Proceedings VCM 2012 42 mô hình hóa và mô phỏng phương tiện ngầm vận hành từ xa

312 Hung Duc Nguyen, Sachith Malalagama and Dev Ranmuthugala VCM2012 Modelling and Simulation of a Remotely Operated Vehicle Mô hình hóa và mô phỏng phương tiện ngầm vận hành từ xa Hung Duc Nguyen, Sachith Malalagama and Dev Ranmuthugala University of Tasmania / Australian Maritime College e-Mails: nguyenhd@amc.edu.au Abstract This paper presents modelling of a newly-built remotely operated vehicle utilising theoretical and CFD simulation methods and the development of simulation programs to predict the behaviour of the ROV using LabVIEW. In order to design and to implement precise control of a ROV during missions, mathematical models with hydrodynamic coefficients are required. Hydrodynamic coefficients of the proposed mathematical model are determined by analytical and CFD simulation methods supplemented by experimental work. A computer simulation is developed to verify the coefficients and mathematical model of the ROV under various manoeuvres. Tóm tắt: Bài báo trình bày mô hình hóa thiết bị ngầm vận hành từ xa mới đuợc thiết kế bằng hai phương pháp lý thuyết và mô phỏng CFD và sự phát triển chương trình mô phỏng để ước ược động thái của thiết bị ngầm dùng LabVIEW. Nhằm thiết kế và thực hiện điều khiển chỉnh xác một thiết bị ngầm vận hành từ xa trong khi làm nhiệm vụ thì cần có mô hình toán có đầy đủ hệ số thủy động học. Các hệ số thủy động học của mô hình toán được xác định bằng phương pháp giải tích và mô phỏng CFD có phụ trợ bằng thực nghịệm. Mô phỏng được thực hiện nhằm kiểm chứng các tham số và mô hình toán của thiết bị ngầm vận hành từ xa theo các điều động khác nhau. Nomenclature Symbol Unit Meaning ν   T u,v,w,p,q,r ν η   T n,e,d, , ,     η M Mass matrix D Damping matrix C Coriolis matrix G Vector of gravitational and buoyancy forces and moments B N Buoyancy force W N Weight U Vector of inputs x G , y G , z G m Coordinates of the centre of gravity l i (i=1,2,3) Distance from each thruster to centre of gravity Abbreviation CFD Computational F luid D ynamics DOF Degree of F reedom ROV Remotely O perated V ehicle AUV Autonomous U nderwater V ehicle HIL Hardware I n the L oop AMC Australian Maritime College UTAS University of Tasmania 1. Introduction When designing ROV/AUV platforms as in [11][12] for educational and research work, the physical and virtual/mathematical models play an important role enabling the designer to understand its dynamics and to develop its control system. However the development of a specialist physical prototype of a ROV or AUV with off the shelf electronics is relatively expensive and in many cases prohibitive within undergraduate programmes. The work in this paper incorporates the development of an inexpensive ROV using easily accessible materials. Although the vehicle in this paper is tethered, i.e. an ROV generally depends on a human operator for the guidance and control [22], it can also be untethered with pre-programmed mission control and both. The ROV described in this paper was fabricated using PVC piping, submersible bilge pump motors connected to model scale propellers, fishing floats and accessories that are easily obtainable from the local hardware shops. The ROV was designed to carry out the following tasks [17][ 18]: Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 313 Mã bài: 67  observe and survey seabed conditions and submersed objects and structures;  observe marine farm facilities and equipment; and  perform basic underwater surveillance operations. The work further develops the mathematical models, control algorithms and computer simulation to predict the dynamic behaviour of the ROV. Thus this paper describes the:  newly-built low cost ROV;  modelling of the ROV/AUV using theoretical and CFD methods;  calculation of the hydrodynamic coefficients of the ROV;  simulation of the ROV under various manoeuvring scenarios;  design and simulation of a trajectory tracking control system to conduct underwater missions; and  conduct experimental work to determine the hydrodynamic coefficients and validation of the model. 