Hydrodynamic Coefficients Identification and Experimental Investigation for an Underwater Vehicle

Transcription

1 Sensors & Transducers 2014 by IFSA Publishing, S. L. Hydrodynamic Coefficients Identification and Experimental Inestigation for an Underater Vehicle 1 Shaorong XIE, 1 Qingmei LI, 1 Peng WU, 1 Jun LUO, 1 Feng LI, 2 Jason GU 1 School of Mechatronics Engineering and Automation, Shanghai Uniersity, 149 Yanchang Road, Zhabei District, Shanghai, , China 2 Department of Electrical and Computer Engineering Dalhousie Uniersity, Halifax, 3J 2X4, NS Canada Tel.: li_qm@shu.edu.cn Receied: 16 December 2013 /Accepted: 28 January 2014 /Published: 28 February 2014 Abstract: Hydrodynamic coefficients are the foundation of unmanned underater ehicles modeling and controller design. In order to reduce identification complexity and acquire necessary hydrodynamic coefficients for controllers design, the motion of the unmanned underater ehicle as separated into ertical motion and horizontal motion models. Hydrodynamic coefficients ere regarded as mapping parameters from input forces and moments to output elocities and acceleration of the unmanned underater ehicle. The motion models of the unmanned underater ehicle ere nonlinear and Genetic Algorithm as adopted to identify those hydrodynamic coefficients. To erify the identification quality, elocities and acceleration of the unmanned underater ehicle as measured using inertial sensor under the same conditions as Genetic Algorithm identification. Cures similarity beteen measured elocities and acceleration and those identified by Genetic Algorithm ere used as optimizing standard. It is found that the cures similarity ere high and identified hydrodynamic coefficients of the unmanned underater ehicle satisfied the measured motion states ell. Copyright 2014 IFSA Publishing, S. L. Keyords: Unmanned underater ehicle, Hydrodynamic coefficients, System identification, Genetic algorithm. 1. Introduction The accuracy of the mathematical model plays a fundamental role in guidance and control system design for the underater ehicle. The most commonly used model for underater ehicles is based on Neton s theorem and the Lagrange equation proposed by Fossen and Ola-Erik [1]. Hoeer, in this model, hydrodynamic forces and torques applied on the ehicle ere presented through a set of unknon hydrodynamic coefficients, hich ere determined by the ehicle shape, motion conditions and flo field around. The increased uncertainties of the model as ell as the difficulties in obtaining hydrodynamic coefficients that can accurately express underater ehicle s motion has become a focus of interest for researchers in the last to decades. In order to precisely model and design controllers for a remotely operated underater ehicle (ROV) in the laboratory, e used data from Article number P_1864

