Path following of unmanned surface vessel under effect of position measurement noise

Science & Technology Development Journal – Engineering and Technology, 2(SI1):SI38-SI48
Open Access Full Text Article Research Article
Ho Chi Minh city University of
Technology, VNU-HCM
Correspondence
Tran Ngoc Huy, Ho Chi Minh city
University of Technology, VNU-HCM
Email: tnhuy@hcmut.edu.vn
History
 Received: 15-1-2018
 Accepted: 19-12-2018
 Published: xx-12-2019
DOI :10.32508/stdjet.v3iSI1.721 
Copyright
© VNU-HCM Press. This is an open-
access article distributed under the
terms of the Creative Commons
Attribution 4.0 International license.
Path following of unmanned surface vessel under effect of
positionmeasurement noise
Tran Ngoc Huy*, PhamNguyen Nhut Thanh
Use your smartphone to scan this
QR code and download this article
ABSTRACT
A manipulation system for unmanned surface vessels (USVs) as well as other unmanned vehicles
and autonomous vehicles are commonly built up by three vital components which are guidance
system, navigation system and control system, regardless of the mechanical aspects. In which, the
navigation system will first use sensors to measure and estimate parameters, then feedback to the
guidance system and the control system as input data. Based on those data and assignments from
user, the guidance system calculates and outputs reference data for the control system. The con-
trol system will drive the vessel according to the reference data from guidance system to achieve
those assignments. However, the process of measuring and estimating, in fact, is always affected
by disturbances which cause input error for guidance system. Consequently, the reference data
provided by the guidance system will be skewed and confused the control system, thereby reduc-
ing the quality of control and may cause instability for the whole system. This paper examines the
problem of controlling an unmanned surface vessel following straight paths created by the way-
points which given by user. To solve the path-following for straight line problem, the paper will
build a guidance system using the Line of Sight (LOS) method with lookahead distance and design
a controller using Backstepping algorithm. In addition, this paper will also study, analyze and pro-
pose amethod to reduce the influence of positionmeasurement noise to the process of calculating
the reference data of guidance system. Thereby, the quality of the built system will be guaranteed
when operating under the influence of measurement noise. The results of the proposed method
will be shown through simulation on MATLAB/SIMULINK software. These simulation results will
demonstrate the effectiveness and feasibility of the proposed method.
Key words: USV, Path-Following, Line of sight (LOS), Backstepping, Sliding mode
INTRODUCTION
In the age of technological explosion, automatic, un-
manned and other intelligent devices are more and
more widely researched and developed at a fast pace
and easily applied to practice. This has created a lot of
premises for people to explore the world and find new
resources, especially the water environment which
covers more than 70% of the earth’s surface. Hence,
we have to use robots in those situations where hu-
mans cannot discover by themselves. As a result, au-
tonomous or unmanned devices working on the wa-
ter’s surface and underwater are being considered and
developed strongly.
The first unmanned surface vessel (USV) Autocat of
MIT published in 2000 for the hydrographic sur-
vey at Boston Harbor had begun a robust develop-
ment process for many unmanned surface vehicles
which used to survey the water environment, such
as USV SESAMO of Italy, USV ROAZ of Portugal,
USV Springer of the University of Plymouth. Besides,
there were also many USVs that had been studied
for military purposes such as USV KATANA of Is-
rael, USV Protector Rafael of the United States. In the
field of civil purposes, there was the autonomous sur-
face vessel (ASV) C-Worker 12P used for transport or
ASVWaste Shark used to clean up the trash on rivers,
lakes, etc. Such applications of those types of un-
manned surface vessel are described in 1,2 , and3. At
the same time, underwater vehicles have also grown
at a dramatic rate. People nowadays tend to incor-
porate USV, autonomous underwater vehicle (AUV),
remotely operated vehicle (ROV) into a more com-
plete system for various purposes. Some applications,
as well as underwater vehicles, are described in 4–7.
