Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 Modelling, Simulation and Control of Underwater Vehicles Mô hình hóa, mô phỏng và điều khiển phương tiện ngầm Hung Duc Nguyen, Riaan Pienaar, Dev Ranmuthugala and William West University of Tasmania / Australian Maritime College e-Mail: nguyenhd@amc.edu.au Abstract Underwater vehicles have been developed over many decades for exploration of seabed, discovery and exploitation of marine resources. Maintaining control of underwater vehicles for various missions at seas requires a good understanding of the underwater vehicle hydrodynamics and control characteristics. In order to get students involved in the development of control systems for underwater vehicles it is necessary to have a working underwater vehicle with a fully- functioned controller to do design and implement missions. This paper presents the modelling, simulation and control of a newly-built underwater vehicle for academic and research purposes. A series of small underwater vehicles have been designed and built at the Australian Maritime College (University of Tasmania) within the maritime engineering course final year programmes. This includes the development of mathematical models of these small underwater vehicles for simulation and control design purposes. This paper focuses on theoretical modelling, simulation, control design and testings of the AMC newly-built ROV/AUV. Tóm tắt: Phương tiện ngầm đã được phát triển qua nhiều thập niên dùng cho nhiều mục đích khác nhau như thám hiểm đáy đại dương, thăm dò và khai thác tài nguyên biển. Điều khiển duy trì phương tiện ngầm làm các nhiệm vụ khác nhau trên biển đòi hỏi cần phải hiểu rõ thủy động lực học và đặc tính điều khiển của phương tiện ngầm. Nhằm để cho sinh viên phát triển hệ thống điều khiển cho phương tiện ngầm cần phải có một mô hình phương tiện ngầm hoạt động được với một bộ điều khiển đầy đủ chức năng để thiết kế và thực hiện nhiệm vụ. Bài báo này trình bày mô hình hóa, mô phỏng và điều khiển một phương tiện ngầm mới đóng để dùng cho mục đích giảng dạy và nghiên cứu. Tại AMC (Đại học Tasmania) sinh viên thiết kế và đóng một số phương tiện ngầm loại nhỏ trong các chương trình cuối năm của khóa học công nghệ hàng hải. Bài báo này bao gồm cả việc phát triển mô hình toán của các phương tiện ngầm lọai nhỏ này dùng cho mục đích mô phỏng và thiết kế điều khiển. Bài báo này tập trung vào mô hình hóa lý thuyết, mô phỏng, thiết kế điều khiển và tthử nghiệm phương tiện ngầm mới đóng của AMC. Nomenclature Symbol Unit Meaning ν T u,v,w,p,q,rν η T n,e,d, , , η Abbreviation DOF Degree of freedom ROV Remotely operated vehicle AUV Autonomous underwater vehicle HIL Hardware in the loop AMC Australian Maritime College UTAS University of Tasmania HAIN Hydroacoustic aided inertial navigation 1. Introduction Underwater vehicles require mathematical models to describe behaviour and dynamics. Modelling underwater vehicles usually has two aspects: one is theoretical modelling and the other physical testing. Around the world there are many institutes developing underwater vehicles for various purposes. AMC has developed a series of ROVs/AUVs for academic uses. The goal is to build a virtual lab (a HIL simulation program) of ROVs/AUVs that interacts CFD software with a simulation program. A virtual ROV/AUV will be controlled by a joystick managed through an appropriate simulation program. Possible applications of ROVs/AUVs are: observe seabed conditions; observe marine farms; conduct underwater seismic survey for discovery of oil and gas and exploitation of marine resources; and surveillance operation. As the first step to realize such a virtual lab for ROVs/AUVs, it is necessary to develop mathematical models for vehicles. The main purpose of this paper is to: describe the AMC ROV/AUV; model the ROV/AUV using relevant theory; simulate the ROV/AUV; design a controller for the ROV/AUV preliminarily; and design captive test for the estimation of the hydrodynamic coefficients and validation of the assumed model. The paper is organized as follows: Section 1 introduction, Section 2 reference frames and 150 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 equations of kinematics and kinetics, Section 3 brief description of the AMC ROV/AUV, Section 4 control algorithms and design of experiments, Section 5 model scaled experiments and Section 6 conclusions. Additional information is given in Appendix. 