2 experiments ith sensors and identifying methods to obtain its hydrodynamic coefficients. Planar-motion-mechanism (PMM) tests carried out ith toing in tank [2] are traditional methods used to identify parameters for marine ehicles. Although operation processes of PMM tests hae been standardized already, scale effects [3] and errors inoled [4] make measured coefficients using PMM are not completely reliable. With the deelopment of computer science, computational fluid dynamics (CFD) softare are adopted to analyze motion phenomenon in the fluid for underater ehicles instead of PMM tests [5]. In spite of cutting don experimental expenses, numerical truncations and difficulties in setting boundary conditions [6] contribute for the uncertainties of the results getting by CFD method. System identification (SI) is a idely used method in recent years for obtaining hydrodynamic coefficients because of both time and cost saings. Furthermore, compared to PMM and CFD, SI can aoid model modification caused by ROV configuration change and becomes a more practical alternatie. The most basic SI method is LS for its simple principles and the fact that it is easy to be realized in hardare. M. Caccia et al. [7] used LS method to identify an open-frame underater ehicle ith propeller affects. ut according to P. Ridao et al. [8], the olume of samples affects the quality and standard deiation of LS identification significantly. Moreoer, hen the model is not linear, LS ill become inalid. Artificial intelligence algorithm has adantages in uncertain system identification. P. W. J. Van De Ven et al. [9] used neural netork (NN) to identify underater ehicles. The eakness of NN is that its netork configuration affects effect of the algorithm and it relays on experience of designer. Inspired by biological genetic and eolement process, GA is able to globally search optimal solution once initial population is set randomly. Then the influence of samples for results is lessened. In addition, GA has seeral appealing properties, like parallel optimization and robustness to disturbance, making it suitable for identification of nonlinear perturbed system as underater ehicles. W. Yuan et al. [10] applied GA and simulated motion to get hydrodynamic coefficients of horizontal plane motion for AUV CRanger-01. The alidity of GA in parameters identification for underater ehicles as proed and the errors beteen real and identified hydrodynamic coefficients ranged from 0.17 % to -3.13%. Hoeer, hen operated in the shallo ater or near the sea surface, ae disturbances in the motion of underater ehicles cannot be ignored as in [10]. What is more important, using measured motion data from sensors to identify parameters for underater ehicles can better reeal their moement characteristics. In this paper, e used GA to obtain both horizontal and ertical planes motion for an underater ehicle hile took ae disturbances into consideration at the same time. In order to improe identification accuracy, data used for identifying processes as measured ith sensor module in the underater ehicle. The hydrodynamic coefficients identified ith method in this paper ere compared ith those identified ith classical LS under the same conditions and the results of GA turned out to be better. 2. ROV Identification Mathematic Model 2.1. ROV Dynamics The ROV used for experiments is shon in Fig. 1. It is equipped ith three thrusters: one ertical thruster and to stern thrusters. As other marine ehicles, to coordinate systems are used to describe the motion of this ROV: the earth-fixed ( o ) and body-fixed ( o ' xyz ) reference frames. Its motion contains translational motion in three directions: surge, say, and heae; and rotational motions: roll, pitch and ya [1]. The position of ROV in the earthfixed system is gien by linear displacement 1 [ x, yz, ] T and Euler angle 2 [,, ] T. The corresponding elocity and angular elocity are V1 [ u,, ] T and V2 [ pqr,, ] T. The graity center of the ehicle is represented by r [ x, y, z ] T. o y g g g g z o' Fig. 1. Coordinate systems for ROV. According to Neton s Theory, the motion of a rigid body ith respect to its body-fixed reference frame is: M C() D() g(), (1) J ( ), (2), (3) here M is the sum of rigid body inertial mass and added fluid inertial mass, C () represents Coriolis and centripetal forces and moments, and g( ) is the restoring J ( ) forces and moments from the ROV and the ater are the Euler transformation matrix A x

3 beteen the body and earth-fixed coordinate systems. A and are the forces and moments generated by thrusters and ater ae respectiely and is total external forces and moments acting on the ROV. A is controlled by the oltages of the thrusters hile is related to the interaction beteen ater and the ROV: k h cos( t), (4) s s here s and ks are the constants; h and are the amplitude and encounter frequency of the ae ROV Hydrodynamic Analysis In the fluid medium, ROV graity W and buoyancy act collinearly through the center of graity O '. They proide restoring force and moment g( ) if ehicle inclines. ( W )sin( ) ( W )cos( )sin( ) ( W )cos( )cos( ) g( ) y cos( )cos( ) z cos( )sin( ) z sin x cos( )cos( ) x cos( )sin( ) y sin, (5) here r ( x, y, z) is the center of buoyancy. When ROV is moing, surrounding ater moes together ith ehicle so its effect is considered as added mass and inertia. Forces and moments caused by them are proportional to ehicle acceleration. For the ehicle is tested in lo speed, the added mass inertial matrix M is simplified as (Fossen, 2002): here X u, Y, a M a diag{ X u, Y, Z, K p, M q, Nr }, (6) Z, K, M and p q Nr are the hydrostatic coefficients. And the added mass Coriolis and centripetal matrix is: Z Y Z 0 Xuu Y Xuu 0 C () 0 Z Y 0 Nrr Mqq Z 0 Xuu Nrr 0 Kpq Y Xuu 0 Mqq Kp p 0, (7) esides, due to skin friction and ortex shedding, fluid brings damping force and moments hich are proportional to ehicle speed. Damping force and moments matrix is simplified as: D() diag{ Xu Xuu u, Y Y, Z Z, Kp Kp p p,, (8) M M q, N N r } q qq r rr here X u, Y, Z, K p, M q and Nr are the linear iscous hydrodynamic coefficients. X uu u, Y, Z, K pp p, M qq q and Nrr r are the quadratic iscous hydrodynamic coefficients. ROV s motion is highly nonlinear and different controllers are used to control its different degrees of freedom. In order to simplify the mathematical model, it is assumed that hen the ROV is orking, it approaches the location first ithout changing depth; then it changes depth to reach the orking point ithout changing course. Thus, the motion can be analyzed in a ertical plane and a horizontal plane respectiely. For ertical motion, only heae is considered hile for horizontal motion, only surge, say and ya are considered. Also, it is assumed that the ehicle is ell balanced and can return to zero pitch and zero roll state by itself, so p, q, and are approximately equal to zero. Thus, combined ith the equations mentioned aboe, the ROV motion identification model can be simplified as: here ( m Z ) Z Z, (9) z ( m X u ( my r X u X u u ) = ) +, (10) u u uu x ( my ) - ( m Xu ) ury Y, (11) ( IZZ + Nr ) r = Nrr + N r r + rr z, (12) Z, Z, Z, X u, X, X uu u, Y, Y, Y, N r, N r and Nrr are the hydrodynamic coefficients need to be identified. Geometric dimension of ehicle is: length 30 cm, idth 23 cm and height 23 cm. The ehicle is arranged to be a symmetrical structure, so I xy, Ixz and I yz are approximate zero hile I zz kg m. The quality m 3. Hydrodynamic Coefficients Identification Using GA is 4.5 kg. We can derie from equations (9)~(12) that the motion of the ROV is decided by forces and moments of thrusters and ater ae as ell as hydrodynamic coefficients. When applied a set of forces and moments on the ROV, generated elocities correspond to the hydrodynamic coefficients of the ROV Objectie function for Identification Associatie relation beteen measured elocities and hydrodynamic coefficients is nonlinear and noises produced by sensors also bring errors. GA can oercome these problems ith good nonlinear mapping characteristics. In order to decide hich