2. Description of AMC ROV-IV AMC-ROV-IV was made of PVC pipes and joints, aluminium frames, and two fishing floats as shown in Fig. 1. Three motors from submerged bilge pumps connected to model scaled propellers were used as thrusters for propulsion and vertical motion. All materials used were easily accessible from a household hardware or marine supplier [18]. The main particulars of the ROV are given in Table 1. The ROV has been tested for watertight integrity to a depth of about 5 metres in the AMC Survival Centre Swimming Pool and the Circulating Water Channel. Fig. 1 AMC ROV-IV Table 1 Main particulars of AMC ROV-IV Length overall [mm] 480 Width of frame [mm] 290 Horizontal distance between centres of the two main thrusters [mm] 180 Overall width [mm] 400 Height without floats [mm] 190 Height with floats [mm] 225 Weight in air [kg] 2.965 Volume [m 3 ] 2.946 x 10 -3 The ROV is equipped with the following sensors and actuators:  actuators/thrusters: three bilge pump motors;  three switch (relay) motor controllers;  two forward lights; and  instrumentation and control electronics. 3. Reference Frames and Equations 3.1 Reference Frames In the design of control systems for underwater vehicles, their kinematics and kinetics are described using the reference frames given in Fig. 2, which includes the Earth-centred reference frames (the Earth-centred Earth-fixed frame x e y e z e and the Earth-centred inertial frame x i y i z i ), and the geographic reference frames (the North-East- Down coordinate system x n y n z n and the body-fixed reference frame x b y b z b ) [3][4]. Fig. 2 The ECEF frame x e y e z e is rotating with angular rate with respect to an ECI frame x i y i z i fixed in space [3][4]. The two reference frames for the AMC ROV are shown in Fig. 3. NED is the earth-fixed reference frame and XYZ is the body-fixed reference frame. 314 Hung Duc Nguyen, Sachith Malalagama and Dev Ranmuthugala VCM2012 The centre of gravity G is at the vertical central thruster. The arrangement of the three thrusters for position control is shown in Fig. 4. Two floats plus a set of adjustable weights are used to adjust the position of the centre of buoyancy and the vehicle’s pitch. Fig. 3 Reference frames for AMC ROV-IV 3.2 Kinematics Referring to Fig. 3, 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 3 3             R Θ 0 J η 0 T Θ (2) with 3 3 S   η  and 3 ν  . Fig. 4 Arrangement of thrsuters of AMC ROV-IV (u i , i = 1 to 3, are the voltage inputs of thrusters) The angle rotation matrix   n 3 3 b  R Θ  is defined in terms of the principal rotations as [3][4], 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 where o 90    (7) It should be noted that    T Θ is undefined for a pitch angle of o 90    and that     1 T   T Θ T Θ . 2.3 Kinetics The 6-DOF kinetic equations in the body-fixed reference frame in the vector form are therefore [3],       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 : gravitational/buoyancy forces and moments vector 0 g : pre-trimming (ballast control) vector τ : control input vector wind τ : wind-induced forces and moments vector wave τ : wave-induced forces and moments vector G u 2 u 1 u 3 x y Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 315 Mã bài: 67 3.1 Mathematical Model with Environmental Disturbances In order to improve performance of the control systems for underwater vehicles it is necessary to consider the effects of external disturbances on the vehicle, 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 and provides useful information to the 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 r c   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]. The model without external forces and moments [3], [4] and [10] is            M ν C ν ν D ν ν g η B η u  (10) 3.2 Mathematical Models for ROV In order to derive the differential equations governing the kinematics and dynamics of the vehicle of which inputs and outputs are shown Fig. 5, 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 vehicle is symmetric about the longitudinal axis x;  the body has an equivalent block shape; and  the vehicle is neutrally buoyant and the mass distribution of the vehicle is homogeneous throughout the vehicle. Thus, the 6-DOF model in Equation (9) is applied to the AMV ROV as follows [2][3][4][10]. Equations for kinematics:    η J η ν  (11) Fig. 5 Input and output variables of the AMC ROV/AUV-IV Equations for kinetics:        M ν C ν ν D ν ν g Bu  (12) where x y z                         η ;   J η as in equation (2); u v w p q r                      ν ; u v w x p y q z r m X 0 0 0 0 0 0 m Y 0 0 0 0 0 0 m Z 0 0 0 0 0 0 I K 0 0 0 0 0 0 I M 0 0 0 0 0 0 I