Content uploaded by Erna Apriliani
Author content
All content in this area was uploaded by Erna Apriliani on Sep 09, 2016
Content may be subject to copyright.
Int’l Conf. on Advanced Mechatronics, Intelligent Manufacture, and Industrial Automation 2015 (ICAMIMIA 2015)
Surabaya, Indonesia, on October 15-17, 2015
Estimate and Control Position Autonomous
Underwater Vehicle Based on Determined Trajectory
using Fuzzy Kalman Filter Method
1Zunif Ermayanti
Mathematics Department of
Institut Teknologi Sepuluh
Nopember,
Surabaya, Indonesia
Zunif.e@gmail.com
2Erna Apriliani
Mathematics Department of
Institut Teknologi Sepuluh
Nopember,
Surabaya, Indonesia
april@matematika.its.ac.id
3Hendro Nurhadi*
Mechanical Engineering of
Institut Teknologi Sepuluh
Nopember,
Surabaya, Indonesia
hdnurhadi@me.its.ac.id
*Corresponding Author,
IEEE Member
4Teguh Herlambang
Post Graduate Program in
Marine Technologi of Institut
Teknologi Sepuluh Nopember,
Surabaya, Indonesia
teguh@unusa.ac.id
Abstract— Unmanned Underwater Vehicle (UUV), known
as underwater drones, are any vehicle that are able to operate
underwater without human occupant. AUV (Autonomous
Underwater Vehicle) are one of categories of these vehicles which
operate independently of direct human input. This AUV is
required to have a navigation system that can manoeuvred 6
Degree of Freedom (DOF) and able to estimate the exact position
based on the determined trajectory. Fuzzy Kalman Filter (FKF)
method is used to estimate the position of the AUV. This process is
used to maintain the accuracy of the trajectory. The performance
of FKF algorithm on some several trajectory cases show that this
method has relatively small Root Means Square Error (RSME),
which is less than 10%.
Keywords— AUV, estimation, Fuzzy Kalman Filter
I. INTRODUCTION
Unmanned Underwater Vehicle (UUV) are any
vehicle that are able to operate underwater without human
occupant. These vehicles are divided into two, there are Remote
Operational Vehicle (ROV), which is operated by remote
control, and Autonomous Underwater Vehicle (AUV), which is
a machine in the water that operate independently by direct
human input [1]. AUV is now quite widely used for several
purposes in many fields, i.e. science, environment, marine
industry, military, national defense and security. In archipelago
country, such as Indonesia, which has widely ocean area, this
AUV can be used as a surveillance tool to see untouched
underwater conditions and can supervise the defense or border
areas in the territory of the Republic of Indonesia. In addition,
the AUV can also be used to see and find out the state of the sea
bottom, i.e. conditions and natural resources in the sea,
geological sampling, inspection of underwater structures, and
construction and maintenance of underwater structures.
A research which has been conducted on the AUV are
investigate the estimation on the AUV by using Ensemble
Kalman Filter [2]. That research estimate some translational
motion, i.e. surging, swaying, and heaving. However, general
forces, such as drag force and lift force, on AUV aren’t taken
into account in detail. The next research is conducted by [1]
with the same topic and method, the difference is those research
also calculate the drag and lift forces of the AUV. A research
which use Fuzzy Kalman Filter method to solve the problem is
the research which is conducted by Mahmuri, H (2011) about
the estimation of the cancer cells development by using Fuzzy
Kalman method [3].
Due to its importance and previous researches, this
research will be further developed on the estimated position and
control on AUV by using all existing motion on AUV, there are
6 DOF (Degree of Freedom) both translational and rotational
motion, whereas the method used is Fuzzy Kalman Filter.
In this research, we use Fuzzy Kalman Filter as our
method because FKF can be used for any parameter variations.
In addition, the merger between Fuzzy and Kalman Filter is
occurred because the Fuzzy system can be used for anything
inappropriate and ambiguous.
The goal of this research is to get the estimated
position of the AUV in accordance to the determined trajectory
with a relatively small error.
II. AUV MODELS
Two important things to note for analyzing AUV are
Earth Fixed Frame (EFF) and Body Fixed Frame (BFF) [4].
EFF is used to describe the position and orientation of the AUV
with the position of the x-axis direct to the north, the y-axis to
the east, and the z-axis toward the center of the Earth. While,
BFF is used to describe the speed and acceleration of the AUV
with the starting point at the center of gravity.
Motion of AUV have 6 DOF (Degree of Freedom)
where 3 DOF for translation motion and 3 DOF for rotational
motion in point x, y, and z. General equation of motion consists
of 3 equations for translational motion and 3 motions for
rotational motion. The general equation of motion translation
and rotation are surge, sway, and heave as motion translation
and roll, pitch, and yaw as rotation [4].