In this paper, we will consider the problem of con-
structing a system for an unmanned surface vessel so
that it can follow a straight path formed by the given
waypoints. In addition, we will also consider the ef-
fect of position measurement noise on the system. A
USV as well as any other unmanned vehicles, in or-
der to follow a trajectory, cannot lack the guidance
and control system as described in8. Hence, this pa-
per will present how to build a guidance system us-
Cite this article : Huy T N, Th ... e+eye
4
!2 : 14 > 0
Implied f (M)  yd  f (M). Noted that f(0)=0 so
f(M)>0>f(-M). We have:
tan(j f (M)j) tan(j f (M)j)
= tan(j f (M)j) tan( f (M))
=
ye+M
4 
ye
4
1+ ye4

ye+M
4
  ye4 yeM4
1+ ye4

yeM
4

= 2yeM24
[42+ye](ye+M)[42+ye(yeM)]
And tan(.) is a covariance function so:
Max
yd=
(
f (M); ye  0
 f (M); ye > 0 (16)
Expanding (16) we can get:
Max
yd= arc tan( jyej4 )arc tan( jyejM4 ) (17)
Next, we consider Max
yd = g(4) with D > 0 and
find the value of D so that g(D) is minimum. Unluck-
ily, those value does not exist. Hence, we will find the
value ofD so thatMax
yd=Pwith P is a value given
by user. P can be interpreted as themaximum allowed
angular error. We have:
Max
yd= P
) tan(Max
yd= P) tanP
, M442+jyej(jyejM)  tanP (18)
Solve (18) we get:8>:
441; jyej M
442; 441; M < jyej  yz
84; jyej> yz
(19)
with8>>>:
41 = MtanP +
q M
tanP

24 jyej(jyejM)
42 = MtanP 
q M
tanP

24 jyej(jyejM)
yz = M2 (1+
1
sinP )
(20)
Becausewewant to keep the value of the desired head-
ing is a continuous function by time so D must be
countinous too. In order to reduce the complexity
when calculating D, we choose8>:
441; jyej M
441; M < jyej  yz
84; jyej> yz
(21)
SI41
Science & Technology Development Journal – Engineering and Technology, 2(SI1):SI38-SI48
METHODOLOGYOF CONTROLLER
The desired heading angle will be provided by guid-
ance and the speed assignment will be given by user,
so we can divide the problem into two control prob-
lems include speed control and heading control12,13.
Where control algorithm applied in speed controller
is Sliding mode and heading controller is Backstep-
ping Sliding Mode (BSM).
Speed controller
Because property of control input which have , we can
approximate U =
p
u2+ v2  u . Suppose the de-
sired velocity is ud , define the speed error eu = uud .
From (6), the time derivative of speed error can be de-
termined:
:
eu =
:
u :ud = (t1 c13rd11u)=m11 :ud (22)
Select the sliding surface su = eu and define the con-
trol Lyapunov functionVu = s2u=2 > 0 whose time
derivative is
:
V u= su
:
su= su

t1 c13rd11u=m11 :ud


(23)
Select the control law
t1=c13r+d11u+m11(
:
ud Kusat(su)) (24)
where Ku is positive constant. From (23) and (24) we
get
:
V u =Kusat(su)su < 0. Follow Lyapunov theory
su! 0 or eu! 0.
Heading controller
We will use Backstepping Sliding mode for design
heading controller. From (6):
:
r = f :r(u;v;r)+g:rt3
where
a :r(u;v;r)= 1m22m33m32m23 [m22c13u
+c23(m22v+m32r)
+v(d22m32d32m22)
+r(d23m32d33m22)] (25)
b :r= m22m22m33m32m23 (26)
Define the heading error ey = y  yd . The first
derivative are :ey = r :yd (27)
Step 1:
Define the first control Lyapunov function (CLF) as
V1 = e2y=2> 0
whose time derivative is
:
V 1 = ey
:
ey = ey (r :yd) (28)
Select the virtual control law
r = sy  k1ey 
:
yd (29)
From (28) and (29), the result of Step 1 becomes
sy = r+ k1ey 
:
yd (30):
V 1 =k1e2y + ey sy (31)
Step 2:
Differentiating (30) with respect to time yields
:
sy =
:
r+ k1
:
ey  ::yd = a :r(u;v;r)+b :r+k1
:
ey  ::yd
Define the second CLF
V2 =V1+ s2y=2
whose time derivative is
:
V 2 =
:
V 1+ sy
:
sy =k1e2y + sy (ey +
:
sy )
=k1e2y + sy (ey +a :r+b :rt3+k1
:
ey  ::yd)
Choose the control law
t3 = [ey + a :r+b:rt3 + k1
:
ey ::yd  k2sy 
Kssat(sy )]=b :r (32)
when the result of Step 2 is
:
V 2 =k1e2y  k2s2y Kssat(sy )sy < 0
We have
:
V 2 < 08ey so sy ! 0 and ey ! 0:
RESULTS ANDDISCUSSION
This section presents simulation results of the com-
bined system between guidance and control. To eval-
uate the results of the combined system, we will con-
sider the simulation conditions in two cases with and