4 group of hydrodynamic coefficients satisfies the measured elocities best, the best matching standard beteen them should be established first, and then GA can automatically search in a range for the optimal global solutions of hydrodynamic coefficients complying ith gien elocities. With the same external forces and moments, if the cures of simulated elocities using hydrodynamic coefficients identified by GA get close to the cures of elocities measured by sensors in tank, hydrodynamic coefficients identified by GA are effectie and can be used for the controllers design for the ROV. The elocities similarity function is defined as: M ( V i ( t) V i( t))( V i( t) V( t)) i1 k, M (13) 2 2 ( V( t) V i( t)) ( V i( t) V( t)) i1 i indiiduals ill generate. The mutation probability is Through the processes before, population is reneed and fitness function max1 is calculated. If max1 max 0, then max 0 max1. When iteratie times reach t max or max 0 does not change for fie generations, iteration stops; otherise, selection, crossoer and mutation processes should be repeated until iteration reaches stopping criteria. 4. Experiments and Results The ROV motion control and data acquisition system is shon in Fig. 2. The management platform is designed for adjusting the control instructions and ROV motion states obseration. here V [ u0, 0, 0, r0] is the measured elocity and acceleration matrix. V is the mean measured alue. V [ u1, 1, 1, r1] is the simulated alue and V is the mean simulated alue. The closer k [ u,,, r] gets to [1, 1, 1, 1] the better the identification quality. GA can only optimize single objectie function. So, u,, and r are combined together to be a eighted fitness function for GA: best 1* u 2* 3* 4* r, (14) here eights 1, 2, 3 and 4 are 0.2, 0.2, 0.25 and Since parameters u, are coupled ith r, proportion of r is set to be bigger than u and GA Algorithm efore identification, a set of hydrodynamic coefficients tested from PMM are gien as the searching region. 10 % of the ranges of the original alues are chosen as the searching scope for GA. Generate n parent indiiduals in searching region randomly and assign maximum number of iteration t max. Calculate the initial fitness function max 0. Conert indiiduals to gene strings using binary coding method. Then stochastic tournament method is used to select a pair of indiiduals each time and the one ith better fitness is inherited to the ne generation. This operation is repeated until the number of ne generation reaches n '. In order to maintain good characteristics of parent and expand group diersity, indiiduals pair randomly and change part of their chromosomes at a single point. The crossoer probability is 0.5. When inherit from parent, deiation may happen in certain probability and ne Fig. 2. ROV system. The position, elocities and attitude information of ROV are obtained by inertial sensor 3DM-GX3-45 hich contains Kalman filter itself so the accuracy of data is improed. All of the motion state of the ROV is transmitted by ireless module to the on-earth management platform. GA identification need fixed searching region to find the best solutions for problems, so hydrodynamic coefficients obtained by PMM are chosen as optimizing references. Then combined ith tests in ater, GA is independent of the deterministic or stochastic nature of the system and the systems can be identified ithout linearly separating parameters. The coefficients identified by GA and comparisons beteen them and those obtained by PMM are shon in the Table 1. It is clear that errors of ya motion are much smaller than surge and say motion. This is mainly because ya motion is independent hile surge and say is coupled ith acceleration, so the errors are superposed for elocity. The hydrodynamic coefficients identified by GA are used to simulate elocities and acceleration of the ROV. Fig. 3-6 shos the comparison beteen measured 0, u 0, 0 and r 0 and the simulated ones 1, u 1, 1 and r 1 using hydrodynamic coefficients from GA, respectiely.