156
Int’l Conf. on Advanced Mechatronics, Intelligent Manufacture, and Industrial Automation 2015 (ICAMIMIA 2015)
Surabaya, Indonesia, on October 15-17, 2015
Position and Angle Euler
Linear and Angular Velocity
Force and Moment
TABLE 1. AUV COORDINATE
DOF
Note
Force/
Moment
Velocity
Position
1
Surge
2
Sway
3
Heave
4
Roll
5
Pitch
6
Yaw
There for the AUV models can be written as follows:
Surge
(1)
Sway
(2)
Heave
(3)
Roll
(4)
Pitch
(5)
Yaw
(6)
III.RESULT AND DISCUSSION
This chapter describes the settlement of AUV models
which are used to estimate the position and determine trajectory
that may be taken by the AUV. Further, we will estimate
position of the AUV motion due to the AUV's determined
trajectory using Fuzzy Kalman Filter method. Furthermore,
based on the results of the estimation, we conduct a control on
the AUV system in order to keep AUV moves at the determined
trajectory.
A. AUV Models Solution
Based on the AUV model on Equation 1-6, those equations
can be built on matric as follows:
(7)
Or can be written as:
(8)
Fig 1. Six Degree of Freedom AUV
157
Int’l Conf. on Advanced Mechatronics, Intelligent Manufacture, and Industrial Automation 2015 (ICAMIMIA 2015)
Surabaya, Indonesia, on October 15-17, 2015
where
E=
(9)
and
(10)
(11)
(12)
(13)
(14)
(15)
B. Linearization
Model of AUV is a non-linear model, therefore, this
model will be converted into common forms as:
(16)
Where c is control.
Equation 8 will be formed into the Equation 16 by means of a
function F in Jacobi to the speed and control.
So we get Equation 17 and 18 :
Jacobi to the speed
(17)
Jacobi to control
(18)
Therefore, we obtained matrices A and B as follows:
(19)
(20)
C. Discretization Model
AUV equation of motion should be changed into the
form of discretization because FKF algorithm can only be
implemented on discrete system. To be able to use different
discretization forward, namely:
(21)
Discretization Equation 9 is obtained generally as follows:
(22)
(23)
(24)
D. Fuzzy Kalman Filter Implementation
1. Fuzzification
Fuzzification is a process that converts input from crisp shape
(firmly) into the form of fuzzy (linguistic variables) that are
usually presented in the form of fuzzy set.
158
Int’l Conf. on Advanced Mechatronics, Intelligent Manufacture, and Industrial Automation 2015 (ICAMIMIA 2015)
Surabaya, Indonesia, on October 15-17, 2015
TABLE 2. INITIALIZATION
Symbol
Note
Initialization
Minimum surge speed
0
Maximum surge speed
1
Minimum yaw speed
0
Maximum yaw speed
1
Minimum Surge
(25)
Maximum Surge
(26)
For more motion performed in the same way
2. Determining the Basic Rules
Basic rules are determined from a combination of the
maximum and minimum as many as where is the number
of models or variables. So that the equation of the AUV motion
with 6 DOF had 6 models or variables. The possibilities that
may occur are (see Table 3). By using the basic rules
in general, namely:
Rule: if is then
Thus fuzzy basic rules which are obtained are as follows: the
ground rules are numbering 64 fuzzy logic rules where the
value
, which will be estimated by using the
Kalman Filter method [5].
System and measurement model
xk + 1 = Ai x+Bu + wk (27)
zk = Hx+ vk. (28)
Initial condition
Time Update
(29)
(30)
Measurement Update
Kalman Gain :
(31)
Update estimation :
(32)
Update Covarian Error :
(33)
TABLE 3. DETERMINING THE BASIC RULES
u
v
w
p
Q
R
output
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
Defuzzification
After the basic rules that are applied to the Kalman Filter
have been obtained, we gain 64 estimations at each step as
below:
(34)
Fuzzification process is done by:
(35)
Where:
(36)
(37)
E. Control position
In correction step, we get the result of position
estimation from the AUV motion. Further, based on the
estimated value, we will conduct the system control by
changing the steering angle of the motion. In general overview,
to determine the steering angle based on the results of the
estimation is given as follows [3]:
In the initial position, we assume the position of
AUV is at the point , further the AUV move in the
position when the AUV should be at determined
trajectory which at the point so that the value of α
which is the steering angle obtained by:
(38)
Fig.2 Control Position
159
Int’l Conf. on Advanced Mechatronics, Intelligent Manufacture, and Industrial Automation 2015 (ICAMIMIA 2015)
Surabaya, Indonesia, on October 15-17, 2015
(39)
F. Result and Simulation
Simulations carried out by applying the Fuzzy Kalman
Filter algorithm in motion dynamics model of AUV. The
simulation will be presented in two-dimensional graph that
describes the position on AUV. The simulation results of this
research will be compared between the trajectories determined
by the results of the estimation using the Fuzzy Kalman Filter
Method. In each case to the estimated position, the changes that
exist in every movement AUV in the form into the
coordinates,, and . by way of [6]:
(40)
(41)
(42)
(43)
Part of this simulation will show the performance of Fuzzy
Kalman Filter. In this study used a model error is 10 % of the
initial conditions. For each case there is provided a
measurement system at 4 motions i.e. surge, sway, heave, and
yaw. At this simulation given its initial velocity i.e.