2. Reference Frames and Equations Two reference frames for underwater vehicles are shown in Fig. 1. NED is the earth-fixed reference frame and XYZ is the body-fixed reference frame. Fig. 1 Reference frames for underwater vehicles 2.1 Kinematics Referring to Fig. 1 the 6-DOF kinematic equations in the NED (north-east-down) reference frame in the vector form are [3][4], η J η ν (1) where n b 3 3 33 R Θ0 J η 0TΘ (2) with 33 Sη and 3 ν . The angle rotation matrix n 3 3 b R Θ is defined in terms of the principal rotations, x, 1 0 0 0 c s 0 s c R , y, c 0 s 0 1 0 s 0 c R and z, c s 0 s c 0 0 0 1 R (3) where s =sin(.), c = cos(.) using the zyx-convention, n b z, y, x, : R Θ R R R (4) or n b c c s c c s s s s c c s s c c c s s s c s s s c s c s c c R Θ (5) The inverse transformation satisfies, 1 n b T T T b n x, y, z, R Θ R Θ R R R (6) The Euler angle attitude transformation matrix is: 1 s t c t 0 c s 0 s /c c /c T Θ 1 1 0 s 0 c c s 0 s c c T Θ o 90 (7) It should be noted that T Θ is undefined for a pitch angle of o 90 and that 1T T Θ T Θ . 2.2 Kinetics The 6-DOF kinetic equations in the body-fixed reference frame in the vector form [3] are therefore, 0 wind wave Mν C ν ν D ν ν g η g τ τ τ (8) where M = M RB +M A : system inertia matrix (including added mass) C ν = RB A C ν C ν : Coriolis-centripetal matrix (including added mass) D ν : damping matrix g η : vector of gravitational/buoyancy forces and moments 0 g : vector used for pretrimming (ballast control) τ : vector of control inputs wind τ : vector of wind-induced forces and moments wave τ : vector of wave-induced forces and moments 2.3 Mathematical Model with Environmental Disturbances In order to improve performance of the control systems for underwater vehicles it is necessary to consider effects of external disturbances on underwater vehicles, which include wind, waves and currents. According to Fossen [3], for control system design it is common to assume the principle of superposition when considering wind and wave disturbances. In general, the environmental forces and moments will be highly nonlinear and both additive and multiplicative to the dynamic equations of motion. An accurate description of the environmental forces and moments is important in vessel simulators that are produced for human operators. With effects of external disturbances Equation (8) is rewritten as [3][4], RB RB A r A r r r r 0 M ν C ν ν M ν C ν ν D ν ν g η g τ w (9) where wind wave w τ τ and rc ν ν ν (where 6 c ν is the velocity of the ocean current expressed in the NED). Further information on modelling environmental disturbances can be found in [2][3]. 3. Brief Description of AMC’s ROV/AUV-3 3.1 Dimensions of AMC ROV/AUV-3 The 3 rd generation of AMC ROV/AUV is named AMC ROV/AUV-3. The main particulars of the vehicle are given in Table 1. Fig.2 shows the AMC ROV/AUV-3 which has been tested for watertight N E D O 151 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 integrity to a depth of 40 metres. Fig. 3 and Fig. 4 show the arrangement of its sensors and actuators. Two boxes named Box 1 and Box 2 are provided for electronics and batteries. Table 1 Main particulars of AMC ROV/AUV-3 Length over all 830 mm Width of frame 285 mm Overall width 445 mm Height 265 mm Height with light 323 mm Weight in the air 17.1 kg Fig. 2 The 3 rd generation of AMC ROV/AUV-3 Fig. 3 Body-fixed reference frame of AMC ROV/AUV-3 Fig. 4 Arrangement of thrsuters of AMC ROV/AUV-3 (u i , i = 1 to 3, are the voltage inputs of thrusters) AMC ROV/AUV-3 is equipped with the following sensors and actuators (see Fig. 5): sensors: 6-DOF IMU, pressure/depth sensor actuators/thrusters: 3 Seabotix thrusters (Model BTD150); servo motor to control the forward camera; and three lights. 