without noise then bring them into comparison. As-
sume that the boundary value of measurement noise
M = 0.5 (m) and the maximum allowed angular error
is:
P=
8>:
2; jyej M
5; M  jyej  2:5 (degrees)
8; jyej> 2:5
From (21) we can choose Delta noise:
4noise =
8>:
20; jyej M
e(jyejM); M  jyej  2:5
8; jyej> 2:5
In all simulations, the desired surge velocity is chosen
as ud = 1m/s and the controller gain coefficients are
chosen as Ku = 10; k1 = 2; k2 = 15; Ks = 10: The
lookahead distances are selected in the common way
are
Delta 1: D1 = 3
Delta 2: D2 = 10
Case 1: Without noise effect
Case 2: With noise effect
The results in two cases show that the combination of
the controller and guidance is very effective, it helps
the vessel converge and stay on the desired path. Fig-
ure 4 and Figure 8 show the guidancewhich hasDelta
noise will converge on the path faster than the other
Delta. The speed assignment always satisfy through
the result in Figure 6 and Figure 10.
Because the guidance with Delta noise converges on
the path faster, it makes the trajectory longer and
needs more time to finish. However, we can see the
heading response from Figure 5 and Figure 9 where
the heading response of Delta noise has the best qual-
ity.
In case 1, themoment control input shown inFigure 7
is possible in practice for all Delta. However, in Fig-
ure 11 of case 2, only the moment control input of
SI42
Science & Technology Development Journal – Engineering and Technology, 2(SI1):SI38-SI48
Figure 4: Desired and simulation path of Delta1 (black dash-dot and red dot, respectively), Delta 2 (blue
dash) and Delta noise (green).
Figure 5: Heading responses relating to the selection ofthe lookahead distance listed as Delta 1, Delta 2 or
Delta noise.
Delta 2 and Delta noise can apply in experiment and
Delta noise has the best quality.
When the vessel reaches wp(k), the desired heading
yd and cross-track error ye will be recalculated ac-
cording to the newwaypoint wp(k+1). Hence, to eval-
uate the results of the selected Delta noise, we need
consider the process from start to reach at the first
waypoint or from t = 0 to t = 42. Through the result in
Figure 12, the selected Delta noise has helped the sys-
tem works very well and the maximum value of yd is
less than 0.6 degrees and obviously satisfies the maxi-
mumallowed angular error P. Summary the proposed
method to reduce the effect of position measurement
noise on the quality control has been verified.
CONCLUSION
In this paper, a guidance and control system for un-
manned surface vessels is developed to solve the con-
trol objective of making the vessel follow a desired
path in the presence of measurement noise which ef-
fect to guidance and quality of heading controller.
Simulation results have demonstrated the effective-
ness and feasibility of the proposedmethod. The com-
bined system helps the vessel converge on the path
SI43
Science & Technology Development Journal – Engineering and Technology, 2(SI1):SI38-SI48
Figure6: Surgevelocity responses relating to theselectionof the lookaheaddistance listedasDelta1,Delta
2 or Delta noise.
Figure 7: Moment control input relating to the selectionof the lookahead distance listed as Delta 1, Delta 2
or Delta noise.
and stay on it, besides that it still guarantee the speed
assignment in case of measurement noise.
Further works focus on applying this method even for
curve path and studying new control algorithm. Be-
side that it is possible to consider the effect of external
disturbances on the system so that simulation results
still ensure the quality when applied in practice.
ACKNOWLEDGEMENT
This research is supported by Laboratory of Advanced
Design and Manufacturing Processes and funded by
Ho Chi Minh City University of Technology, VNU-
HCM under grant number T-ĐĐT-2018-72.
CONFLICT OF INTERESTS
The author declares that this paper has no conflict of
interests.
AUTHORS’ CONTRIBUTIONS
TranNgocHuyhas developed the proposed algorithm
andwrote themanuscript. PhamNguyenNhutThanh
implemented simulation and wrote the manuscript.