N                             M       w v w u v u w v z r y q w u z r x p v u y q x p 0 mr mq 0 Z w Y v mr 0 mp Z w 0 X u mq mp 0 Y v X u 0 ( ) 0 Z w Y v 0 (I N )r (I M )q Z w 0 X u (I N )r 0 (I K )p Y v X u 0 (I M )q (I K )p 0                                         C ν                  u uu v vv w ww p pp q qq r r r X X u 0 0 0 0 0 0 Y Y v 0 0 0 0 0 0 Z Z w 0 0 0 ( ) 0 0 0 K K p 0 0 0 0 0 0 M M q 0 0 0 0 0 0 K K r                              D ν B B 0 0 0 ( ) z Bcos sin z Bsin 0                       g η ; 1 2 3 3 3 k k 0 0 0 0 0 0 k 0 0 0 kl kl kl kl kl 0                       B ; and 1 2 3 u u u            u . The determination of all coefficients of (12) is discussed in the following sections. 4. Parameter Identification 316 Hung Duc Nguyen, Sachith Malalagama and Dev Ranmuthugala VCM2012 4.1 Theoretical Parameter Estimation Translational added mass of the vehicle due to the translational accelerations were determined by the analytical method using the geometrical parameters of the vehicle (see Table 1). The added mass for each direction of translational motion, i.e. surge, sway and heave were calculated for each component and then added arithmetically to obtain the added mass for the complete ROV for the given direction. Where the added masses for two dimensional potential flows are not available, the projected area of a particular component for the given direction was obtained and using its principle dimensions the added mass in the given direction was calculated using the following formula [24][29]. 2 2 i i ii i i (a )(b ) 4 M 3 (a b )    (13) where M ii = translational added mass and a i , b i = two principal dimensions of the projected area (b i > a i ). The values of added mass in three directions are given in Table 2. Table 2 Estimated added mass in three directions Added mass Added mass [kg] Surge 1.251 Sway 1.919 Heave 2.11 For estimation of added moments of inertia, it is assumed that the added moment of inertia around each axis of rotation is represented by half of the moment of inertia around the particular axis as given in Table 3. Table 3 Estimated added moments of inertia Axis of rotation Moment of inertia (kgm 2 ) Added moment of inertia(kgm 2 ) X I x = 0.067 p K  =0.0335 Y I y = 0.091 q M  = 0.045 Z I z = 0.05 r N  = 0.025 4.2 Experimental Parameter Estimation The geometrical parameters measured are given in Table 4 and the experimentally determined mass and moments of inertia are given in Table 5. Table 4 Geometrical parameters of the ROV Vertical distance between port and STBD thrusters to centre of gravity (l 1 ) 0 [mm] Longitudinal distance between vertical thrusters and centre of gravity (l 2 ) 0 [mm] Horizontal distance between Port and STBD thrusters to centre of gravity (l 3 ) 180 [mm] Table 5 Mass and inertia properties Parameter Value Mass (m) 2.965 kg Moment of inertia around x- axis (I x ) 0.067072131 kgm 2 Moment of inertia around y-axis (I y ) 0.091018248 kgm 2 Moment of inertia around z- axis (I z ) 0.050413326 kgm 2 To determine the damping coefficients a series of experiments were carried out to measure the damping forces acting on the ROV in different orientations. These experiments were conducted in the AMC Circulating Water Channel shown in Fig. 6. Fig. 6 Schematic diagram of the CWC In this project the forces acting on the umbilical were not considered. Hence, the experiments were carried out only on the ROV (vehicle) as follows:  The ROV was detached from the umbilical.  As the ROV is slightly positively buoyant, ballast weights were attached to the ROV to make it negatively buoyant.  Loops were attached to the neutral axis of the ROV as shown in Fig. 7.  A load cell was calibrated with known weights. Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 317 Mã bài: 67  The ROV was then attached to the load cell from the loops.  ROV was submerged in the circulating water channel and the circulation of water was initiated.  The calculated drag forces from the experiments are plotted together with the corresponding drag forces obtained from computational fluid dynamics simulations.  