5 Table 1. Identified Results. Hydrodynamic Error PMM GA coefficients (%) Z Z Z X u X u X uu Y Y Y N r N r Nrr Fig. 3. Comparison beteen measured and simulated and error. Fig. 4. Comparison beteen measured and simulated r and error. Fig. 5. Comparison beteen measured and simulated u and error. Fig. 6. Comparison beteen measured and simulated and error.

6 In Fig. 3, the correlation coefficient of the 0 and 1 cures is ; the error ranges beteen 0.1 m/ s. Correlation coefficients for the r 0 and r 1 cures is In the Fig. 4-6, correlation coefficients for u, and r are , and , respectiely. The trends of simulated cures agree ith measured cures. The error range for r is m/ s, for u it is m / s hile for it is m / s. Velocities and acceleration identified by GA for the ROV model approximate ith the real measured motion. So, the hydrodynamic coefficients obtained in this paper are effectie and they appropriately reflect the hydrodynamic forces and moments in ROV s motion. 5. Conclusions In this paper, a dynamic model for an ROV as built. In order to reduce the number of hydrodynamic coefficients to be identified and for conenience in designing controllers, the 6 DOFs model is decoupled to a ertical plane model and a horizontal model. Hydrodynamic characteristics of the ROV are analyzed. Then GA is used to identify ROV motion. In order to erify identification alidity, hydrodynamic coefficients obtained by GA are used for motion simulation of the ROV. Simulated cures of elocities and acceleration are compared ith those measured by sensors hen the ROV is operated in tank. Results sho that simulated cures can ell follo the ariation trends of measured cures and correlation coefficient is higher than 0.9 and the errors are small. This indicates that the hydrodynamic coefficients identified in this paper agree ith the actual motion of the ROV and they are accuracy enough for further controllers design. Acknoledgments This ork as supported by Shanghai Rising-Star Tracking Program (12QH ) and Shanghai Committee of Science and Technology Foundation ( and ). References [1]. T. I. Fossen, Guidance and control of ocean ehicles, Second Edition, John Wiley and Sons Ltd., Ne York, [2]. S.. Fan, L. Lian, P. Ren and G. L. Huang, Oblique toing test and maneuer simulation at lo speed and large drift angle for deep sea open-framed remotely operated ehicle, Journal of Hydrodynamics, Vol. 24, Issue 2, 2012, pp [3]. J. Julca Aila, K. Nishimoto, J. C. Adamoski, C. Mueller Sampaio, Experimental inestigation of the hydrodynamic coefficients of a remotely operated ehicle using a planar motion mechanism, Journal of Offshore Mechanics and Arctic Engineering, Vol. 134, Issue 2, 2012, pp [4]. J. Kim, K. Kim, H. S. Choi, W. Seong, K. Y. Lee, Estimation of hydrodynamic coefficients for an AUV using nonlinear obserers, IEEE Journal of Oceanic Engineering, Vol. 27, Issue 4, 2002, pp [5]. H. Zhang, Y. Xu, and H. Cai, Using CFD softare to calculate hydrodynamic coefficients, Journal of Marine Science and Application, Vol. 9, Issue 2, 2010, pp [6]. Q. Meng, Y. Guan, A. Xie, A reie of CFD-based system identification, in Proceedings of the IEEE Control and Decision Conference, Mianyang, China, May 2011, pp [7]. M. Caccia, G. Indieri G. Veruggio, Modeling and identification of open-frame ariable configuration unmanned underater ehicles, IEEE Journal of Oceanic Engineering, Vol. 25, Issue 2, 2000, pp [8]. P. Ridao, J. atlle and M. J. Carreras, Model identification of a lo-speed UUV, in Proceedings of the 1 st IFAC Workshop on Guidance and Control of Underater Vehicles, Glasgo, Scotland, UK, April 2003, pp [9]. P. W. J. Van De Ven, T. A. Johansen, A. J. Sørensen, C. Flanagan, D. Toal, Neural netork augmented identification of underater ehicle models, Control Engineering Practice, Vol. 15, Issue 6, 2007, pp [10]. W. J. Yuan, G. J. Liu, S. F. Zhu, Identification method of hydrodynamic parameters of autonomous underater ehicle based on genetic algorithm, Journal of Mechanical Engineering, Vol. 46, Issue 11, 2010, pp Copyright, International Frequency Sensor Association (IFSA) Publishing, S. L. All rights resered. (