SI44
Science & Technology Development Journal – Engineering and Technology, 2(SI1):SI38-SI48
Figure 8: The trajectory of the vessel relating to theselection of the lookahead distance listed as Delta 1,
Delta 2 or Delta noisewhenmeasurements have noise.
Figure 9: Heading responses relating to the selection ofthe lookahead distance listed as Delta 1, Delta 2 or
Delta noise whenmeasurementshave noise.
ABBREVIATIONS
LOS: Line of Sight
USV: Unmanned Surface Vessel
AUV: Autonomous Underwater Vehicle
ROV: Remotely Operated Vehicle
BSM: Backstepping Sliding Mode
CLF: Control Lyapunov Function
REFERENCES
1. Ferreira H, Almeida C, Martins A, Almeida J, Dias N, Dias A,
et al. Autonomous bathymetry for risk assessment with ROAZ
robotic surface vehicle. OCEANS 2009-EUROPE. 2009;p. 1–
6. Available from: https://doi.org/10.1109/OCEANSE.2009.
5278235.
2. Caccia M, Bibuli M, Bono R, Bruzzone G, Bruzzone G, Spiran-
delli E. Aluminumhull USV for coastalwater and seafloormon-
itoring. OCEANS 2009-EUROPE. 2009;p. 1–5. Available from:
https://doi.org/10.1109/OCEANSE.2009.5278309.
3. Tokekar P, Bhadauria D, Studenski A, Isler V. A robotic sys-
tem for monitoring carp in Minnesota lakes. Journal of Field
Robotics. 2010;27(6):779–789. Available from: https://doi.org/
10.1002/rob.20364.
4. Ramos P, Cruz N, Matos A, Neves M, Pereira F. Monitor-
ing an ocean outfall using an AUV,” in MTS/IEEE Oceans
2001. An Ocean Odyssey. Conference Proceedings (IEEE Cat
No01CH37295);3:2009–2014.
5. Fiorelli E, Leonard N, Bhatta P, Paley DA, Bachmayer R,
Fratantoni DM. Multi-AUV Control and Adaptive Sampling
in Monterey Bay. IEEE Journal of Oceanic Engineering.
SI45
Science & Technology Development Journal – Engineering and Technology, 2(SI1):SI38-SI48
Figure 10: Surge velocity responses relating to theselection of the lookahead distance listed as Delta 1,
Delta 2 or Delta noisewhenmeasurements have noise.
Figure 11: Moment control input relating to the selectionof the lookahead distance listed as Delta 1, Delta
2 or Delta noise whenmeasurementshave noise.
2006;31(4):935–948. Available from: https://doi.org/10.1109/
JOE.2006.880429.
6. Kim A, Eustice R. Toward AUV Survey Design for Optimal Cov-
erage and Localization Using the Cramer Rao Lower Bound.
IEEE. 2009;.
7. Encarnacao P, Pascoal A. Combined trajectory tracking and
path following: An application to the coordinated control of
autonomous marine craft. Proceedings of the 40th IEEE Con-
ference on Decision and Control. 2001;.
8. Pettersen K. Way-point tracking control of ships. Proceedings
of the 40th IEEE conference on decision & control. IEEE, Or-
lando, FL, USA. 2001;p. 940–945.
9. Fossen T. Handbook of Marine Craft Hydrodynamics and Mo-
tion Control. Wiley. 2011;Available from: https://doi.org/10.
1002/9781119994138.
10. The Society of Naval Architects and Marine Engineers.
Nomenclature for treating the motion of a submerged body
through a fluid. Technical and Research Bulletin;(1-5).
11. Bai Y, Zhao Y, Li T. The USV path following controller design.
2017 4th International Conference on Information, Cybernet-
ics and Computational Social Systems (ICCSS). 2017;Available
from: https://doi.org/10.1109/ICCSS.2017.8091500.
12. Yong L, Ren-Xiang B, Hai-Jun X. Straight-Path Tracking Con-
trol of Underactuated Ship Based on Backstepping Method.
Ninth International Conference on Frontier of Computer Sci-
ence and Technology. 2015;PMID: 25134927. Available from:
https://doi.org/10.1109/FCST.2015.24.
13. Li M, Liu C, Li T, Chen CP. New second order slidingmode con-
trol design for course-keeping control of ship with input sat-
uration. International Conference on Advanced Mechatronic
Systems (ICAMechS). 2017;Available from: https://doi.org/10.
