MODELING, DESIGN AND EXPERIMENT OF IMPROVED SUPER-MINI UNDERWATER ROBOT. Received November 2009; revised March 2010

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1 International Journal of Innovative Computing, Information and Control ICIC International c 2011 ISSN Volume 7, Number 3, March 2011 pp MODELING, DESIGN AND EXPERIMENT OF IMPROVED SUPER-MINI UNDERWATER ROBOT Xin Song 1, Zao-Jian Zou 2 and Jia-Wei Ye 3 1 School of Naval Architecture, Ocean and Civil Engineering 2 State Key Laboratory of Ocean Engineering Shanghai Jiao Tong University No. 800, Dongchuan Rd., Shanghai , P. R. China songxsx@gmail.com 3 Department of Naval Architecture and Ocean Engineering South China University of Technology No. 381, Wushan Rd., Tianhe District, Guangzhou , P. R. China Received November 2009; revised March 2010 Abstract. To overcome the disadvantages appeared in the application of some supermini underwater robots, a simple improved design framework is proposed. A mechanical improvement scheme is proposed. An easy handle, powerful and computer aided software system including the closed-loop control algorithm is developed for solving the shortcomings that are existed in the manual operation. The modeling of underwater robot plays an important role in the closed-loop control design. The hydrodynamic derivatives are estimated by the experiment based on the decoupled motions in different directions. A new self-tuning PID algorithm is proposed for the controller design. The experimental results in different environment demonstrate the performance. Keywords: Modeling, Autonomous control, Underwater, ROV, Self-tuning 1. Introduction. Until now, many underwater robots including remotely operated vehicle (ROV) and autonomous underwater vehicles (AUV) have been developed and applied for detection, salvage, mine hunting, fishery study, etc. More recently, there has been a trend to use the super-mini underwater robots in lakes and rivers. The implementation of AUV is complex as the individual intelligent platform. AUV is generally expensive and has not been popularly applied in the practical works. This paper mainly considers the improvement of ROV. For the low cost and easy manual operation, ROV draw the attention of many users. Recent results show that the super-mini underwater robots have significant potential to carry out the tasks such as the target reconnaissance, inspection, repair of underwater structures, etc. However, due to the reply from the pilots, the shortcomings of some underwater robots come out in practical tasks, such as the steady station-keeping near the dyke or bridge piers. The drift, waves, etc always cause the troubles. The manual operation is often impossible to catch up the time-varying disturbance, as the microoperation is uneasy to handle by the pilots. In this paper, an improved design framework is proposed including two parts. One improvement is focused in mechanical design. The other improvement includes the underwater robot deployed with integrated, intelligent, close-loop control platform such as the implementation of the obstacles avoidance, the steady station-keeping, etc. This close-loop control is consisted of a new self-tuning PID controller. The pilots only need to give easy commands such as navigation, station-keeping or depth-keeping, etc. Meanwhile, this computer aided control platform requires proper dynamic models. 1109

2 1110 X. SONG, Z.-J. ZOU AND J.-W. YE Considering the previous studies [1-3], the dynamic models are crucial to the realization of their prediction performance, precision autopilots. Although there are many works concerning underwater robot, the modeling and control design remains very difficult. The existed dynamics of underwater robots are well clear and understood, whereas they are difficult to handle for practical design and control purposes. The problem includes many nonlinearities and modeling uncertainties. In addition, unlike space or terrestrial environment, the underwater one typically requires more restrictive conditions and sensor limitations (e.g., weight, leaks, acoustic variability, corrosion), especially for this supermini type. In order to ensure the underwater robots accomplish the missions successfully, they should be robust and reliable both in electrical and mechanical design. Modeling is considered to be a general way in describing the corresponding physical terms. The software and hardware configuration are in relation to the functional implementation. Simulation is generally processed for the dynamics and control algorithms. This main purpose is to accurately replicate the actual robots response, subject to a variety of disturbances, such as waves, drift, etc. This is suitable for the theoretical analysis of the dynamics and motion controller design. In general, modeling techniques tend to consist of two ways [4]. One is the predictive methods based on either computational fluid dynamics [5,6]. The other is the experimental techniques including the common identification process [3] or the intelligent ways such as the neural network method [7,8], etc. The general rule for modeling and simulation is to closely match the corresponding physical system. In this paper, the simulation is directly connected to the system hardware and software and the control algorithm is applied and tested in real application. In this paper, the importance of this work is to solve the shortcomings of some previous underwater robot. The main objective is to summarize the research on the mechanical design improvement and the configuration of the software architecture including the modeling, data processing, control algorithm, etc. The detailed modeling steps are presented. A drift disturbance is considered in the experiment, which is always ignored in the previous works. A new self-tuning PID controller is proposed and compared with other control algorithms in the same working environment. The experimental results demonstrate its performance. The rest of this paper is organized as follows: Section 2 develops the mechanical improvement work; Section 3 develops the framework of the software; Section 4 describes the modeling and parameter identification technologies; Section 5 presents a new self-tuning PID control algorithm and the constraints within this method. In Section 6, the results of the experiment in the pool with and without time-varying drift disturbance are presented and discussed. The future works are pointed out. The final section provides concluding remarks. 2. Improvement of the Mechanical Structure. The improvement design is aimed to solve the problems appeared in the application. The main disadvantages can come into two categories: 1) the shortcomings in mechanical design; 2) the manual operation is not enough and the computer aided software system is not provided. In order to lower the risk from this whole closure design, the supporting frame and anti-crash metal frame are added to prevent the super-mini underwater robot from the accidental collisions. Some special technologies are applied to the inner devices protection and the preventability of the magnetic interference. Moreover, some underwater robots are equipped with two bilateral forwarding propellers and one propeller for heave motion (see Figure 1). Based on the theory study, they can realize the surge, yaw motion. Through the adjustment of the yaw angle, they can realize the motion in every direction. In the environment with the negligible disturbance, this mode of propulsion is suitable though the radius of gyration is large. However, when the underwater robot is working near dykes