= 1.5
, = 1.5
, = 1.5
, = 0
, = 0
, =
0
.
The initial angle and so that the point
corresponding to the trajectory and the value of the time change
. The number of experimental results of running as
many as 30 times.
Fig.3 Case 1
Fig.3 Case 1
Fig.5 Case 3
Fig.5 Case 3
Fig.4 Case 2
Fig.4 Case 2
Fig.6 Case 4
Fig.6 Case 4
160
Int’l Conf. on Advanced Mechatronics, Intelligent Manufacture, and Industrial Automation 2015 (ICAMIMIA 2015)
Surabaya, Indonesia, on October 15-17, 2015
TABLE 4. RMSE
POSITION
CASE 1
CASE 2
CASE 3
CASE 4
X
0.02192
0.06361
0.015666
0.011044
Y
0.0368
0.000805
-
-
Z
-
-
0.004019
0.022705
Angle
0.00096
0.00115
0.001165
0.005212
Time
0.782187
0.8982
0.80199
0.9228
From the case above, we can conclude that FKF can
work better to estimate the position of the determined
trajectory. However, the time required by every case depends
on the complexity of the trajectory. This condition occurs
because the speed of six DOF on AUV is varying depend on its
trajectory. RSME on the X axis is greater if the trajectory is
made on the XY dimension than on the XZ dimension. As for
the Y axis, the straight trajectory has greater error than the
curved trajectory because the distance of the straight trajectory
farther than the curved. However, on the Z axis or diving
trajectory, RMSE on the trajectory which has more curve is
greater than the RMSE on the trajectory with less curve.
Therefore, the angle RMSE on the Case 4 is greater than others.
IV. CONCLUSION
Fuzzy Kalman Filter and Kalman Filter methods can
be used to estimate the position of AUV with the desired
trajectory. Due to the parameter measurements, i.e. in motion
surge, sway, heave, and yaw, each position has relatively small
RMSE. In other words, this estimation method can be applied
to translational and rotational motion on AUV.
V. CONTRIBUTION OF THIS WORK
This research is one of our contribution as a tool to
support for the next research on AUV field in science,
environment, marine industry, military, and national defense
purposes.
REFERENCES
[1] Hendro Nurhadi, Subchan, Gustiyadi FR, Design of Position Estimation
Algorithm of Navigation and Trajectory System for Unmanned Underwater
Vehicle ITS AUV-01 using Ensemble Kalman Filter (ENKF) Method, 13th
Seminar on Intelligent Technology and Its Applications (SITIA 2012),
Surabaya, 23 May 2012.
[2] Fitria, Risa.2011.Implementation Ensemble Kalman Filter on estimates
Speed of the submarine. Institute Teknologi Sepuluh Nopember,. Surabaya
[3] Mahmuri, H. (2011), Estimates spread of cancer cells
by using fuzzy Kalman Filter, Department Mathematics,Intitute Sepuluh
Nopember, Surabaya.
[4] Yang, C.(2007), Modular Modeling and Control for Autonomous
Underwater Vehicle (AUV), Department of Mechanical Engineering
National University of Singapore, Singapore.
[5] [Chen, G.(1997), “Fuzzy Kalman Filtering “, Department of Electrical and
Computer Engineering University of Houston, Houston.
[6] Ataei,M.Koma,A.Y(2014), “Three-dimensional optimal Path planning
For waypoint guidance of an autonomous Underwater vehicle “, Center of
Advanced System and Technologies, Faculty of Mechanical Engineering,
College of Engineering, University of Tehran, Iran.
[7] Nurhadi,H. (2011).”Rule Based Positioning Optimization for High –
Precision LPAT”, IEEE Transactions on Instrumental and Measurement,
Volume 60, Issue 10, on Page: 3411-3443.
161
