e proposed simulation study of the system, parameters of micro

alue WX +! ?YZQ T + \ +! [\ WX

The applied disturbance considered in the study is a harmonic force that emulates a constant vibratory excitation with a , i.e., according to as shown in Fig. 7. The disturbance shall act as a test for the robustness of the system performance via observation of the response obtained.

disturbance considered in the

[image:4.612.329.553.635.732.2]

(5)

[image:5.612.74.298.47.274.2] [image:5.612.74.300.322.664.2]

Figure

Figure plus

From perform the responses to Figure 8: Effect of

for PID controller only (AFC

Figure 9: Effect of harmonic force on the p plus AFC scheme

From Fig. 8, it can be seen that the perform the trajectory tracking task the responses to converge to the reference

(b)

(c)

Effect of harmonic disturbance on system response for PID controller only (AFC

conditions

(a)

(b)

(c)

Effect of harmonic force on the p AFC scheme (AFC – ON)

it can be seen that the the trajectory tracking task

converge to the reference (b)

(c)

disturbance on system response for PID controller only (AFC – OFF) for various input

conditions

(a)

(b)

(c)

Effect of harmonic force on the performance of ON) for various input conditions it can be seen that the PID controller is able to the trajectory tracking task satisfactorily by bringing

converge to the reference positions

disturbance on system response OFF) for various input

erformance of PID for various input conditions

PID controller is able to satisfactorily by bringing positions but at the disturbance on system response

PID for various input conditions PID controller is able to satisfactorily by bringing at the

expense of relatively large track ripples or oscillation

disturbance (vibratory) shown through the

clearly demonstrated that the PID

ON) manages to accurately and readily track the desired responses. This shows that the latter system is much more robust than its counterpart

disturbance at relatively high frequency pneumatically actuated micro

effectively

with the given loading and operating

In this study a pneumatic worm modelled

the PID incorporated with the AFC was employed to ensure an accurate

under the presence of operating environment tuned using the typical achieve satisfactory performance the proposed schemes

of the closed

with AFC method (AFC

the rigorous study on sensitivity analysis related to the effects of other loading and operating conditions. The possibility of performing practical

system should

The authors would like to thank the Universiti Teknologi Malaysia (UTM) for their continuous support in the research work.

[1] S. Aoshima et al.,

mobility in a thin tube.

270-278. [2] T. Idogaki et al.,

for an in

Micro Machine and Human Sciences. pp. [3] T. Matsumoto

mobile machine with piezoelectric driving force actuator.

IEEE 5th Int. Symp. Micro Machine and Human Sciences. pp. 47 [4] T. Fukuda

magnetostrictive alloy (GMA) applications to micro mobile robot as a micro actuator without power supply cables.

Workshop Micro Electro Mechanical Systems (MEMS). pp. 210 [5] Suzumori, K. and Abe T.,

pipeline inspection robots.

Int. Symp. Robotics and Manufacturing Systems. pp. 515 [6] M. Takahashi,

in-pipe microrobot applying the motion of an earthworm.

5th Int. Symp. Micro Machine and Human Sciences. pp. 35 [7] S. Iwashita

in-pipe operation micro robots.

Machine and Human Sciences. pp. 41 [8] Lim, J.,

line based inchworm

2008, Mechatronics, pp. 315

[9] A. Manuello Bertetto and M. Ruggiu,

flexible robot.

Conference on Advanced Intelligent Mechatronics. pp. 1226 [10] J.R. Hewit, J.S. Burdess, Fast

Robotics using Active Force Control

Theory, 16(5), 1981, pp. 535 expense of relatively large track

ripples or oscillation, largely due to the nature of the applied disturbance (vibratory).

shown through the second set of graphs clearly demonstrated that the PID

manages to accurately and readily track the desired responses. This shows that the latter system is much more robust than its counterpart

disturbance at relatively high frequency ically actuated micro

effectively based on the

with the given loading and operating V.

In this study a pneumatic worm

and simulated. A hybrid control strategy including the PID incorporated with the AFC was employed to ensure an accurate and robust trajectory trac

under the presence of

operating environment. The PID using the typical

achieve satisfactory performance

the proposed schemes clearly demonstrated the effectiveness closed-loop control algorithm

with AFC method (AFC

the rigorous study on sensitivity analysis related to the effects of other loading and operating conditions. The possibility of performing practical experimenta

system should also be explored and investigated.

VI. A

S. Aoshima et al., A miniature mobile robot using piezo vibration mobility in a thin tube.

278.

T. Idogaki et al.,Characteristics of piezoelectric locomotive mechanism for an in-pipe micro inspection machine.,

Micro Machine and Human Sciences. pp. Matsumoto, H. Okamoto, and M. Asano

IEEE 5th Int. Symp. Micro Machine and Human Sciences. pp. 47 T. Fukuda, H. Hosokai, H. Ohyama, H. Hashimoto,

Workshop Micro Electro Mechanical Systems (MEMS). pp. 210 Suzumori, K. and Abe T.,

pipeline inspection robots.

Int. Symp. Robotics and Manufacturing Systems. pp. 515 Takahashi, I. Hayashi,

pipe microrobot applying the motion of an earthworm.

5th Int. Symp. Micro Machine and Human Sciences. pp. 35 Iwashita, I. Hayashi, N.

pipe operation micro robots.

Machine and Human Sciences. pp. 41 Lim, J., Park, H., An, J.,

line based inchworm-like micro robot for half

2008, Mechatronics, pp. 315

A. Manuello Bertetto and M. Ruggiu,

flexible robot. Como, Italy

Conference on Advanced Intelligent Mechatronics. pp. 1226 J.R. Hewit, J.S. Burdess, Fast

botics using Active Force Control

Theory, 16(5), 1981, pp. 535

expense of relatively large tracking errors

, largely due to the nature of the applied . This is in stark contrast

second set of graphs

clearly demonstrated that the PID with AFC scheme manages to accurately and readily track the desired responses. This shows that the latter system is much more robust than its counterpart in compensating the harmonic disturbance at relatively high frequency

ically actuated micro robot is able to operate based on the closed-loop control

with the given loading and operating conditions. . CONCLUSION

In this study a pneumatic

worm-and simulated. A hybrid control strategy including the PID incorporated with the AFC was employed to ensure trajectory tracking of the robot system under the presence of the prescribed

. The PID controller was using the typical Ziegler-Nichols

achieve satisfactory performance. The simulation results clearly demonstrated the effectiveness ontrol algorithms, particularly th with AFC method (AFC – ON). Future works

the rigorous study on sensitivity analysis related to the effects of other loading and operating conditions. The possibility of experimentation on the micro robot also be explored and investigated.

ACKNOWLEDGEMENT

REFERENCES

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controller was

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s, particularly th . Future works may include the rigorous study on sensitivity analysis related to the effects of other loading and operating conditions. The possibility of tion on the micro robot also be explored and investigated.

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