3 MODELING, DESIGN AND EXPERIMENT OF UNDERWATER ROBOT 1111 or bridges, etc, the shortcomings become serious and they are impossible to accomplish the tasks. A simple improvement is to add two lateral propellers (see Figure 2). Figure 1. Original propulsion mode Figure 2. Improved propulsion mode The aim of these two propellers is to solve the problems caused from the terrible radius of gyration due to the complex waves or current disturbance and enhance the propulsion capabilities, the station-keeping inspection abilities. For example, when the underwater robot is expected to survey the corrosion situation of the underwater building, it should keep the same yawing angle and steady posture, as the camera is located in the front part of the body. Thus, the bilateral forwarding propellers need to resist the drift disturbance. Unfortunately, the force is obviously not enough for the station keeping. With the improved forwarding propulsion mode, more practical propulsion choices are provided. The experimental results demonstrate the effectiveness. 3. Software Architecture. For the second shortcoming mentioned in part 2, the computer aided close-loop control software with easy and visual manipulator interface is proposed and developed. Some previous underwater robots are operated with the manual operation box which includes the power circuit, joystick circuit, depth control switch, light, camera, LCD, other feedback lights, etc. Though there are a number of devices, the open control framework remains not enough to help the pilots to master the underwater robot well. If the underwater robot is cruising in the long distance, it may work well with the manual operation box. However, if it moves in a relatively small area with some obstacles avoidance [9] or station-keeping movement, the manipulator should be very professional to control it with the operation box through the LCD images and some sensors feedback data. Generally, it is not applicable for the common user who only needs an easy handling device to replace the divers. In order to solve the weakness shown in the application, a closed-loop control software is developed with respect to integrate the complex manual operations into simple commands such as the station-keeping command, depth holding command, etc. This software is aimed to support complex tasks. The high-level computer aided system is built upon a global shared memory that allows the underwater robot to deal with the periodic tasks and regular tasks. Through the communication with manual operation box, different tasks can be processed in high-level computer software and the commands can be transmitted into the underwater robot directly. Meanwhile, the pilot can easily choose the intelligent self-control methods or the semi-manual operation through the human-computer interaction techniques. In this research, the high-level control software is implemented based on LabVIEW platform, which is a visual programming language from National Instruments Company. This whole control software consists of several parts including station-keeping

4 1112 X. SONG, Z.-J. ZOU AND J.-W. YE module, sensor data processing module, depth module, etc. The detailed software architecture is shown in Figure 3. Figure 3. Software architecture 4. Modeling and Parameter Identification. Underwater robot model is conveniently represented using nonlinear series of first order differential equations of motion. Generally, six degrees of freedom are defined as surge, sway, heave, roll, pitch and yaw. The globally inertial referenced frame comprises six positions and attitude components. The mathematical model of an underwater robot can be expressed with respect to a globally inertial referenced frame, by the nonlinear equation of motion in matrix form: M(η) η + C(η, η) η + D(η, η) η + g(η) = J T (η)τ, (1) η = J(η)v (2) where η = [x, y, z, ϕ, θ, ψ] T is the position and attitude vector; M(η) R 6 6 is the inertial matrix including adding inertial part; C(η, η) η R 6 is the centripetal and coriolis term; D(η, η) η R 6 is the damping term including the quadratic and linear drag terms; g(η) R 6 is the hydrostatic restoring force terms; J(η) R 6 6 is the transform matrix between the body-fixed reference and the earth-fixed reference; τ R 6 1 is the thruster input vector. More detailed models of the underwater dynamics are reported in [3,10,11]. In these papers, the moments of inertia I xx, I yy, I zz, etc are introduced. The external forces and moments such as the mentioned hydrodynamic drag force, thruster force, hydrodynamic added mass forces, etc can be described in terms of the corresponding hydrodynamic coefficients. These coefficients can be found in the reference [3]. As the underwater robot in this research is symmetric about x-z plane, close to symmetric about y-z plane, the motions in surge, sway, pitch and yaw are assumed to be decoupled [3]. Due to the low speed of the underwater robot, the surge and heave motions are decoupled as the coupling effects can be negligible though the x-y plane is not symmetric. Many experiments verified this assumption. The inertia matrix includes the mass and moments of inertia. In this research, the common oscillation experiment with a small swing angle around the principle axis has been performed to determine the moment of inertia I xx, I yy, I zz (See Table 1). Generally, the other hydrodynamic derivatives are calculated experimentally in towing tank tests or in flumes with controlled flowing water. The hydrodynamic forces are recorded and the data is sampled by the data acquisition system under the condition of the controlled flowing water.