3.2 4-DOF Mathematical Model (block-shaped ROV) In order to derive the differential equations governing the dynamics of the vehicle, it is assumed that: the origin of the body-fixed reference frame is at the centre of gravity where the vertical thruster is located; the body has an equivalent block shape; and the rolling and pitch motion can be neglected. Fig. 5 Input and output variables of the AMC ROV/AUV-3 Thus, the 6-DOF model in Equation (9) is simplified to a 4-DOF model as follows [2][3][4]. Kinematics: η J η ν (10) Kinetics: Mν C ν D ν g Bu (11) where: x y z η ; c s 0 0 s c 0 0 0 0 1 0 0 0 0 1 J ; u v w r ν ; u v w zr m X 0 0 0 0 m Y 0 0 0 0 m Z 0 0 0 0 I N M ; v u vu 0 mr 0 Y v mr 0 0 X u 0 0 0 0 Y v X u 0 0 C ν ; uu vv ww rr X u 0 0 0 0 Y v 0 0 0 0 Z w 0 0 0 0 N r D ν ; 0 0 0 0 g ; k 0 k 0 0 0 0 0 k kl 0 kl B ; and 1 2 3 u u u u Numerical values of the coefficients in Equations (10) and (11) are given in Table 2 in Appendix. 4. Control Algorithms and Design of Experiments In order to design a controller for missions at sea, the automatic control system as a whole is illustrated in Fig. 6 showing the signal flow of guidance, navigation and control systems. G u 2 u 1 u 3 Thruster 1 Thruster 2 Thruster 3 Box 1 Box 2 Torch 1 Camera house Torch 2 Pressure sensor Y Z X 152 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 Guidance system: to receive prior information, predefined inputs and waypoints and generate desired trajectory including desired speed, depth (heave), yaw and position. A joystick may be used to generate reference signals [3][4][7]. Navigation system: equipped with GNSS/INS receivers and other sensors to provide measurement of speed, depth, yaw and position [3][4][7]; and Control system: to detect error by comparing speed, depth, heading angle and position with desired values and calculate control signals and send them to the controller allocation devices (actuators) [3][4][7]. Fig. 6 Guidance, Navigation and Control signal flow [3] Fig. 7 shows an arrangement of sensors, actuators and target PC (onboard equipment) and their connection to a host PC with software. Fig. 7 Arrangement of sensors, actuators and connection of the target PC to the host PC In general controls of a ROV/AUV include: heading control: speed, depth (heave) and pitch control; roll, surge and sway; and position control. As the first step to realize a hardware-in-the-loop system, computer simulation programs are developed using the mathematical model in Equations (10) and (11). A number of tests are carried out for the simulation programmes including: open-loop system tests; manoeuvring tests; and closed-loop system tests. In the simulation programs for closed-loop control systems (including depth and course keeping, pitch and roll control and position control) the conventional PID control law was used: P I D dt u K e t K e t dt K dt (28) 4.1 Open-Loop System: Straight ahead and Turning Circle Manoeuvres With different values of voltage inputs of two thrusters at a certain depth, the following were tested with the simulation programmes: u = [12 12 0] straight ahead (Fig. 8) u = [12 -12 0] left turn (Fig. 9) u = [-12 12 0] right turn (Fig. 10). -80 -60 -40 -20 0 20 -1 -0.5 0 0.5 1 -101 -100.5 -100 -99.5 -99 z pos. x pos. y pos. Fig. 8 Straight ahead (z(0) = 100 m) -2 0 2 4 6 -5 0 5 10 -101 -100.5 -100 -99.5 -99 z pos. x pos. y pos. Fig. 9 Left turn (z(0) = 100 m) -2 0 2 4 6 -10 -5 0 5 -101 -100.5 -100 -99.5 -99 z pos. x pos. y pos. Fig. 10 Right turn (z(0) = 100 m) Estimated position and velocities 153 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 4.2 Open-loop System: Depth Control Manoeuvres Depth control (including driving and surfacing) of the AMC ROV/AUV-3 was done by the computer simulation as follows: u = [12 12 12]: diving (Fig. 11) u = [12 12 -12]: surfacing (Fig. 12). -80 -60 -40 -20 0 20 -1 -0.5 0 0.5 1 -160 -150 -140 -130 -120 -110 -100 x pos. y pos. z pos. Fig. 11 Diving (z(0) = 100 m) -80 -60 -40 -20 0 20 -1 -0.5 0 0.5 1 -100 -90 -80 -70 -60 -50 -40 x pos. y pos. z pos. Fig. 12 Surfacing (z(0) = 100 m) 4.3 Depth and Yaw Control (Zigzag Manoeuvres, Course/Depth Keeping and Changing) In order to design automatic multitask mission manoeuvring systems for the ROV/AUV, zigzag tests (depth), depth control and course keeping and changing control were carried out as shown below. Zigzag tests (depth) (Fig. 13); -50 0 50 100 150 -1 -0.5 0 0.5 1 -115 -110 -105 -100 -95 -90 -85 x pos. y pos. z pos. Fig. 13 Zigzag test (u 3 = 10 V, change in z = 10 m) Depth control with PID controller (Fig. 14); 0 50 100 150 200 250 300 -115 -110 -105 -100 -95 -90 -85 Depth Control - 2D Plotting Time [s] Heave [m] (a) 2-D plotting -150 -100 -50 0 50 -1 0 1 2 x 10 -14 -115 -110 -105 -100 -95 -90 -85 x pos. Depth Control - 3D Plotting y pos. z pos. (b) 3-D plotting Fig. 14 Depth control with a PID controller Course keeping/changing with PID controller (Fig. 15); 0 50 100 150 200 250 300 -20 -10 0 10 20 Course Keeping and Changing Input 1 [V] 0 50 100 150 200 250 300 -20 -10 0 10 20 Time [s] Input 2 [V] 0 50 100 150 200 250 300 0 20 40 60 80 Course Keeping and Changing Yaw (deg) 0 50 100 150 200 250 300 -10 0 10 20 Time (s) Yawrate (deg/s) Fig. 15 Course keeping and changing manoeuvres 154 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 5. Experiments for AMC ROV/AUV-3 Before conducting experiments with model-scaled ROV/AUV, it is important to design the experiments using the mathematical model-based simulators described in Section 4. At the AMC experiments to test the above control algorithms with AMC ROV/AUV-3 can be conducted in the Circulating Water Channel (CWC), the Model Test Basin (MTB) and the Survival Pool. The CWC is the best option with a 2.5 m depth as it is possible to observe the vehicle during experiments. Fig. 16 shows the CWC and its arrangement. Fi.g 16 The CWC and its arrangement It is planned to install a PC\104 target PC and electronics on the AMC’s vehicle. The target computer is connected to the onshore host computer via an Ethernet cable. The host PC is installed with control programmes developed using software such as MATLAB / Simulink / Real-time Workshop and RT- LAB software. Fi.g 17 Target and host computers and software Control hardware and software will be developed in two stages as shown below: Stage 1: ROV (PC\104, Ethernet connection); Stage 2: AUV (Microcontroller, Ethernet or Wireless connection). The following experiments are planned for each stage: depth zigzag test (yaw is kept constant); depth control test; course keeping and changing tests; yaw zigzag test (depth is kept constant); yaw turning circle test (depth is kept constant); and trajectory tracking control tests. 6. Conclusions The paper has described the: reference frames for description of ROV/AUV kinematics and kinetics; development of mathematical models (4-DOF and 3-DOF) of the AMC ROV/AUV-3 based on relevant theory; development of simulation programs and design of experiments for various scenarios; including: open-loop manoeuvres and closed- loop control manoeuvres with PID control law; AMC experimental facilities; and computer simulation results showing the feasibility of the control algorithms for various manoeuvres of the AMC ROV/AUV. The following recommendations are proposed for future work: conduct experiments in the CWC, Survival Pool or Model Test Basin; analyse data from the experiments and verify the mathematical models; use CFD simulation method for modelling; use experimental system identification methods and experimental data for estimation of hydrodynamic coefficients; determine coefficients of the vehicle; and develop 3D trajectory tracking control systems. 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[15] Bose, N., Lewis, R., Adams, S Use of an Explorer class autonomous underwater vehicle for missions under sea ice, 3rd International Conference in Ocean Engineering, ICOE 2009, IIT Madras, Chennai, India. Keynote presentation, 2009. [16] Burcher, R. and L. Rydill Concepts in Submarine Design. Cambridge University Press. [17] Christ, R.D. and R.L. Wernli Sr (2007). The ROV Manual – A User Guide for Observation Class Remotely Operated Vehicles. Butter- Heinemann (Elsevier). Oxford, 1994. [18] Griffiths, G. (Editor) (2003). Technology and Applications of Autonomous Underwater Vehicles. Taylor and Francis. [19] Groves, P.D GNSS, Inertial, and Multisensor Integrated Navigation Systems. Artech House, 2008. [20] Pienaar, R Simulation and Modelling of ROVs and AUVs. BE Thesis. Australian Maritime College, Launceston, 2011. [21] Kongsberg Maritime. Acoustic Underwater Positioning and Navigation Systems HiPAP and HPR, accessed on 19/11/2011 http://www.km.kongsberg.com/ [22] Bernstsen, M. and Olsen, A Hydroacoustic Aided Inertial Navigation System – HAIN A New Reference for Dynamic Positioning. Proceedings of Dynamic Positioning Systems Conference, Houston, 2007. [23] Underwater GPS: http://www.underwater- gps.com/ [24] Vickery, K