The experimental results were non- dimensionalised and then compared with the CFD simulation results in order to validate the obtained model. Fig. 7 Attachment of loops to approximately to the neutral axis Fig. 8 shows the experiment being carried out for the surge direction. Fig. 9 shows the comparison of the total drag force obtained by the experiments for the surge orientation to that obtained by CFD. It can be seen from Fig. 9 that the experimental results and the CFD simulation results are sufficiently similar. Fig. 8 Drag test in the surge orientation Fig. 9 Drag force against flow velocity for surge orientation Fig. 10 and Fig. 11 show drag test and the graph of drag force vs the flow velocity for sway orientation. Fig. 10 Drag test in the sway orientation Fig. 11 Drag force against flow velocity for sway orientation Fig. 12 and Fig. 13 show the drag force in the heave orientation and the respective graph of the drag force vs the flow velocity. 318 Hung Duc Nguyen, Sachith Malalagama and Dev Ranmuthugala VCM2012 Fig. 12 Drag test in the heave orientation Fig. 13 Drag force against flow velocity for heave orientation 4.3 Thruster Coefficient Identification The thruster coefficient matrix and the thruster input matrix were determined based on the assumption that the characteristics of all three thruster motors used in the ROV were identical. The experiment setup is shown in Fig. 14 and Fig. 15. Fig. 14 Experiment setup for thruster coefficient determination Fig. 15 Experiment setup in the laboratory Fig. 16 shows the graph of the thruster force vs the supply voltage. It is seen that from the graph no thrust is generated when the supply voltage is less than 2 V. Hence, the value of thrust force coefficient, k was found as, k = 0.373 N/V. Fig 16 Thruster force vs supply voltage 4.4 CFD Method Simulations of the ROV using a CFD model were used to determine the linear and quadratic damping derivatives. The results obtained from the CFD analysis were validated against the Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 319 Mã bài: 67 experimental data. The CFD was carried out using the commercial software ANSYS-CFX. 4.4.1 Geometry Creation The 3D model used for the CFD was developed using the AutoCAD and then imported into ANSYS® Design Modeller in IGES 144 format. In Design Modeller the fluid domain required for the simulation was created. The complete geometry is shown in Fig. 17 and Fig. 18. Fig. 17 Flow domain plan front view Fig. 18 Flow domain plan side view 4.4.2 Mesh Generation Meshing is the discretization of the fluid domain volume into adjoining finite volumes. Mesh quality and distribution are critical to obtain accurate results from a CFD simulation. The entire fluid domain mesh was created with the automatic method control, as shown in Fig. 19. The mesh independence study was carried out by changing the curvature normal angle from 18 o to 4.5 o . The rest of the settings were kept constant. 4.4.3 Mesh Independence A mesh independence study was done in order to establish the results obtained from the CFD simulations independent of the number of elements in the mesh. Fig. 19 shows overall mesh of the ROV. The number of elements of the mess was changed by varying changing the curvature normal angle as shown in Table 6. Fig. 19 Overall mesh of the ROV Table 6 Changed setting for mesh independence study (*) Quadratic damping derivative in the surge direction The quadratic damping derivatives obtained with different mesh sizes for the surge direction are plotted in Fig. 20 [22]. By considering the accuracy compared to the experimental results as in Section 4.2 and the time available time for simulations it could be concluded that the mesh generated with a 9 o curvature normal angle is the most suitable to carry out the rest of simulations. Curvature normal angle Number of Elements u u X (*) 18 o 2150311 15.58 13.5 o 2875855 13.31 9 o 4590472 10.88 6.5 o 8171510 10.07 4.5 o 9164514 10.07 320 Hung Duc Nguyen, Sachith Malalagama and Dev Ranmuthugala VCM2012 Fig. 20 Quadratic damping coefficients u u X against the number of elements 4.4.4 Physics and Fluid Properties When running the CFD simulations it was necessary to set physical and fluid properties used for translational and rotational motions. These properties are summarised in Tables 7 and 8. Table 7 Flow physics used for the CFD simulation (translational) Table 8 Flow physics used for the CFD simulation (rotational) 4.4.5 Boundary Conditions Boundary conditions for translational motion and rotational motion are shown in Tables 9 and 10. Table 9 Boundary conditions (translational) Table 10 Boundary conditions (rotational motion) 4.4.6 CFD Simulation Results