SI46
Science & Technology Development Journal – Engineering and Technology, 2(SI1):SI38-SI48
Figure 12: The angular error between theheading anglewithnoise andwithout noise related to cross-track
error ye from t=0 to t=42(s).
1109/ICAMechS.2017.8316518.
SI47
Tạp chí Phát triển Khoa học và Công nghệ – Kĩ thuật và Công nghệ, 2(SI1):SI38-SI48
Open Access Full Text Article Bài Nghiên cứu
Trường Đại học Bách Khoa,
ĐHQG-HCM
Liên hệ
Trần Ngọc Huy, Trường Đại học Bách Khoa,
ĐHQG-HCM
Email: tnhuy@hcmut.edu.vn
Lịch sử
 Ngày nhận: 15-10-2018
 Ngày chấp nhận: 19-12-2018
 Ngày đăng: 13-12-2019
DOI : 10.32508/stdjet.v3iSI1.721
Bản quyền
© ĐHQG Tp.HCM. Đây là bài báo công bố
mở được phát hành theo các điều khoản của
the Creative Commons Attribution 4.0
International license.
Bám đường cho phương tiện tàu tự hành dưới sự ảnh hưởng của
nhiễu đo lường vị trí
Trần Ngọc Huy*, PhạmNguyễn Nhựt Thanh
Use your smartphone to scan this
QR code and download this article
TÓM TẮT
Một hệ thống vận hành cho tàu không người lái trên mặt nước (USV) nói chung cũng như các
phương tiện không người lái và tàu tự hành nói riêng thường được xây dựng bởi ba thành phần
chính là hệ thống dẫn đường, hệ thống định vị và hệ thống điều khiển. Trong đó bộ định vị sẽ
dùng các cảm biến để đo đạc và ước lược các thông số để cung cấp các giá trị đầu vào cho bộ dẫn
đường và bộ điều khiển. Dựa trên các dữ liệu nhận được từ bộ định vị và các chỉ tiêu mà người
dùng đề ra, bộ dẫn đường sẽ tính toán và xuất dữ liệu tham chiếu đầu vào cho bộ điều khiển. Bộ
điều khiển sẽ lái phương tiện theo các dữ liệu tham chiếu được cung cấp từ bộ dẫn đường để đạt
được các chỉ tiêu đã đề ra. Tuy nhiên, trong thực tế việc đo đạc và ước lượng thường bị ảnh hưởng
bởi nhiễu gây ra sai số đầu vào cho bộ dẫn đường. Điều này dẫn đến dữ liệu mà bộ dẫn đường
tính toán sẽ có sai lệch và gây rối loạn bộ điều khiển, từ đó làm giảm chất lượng điều khiển cũng
như có thể dẫn đến mất ổn định cho toàn hệ thống. Trong bài viết này ta sẽ xét bài toán điều
khiển một tàu không người lái trên mặt nước bám theo quỹ đạo thẳng do các điểm waypoint cho
trước tạo thành. Để giải quyết bài toán bám đường thẳng này, bài viết sẽ sử dụng phương pháp
Line of sight (LOS) để thiết kế bộ dẫn đường và giải thuật Backstepping sliding mode cho việc xây
dựng bộ điều khiển. Đồng thời nghiên cứu, phân tích và đề xuất một phương pháp nhằm giảm
ảnh hưởng của nhiễu đo lường đến quá trình tính toán giá trị tham chiếu của bộ dẫn đường. Từ
đó chất lượng của hệ thống đã xây dựng sẽ được đảm bảo khi hoạt động dưới tác động của nhiễu
đo lường. Kết quả cũng quả của phương pháp đề xuất sẽ được trình bày qua mô phỏng trên phần
mềmMATLAB/SIMULINK. Các kết quả này sẽ minh chứng cho tính hiệu quả và khả thi của phương
pháp đề xuất.
Từ khoá: Thuyền tự hành, Điều khiển bám quỹ đạo, Line of sight (LOS), Điều khiển trượt, Điều
khiển cuốn chiếu
Trích dẫn bài báo này: Huy T N, Thanh P N N. Bám đường cho phương tiện tàu tự hành dưới sự ảnh
hưởng của nhiễu đo lường vị trí. Sci. Tech. Dev. J. - Eng. Tech.; 2(SI1):SI38-SI48.
SI48