Acoustic Positioning Systems “A Practical Overview of Current Systems”. Proceedings of Dynamic Positioning Conference, 1998. [25] Kongsberg Maritime. Multi-User Long Baseline System, accessed on 19/11/2011 http://www.km.kongsberg.com/ [26] Kongsberg. A New Reference for Dynamic Positioning of Vessels – Hydroacoustic-aided Inertial Navigation. Technical Report, 2006. [27] IMCA. Deep Water Acoustic Positioning, 2009. Accessed on 20/10/2011 at http://www.imca- int.com/documents/divisions/survey/docs/IMCA S013.pdf. Biography Dr. Hung Nguyen is a lecturer in Marine Control Engineering at National Centre for Maritime Engineering and Hydrodynamics, Australian Maritime College, Australia. He obtained his BE degree in Nautical Science at Vietnam Maritime University in 1991, then he worked as a lecturer there until 1995. He completed the MSc in Marine Systems Engineering in 1998 at Tokyo University of Marine Science and Technology and then the PhD degree in Marine Control Engineering at the same university in 2001. During April 2001 to July 2002 he worked as a research and development engineer at Fieldtech Co. Ltd., a civil engineering related nuclear instrument manufacturing company, in Japan. He moved to the Australian Maritime College, Australia in August 2002. His research interests include guidance, navigation and control of marine vehicles, self-tuning and optimal control, recursive system identification, real-time control and hardware-in-the-loop simulation of marine vehicles and dynamics of marine vehicles. Mr. Riaan Pienaar is a fourth year engineering student. He has a special interest in Subsea Engineering and hence decided to study Ocean Engineering at the Australian Maritime College. He also has a keen interest in UUVs and for this reason chose to complete a final year project entitled “Simulation and Modelling of ROVs and AUVs”. Riaan is now about to graduate and enter into the offshore engineering industry. Dr Dev Ranmuthugala is the Associate Dean, Teaching & Learning, and Associate Professor in Maritime Engineering at the Australian Maritime College, University of Tasmania. He has also served as Head of Department in Maritime Engineering and Vessel Operations over the past 15 years. Prior to joining AMC, he worked as a marine engineer and in the 156 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 design and sales of piping systems. His research includes: experimental and computational fluid dynamics to investigate the hydrodynamic characteristics of underwater vehicles, behaviour of submarines operating near the free surface, stability of surfaced submarines, towed underwater vehicle systems, and maritime engineering education. Mr. William West jointed the Australian Army as a Fitter and Turner when awarded Apprentice of the Year by BHP and Ansett Australia in 1979. He worked on several projects as: commissioning HMAS Tobruk and Marine Engineering. On discharge he began work with Caterpillar (South Australia) as an Industrial Engines Technician where he assembled and maintained diesel powered generators for the oil & gas sector. In 1986 he returned to Western Australia; employed as a Mechanic, Maritime Aids (Australian Maritime Safety Authority) upgrading, repairing and surveying lighthouses. On completing his engineering diplomas’ in Mechanical and Industrial Fluid Power, he took employment with EMS Services (WA) as a specialist in naval hydraulics. In 2005 he commenced study at the Australian Maritime College (AMC) toward his degree in Engineering (Marine and Offshore Systems). Graduating in 2009 he took casual work with AMC to design and build the ROV/AUV used in this paper for the purposes of observation and academic research. Appendix A1. Numerical values of the 4DOF Mathematical Model for AMC ROV/AUV-3 Table 2 Numerical values of ROV/AUV parameters m [kg] 17.1 I z [kgm 2 ] 24.7 l [m] 0.2225 g [m/s 2 ] 9.81 u X 26.0 v Y 186.4 w Z 65.95 r N 3.704 uu X 139.2 vv Y 53.5 ww Z 79.3 rr N 0.0 k 0.107 A2. 