This section presents some of CFD simulation results for translational motion, rotational motion and hydrodynamic lift. 4.4.6.1 Translational Motion Translational motion includes surge, sway and heave. Table 11 and Fig. 21 through to 23 show main results from the CFD simulation by which coefficients were determined. Table 11 CFD simulation results (translational) Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 321 Mã bài: 67 Fig. 21 Drag force vs velocity (surge) Fig. 22 Drag force vs velocity (sway) Fig. 23 Friction drag force vs velocity (heave) 4.4.6.2 Rotational Motion Rotational motion of the ROV includes roll, pitch and yaw. The CFD simulation results are summarised in Table 12 and Fig. 23 through to 25. Table 12 CFD simulation results for rotational motion Fig. 23 Torque vs angular velocity (roll) Fig. 24 Torque vs angular velocity (pitch) [...]... Manoeuvring Systems Using Recursive Optimal Control Algorithms Proceedings of HUT-ICCE 2008, pp 54-59 Hoi An, Vietnam, 2008 [8] Nguyen, H.D Recursive Identification of Ship Manoeuvring Dynamics and Hydrodynamics Proceedings of EMAC 2007 (ANZIAM), pp 681697, 2008 [9] Nguyen, H.D Recursive Optimal Manoeuvring Systems for Maritime Search and Rescue Mission, Proceedings of OCEANS'04 MTS/IEEE/TECHNO-OCEAN'04 (OTO’04),... programmes developed using software such as Arduino software (open source), MATLAB / Simulink software or LabVIEW Table 12 Estimated costs for electronics Item Cost (AUD) Arduino and 260 IMU/GPS boards VCM2 012 Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 325 50 50  computer simulation results showing the feasibility of the control algorithms for various manoeuvres of ROVs 80 440 Motor... generate desired trajectory including desired speed, depth (heave), yaw and position A joystick may be used to generate reference signals [3][4][7][23] Fig 27 Guidance, navigation and control systems VCM2 012 The computer simulation using the above mathematical model was developed using National Instruments LabVIEW 2010 This allowed the verification of the developed mathematical model and the estimated... extraction http://oils.gpa.unep.org [24] Heron, A., Woods, A & Anderson, B Determination of Manoeuvring Coefficients for the Triton ROV in the Circulating Water Channel Australian Maritime College, 2000 VCM2 012 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... A2.1 Front Panel window of the simulation program Mã bài: 67 328 Hung Duc Nguyen, Sachith Malalagama and Dev Ranmuthugala Fig A2.2 Block diagram window (mathematical model) of the simulation program VCM2 012 ... Thesis Australian Maritime College, Launceston, 2011 [18] Malalagama, S Modelling and Simulation of a Remotely Operated Vehicle, BE Thesis Australian Maritime College, University of Tasmania, Launceston 2012 [19] Blohm, H & Jensen, V Build Your Own Underwater Robot and Other Wet Projects, Vancouver, Westcoast Words, 1997 20] Brennen, C E A Review of Added Mass and Fluid Inertial Forces California: Naval... 60 80 1 0 -1 0 Fig 31 Linear and angular velocities for Manoeuvre 2 5.2 Closed-Loop Control Manoeuvres A ROV/AUV often does various underwater missions that are based on predefined trajectories, for examples, water sampling, survey of submerged pipelines and cables, or hydrographical surveys As the first step to realise a trajectory tracking control system for a ROV close loop control manoeuvring simulations... 2004 Mã bài: 67 326 Hung Duc Nguyen, Sachith Malalagama and Dev Ranmuthugala [10] Nguyen, HD and Pienaar, R and Ranmuthugala, D and West, W, ‘Modeling, Simulation and Control of Underwater Vehicles’, Proceedings of The 1st Vietnam Conference on Control and Automation, 25-26 November 2011, Hanoi, Vietnam, pp 150-159, 2011 [11] West, W.J Remotely Operated Underwater Vehicle, BE Thesis Australian Maritime . trình bày mô hình hóa thiết bị ngầm vận hành từ xa mới đuợc thiết kế bằng hai phương pháp lý thuyết và mô phỏng CFD và sự phát triển chương trình mô phỏng để ước ược động thái của thiết bị ngầm dùng. Malalagama and Dev Ranmuthugala VCM2 012 Modelling and Simulation of a Remotely Operated Vehicle Mô hình hóa và mô phỏng phương tiện ngầm vận hành từ xa Hung Duc Nguyen, Sachith Malalagama. xác định bằng phương pháp giải tích và mô phỏng CFD có phụ trợ bằng thực nghịệm. Mô phỏng được thực hiện nhằm kiểm chứng các tham số và mô hình toán của thiết bị ngầm vận hành từ xa theo các điều