3-DOF Model Assumptions for modeling AMC ROV/AUV-3 are [20]: the ROV/AUV operates at low speeds; there are no couplings between the six degrees of freedom; the vehicle does not develop an angle of trim or roll during any manoeuvres; when manoeuvring the sway velocity is negligible; and the influence from disturbances such as current or waves are negligible. The 3-DOF model of AMC ROV/AUV-3 is summarized as follows [2][6][20]: Mν Dν τ (12) where τ Bu ; u w r ν ; u w zr m X 0 0 0 m Z 0 0 0 I N M ; uu ww rr X u 0 0 0 Z w 0 0 0 N r D ; k k 0 0 0 k lk lk 0 B ; and T 1 2 3 v v vu . A3. An Overview of Acoustic Underwater Positioning and Navigation Systems This appendix outlines hydroacoustic positioning and navigation systems as recommended by the reviewers. One of the great challenges in control and operation of ROVs/AUVs is the difficulty in underwater data communication, positioning and navigation. Radio frequency (RF) wave and wireless transmission underwater is very weak, so RF navigation systems like GNSS/D-GNSS and wireless communication systems are not applicable in underwater vehicles. Underwater acoustic positioning and navigation methods help to control and operate ROVs/AUVs. The main elements of a hydroacoustic positioning and navigation system as shown in Fig. A1 include a transmitter (transducer), receiver (transponder), signal processing and corrections, incorporation of peripheral data, display of position and some form of noise and interference mitigation. Fig. A1 Illustration of hydroacoustic principles (courtesy of Kongsberg) A signal (pulse) is sent from the transducer, and is aimed towards the seabed transponder. This pulse activates the transponder, which responds 157 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 immediately to the vessel transducer. The transducer, with corresponding electronics, calculates an accurate position of the transponder relative to the vessel [20][21]. Transmission and reception of acoustic pulses are to track or position a limited number of objects, both static and mobile [27]. According to Kongsberg Maritime [20], there are several typical problems for underwater positioning and navigation. Sound waves do not follow a straight path. Deflection occurs when the sound passes through different thermo clines in the sea. Thermo clines are a result of differences in temperature and salinity. The velocity of sound varies accordingly to these factors, and shadow zones can occur. Another problem with sound in water is noise generated from the vessel itself and surrounding objects. A3.1 Operating Principles Underwater acoustic positioning and navigation systems use different principles for measurements and calculations below: super short baseline (SSBL); short baseline (SBL); long baseline (LBL); multi-user long baseline (MULBL); and combined mode system. A3.1.1 SSBL - Super Short Baseline The calculation of positioning is based on range, and on vertical and horizontal angle measurements, from a single multi element transducer. The system (as shown in Fig. A2) provides three-dimensional transponder positions relative to the vessel [21]. Fig. A2 Super short baseline principle [24] A3.1.2 SBL - Short Baseline The calculation of position is based on range, and vertical and horizontal angle measurements from a minimum of three hull mounted transducers. The system provides three-dimensional transponder positions relative to the vessel [21] (see Fig. A3). A3.1.3 LBL - Long Baseline The calculation of position is based on range measurements only. The vessel is positioned relative to a calibrated array of transponders [21] as shown in Fig. A4. Fig. A3 Short baseline principle [24] Fig. A4 Long baseline principle [24] Advantages and disadvantages of SSBL, SBL and LBL methods are given in Table 2. Table 2 Advantages and disadvantages of SSBL, SBL and LBL systems [27] System Advantages Disadvantages SSBL Good potential accuracy Requires only a single subsea pinger or transponder One time calibration Highest noise susceptibility Accuracy dependent on shipboard VRU (vertical reference unit) SBL Good potential accuracy Requires only a single subsea pinger One time calibration Accuracy dependent on shipboard VRU and heading sensor/gyro compass Multiple hydrophones required through the hull LBL Highest potential accuracy Accuracy preserved over wider operating area One hydrophone needed Redundant data for statistical testing/quality control Requires multiple subsea/seabed transponders Update intervals long compared to SBL/SSBL systems Need to redeploy and recalibrate at each site A3.1.4 Combined Mode Systems Any combination of the three principles above secures flexibility as well as a high degree of redundancy and accuracy [21]. Combined systems come in many varieties below: long and super short baseline; long and short baseline; 158 Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 short and super shot baseline; and long, short, super short baseline. A3.1.5 Multi-user Long Base Line System The long base line system is extended to multi-users. A transponder array is deployed and calibrated using subsea baseline measurements, or run time calibration. The transponder array must be deployed in such a way that one of the transponders in the array has communication with all the other transponders in the array. This transponder is used as a Master in the positioning phase. The other transponders are called Slaves. See Fig. A5. The Master transponder acts as a beacon. It starts a positioning sequence by performing the steps below [25]: 1. the Master interrogates the Slaves in the array by transmitting the common LBL interrogation channel to them; 2. after “a turn-around” delay from its own interrogation, the Master transmits the individual transponder channel to be received by the vessels/ROVs/AUVs positioned in the array; and 3. each Slave transponder receives the interrogation from the Master beacon, and transmits its individual reply channels after a turn-around array. Fig. A5 Multi-user long baseline principle [21] If the Slave misses an interrogation from the Master, it will still reply because it knows the position update rate. The same principle may be used to save battery for the Master. The Master may be programmed to send an interrogation with lower rate, and the Slaves will use this interrogation to adjust its timing and still send pulses at the position update rate [25]. The calculation of the position is based on the measured differences in range between the transponders in the array. In addition, any measured angles towards the transponder will be used. Together with the known coordinates of each transponder, this is enough to calculate position. Compared to the standard LBL, the MULBL needs one more transponder in the array. All vessels that are going to use the MULBL array need the coordinates of the transponders and the channel numbers. These data are distributed on a file [25]. A3.2 Hydroacoustic Aided Inertial Navigation System There are many position reference systems that can be used for marine vehicles. But when a vessel is alone in the open ocean far way from shore it is only the satellite based GNSS and the seabed transponder based hydroacoustic position reference system that can give reliable reference position [22]. Fig. A7 shows various position reference systems that can be used for a vessel. It is ideal to combine acoustic and inertial positioning principles because they have complementary qualities. The underwater acoustic positioning and navigation system itself is characterised by relatively high and evenly distributed noise and no drift in the position, while inertial positioning has very low short- term noise and relatively large drift in the position over time [22]. Based on the combined acoustic and inertial positioning principles a hydroacoustic aided inertial navigation (HAIN) system has been proven its highly reliable reference position. Main advantages of the HAIN system are: Fig. A7 Various position reference systems for a marine vehicle [22][26] improved acoustic position accuracy higher position update rate extends operational depth capabilities longer transponder-battery lifetime; and position update during acoustic drop-out. Slave 1 Slave 2 Slave 3 Slave 4 Master ROV/AUV 159 . triển mô hình toán của các phương tiện ngầm lọai nhỏ này dùng cho mục đích mô phỏng và thiết kế điều khiển. Bài báo này tập trung vào mô hình hóa lý thuyết, mô phỏng, thiết kế điều khiển và tthử. cho phương tiện ngầm cần phải có một mô hình phương tiện ngầm hoạt động được với một bộ điều khiển đầy đủ chức năng để thiết kế và thực hiện nhiệm vụ. Bài báo này trình bày mô hình hóa, mô phỏng. nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011 VCCA-2011 Modelling, Simulation and Control of Underwater Vehicles Mô hình hóa, mô phỏng và điều khiển phương tiện ngầm Hung Duc Nguyen,