5 MODELING, DESIGN AND EXPERIMENT OF UNDERWATER ROBOT 1113 Table 1. Moment of inertia Value Units I xx kg.m 2 I yy kg.m 2 I zz kg.m 2 The thruster input consists of the forces and moments acting on the underwater robot. Forward and backward thrusters are generally non-symmetrical [12], unless a special design is implemented. Considering the thruster s energy balance of the control volume, the simplified nonlinear equations are given as follows: ṅ = βτ m an n, (3) T = C t n n, (4) where n is the rotational motor speed vector, τ m is the input torque provided by the thruster s motor, β, a and C t are thruster constants, T is the thrust force. In this research, there are five thrusters in the underwater robot. Each one has the individual driver that controls the rotational speed. Since the propeller diameter, mass and the motors are small, the speed of the thruster in Equation (3) is much faster than the underwater robot. So the dynamics are neglected. Only the parameter C t needs to be identified. Here, the least square method is applied to compute the coefficients for the different thrusters. The results are shown in Table 2. Table 2. Thruster coefficients Thruster C t (N) Forward Backward Horizontal Lateral Vertical Following the traditional identification methods, a series of experiments have been done to get the drag coefficients, etc. Some coefficients that cannot be estimated by the experiment are estimated by the theoretical calculation. Note that the linear drag is much smaller than quadratic drag. Therefore, the linear drag can be neglected [3]. Here, some coefficients are listed in Table 3. Table 3. Coefficients Added mass X u Y v Zẇ Kṗ M q Nṙ Quadratic drag coefficients X u u Y v v Z w w K p p M q q N r r Close-loop Control Algorithm. The control algorithms of robot include many parts. Many papers present the corresponding control algorithm such as the PD, PID method [10], fuzzy logic [14,16], neural network [17] and sliding mode method [13,15,18,19],

6 1114 X. SONG, Z.-J. ZOU AND J.-W. YE etc. Since the implementation of PID control method is easy and effective, PID control algorithm is applied in this research. Meanwhile, in this experiment, this control algorithm is applied in the realization of keeping the yaw angle. The original super-mini underwater robot in this research chooses the open control framework. When the outside disturbance is complex, the motion can hardly be well controlled. In order to satisfy the actual work requirement, the yaw angle keeping algorithm is applied to enhance the super-mini underwater robot to work normally in the path keeping or the observation of the fixed target, etc. In this research, the yaw angle keeping algorithm is developed by a new self-tuning PID control algorithm and the dynamic motion models. In order to testify this algorithm, the underwater robot is closely observing some fixed targets with and without time-varying flow disturbance. With respect to the dynamic model, the following motivated assumptions are given: 1) The underwater robot moves at low velocity; 2) The damping force is non-coupling; 3) The linear damping force is negligible; 4) The gravity and the buoyancy are nearly in balance; 5) Water kinetic coefficient is constant; 6) In the parts of the roll and pitch angle, the system is stable, and therefore the hydrodynamic equations are not considered in these directions. Refer to the definition of motion Equation (1), the motion parameters of the equations can be obtained with the following characteristics: C.1 Inertia matrix is symmetric and positive, defined as M(η) = M T (η) η R 6. The positive constants m m and m M compose m m M(η) m M ; C.2 Ṁ(η) 2C(η, η) is a skew symmetric matrix; C.3 Ṁ(η) = C(η, η) + CT (η, η); C.4 Damping matrix D(η, η) is strictly positive and within limited boundary; C.5 Coriolis matrix C(η, η), η is in limited boundary and η is linear, as x R 6. C(η, η) = C(η, x) η always exists. There is positive number k c that keeps C(η, η) k c η. In general, the underwater robot simulation neglects the outside wave interference and considers the impact of water flow. The water density is assumed constant and the sand stone effects are ignored. Meanwhile, the vertical inclination angle is assumed less than π/2 in this experiment. Since the kinetic knowledge of the underwater robot is limited, the design for precise control and navigation is very difficult. Therefore, the dynamic models of the underwater robot for the system simulation and control system kinematics are helpful. The parameters of underwater robot dynamic equation are non-linear, coupled, timevarying and unstable. Thus, it is difficult to obtain accurate hydrodynamic equations. On the other hand, if there is the interference of drift, etc, it is also difficult to get the accurate model. Here, equation δ = λq(η)v is introduced to express the unknown constant forces of the sensors, etc, where v = [v B v Sx v Sy v Sz ] T. v is an unknown constant parameter vector, v B is an unknown buoyancy and the three parameters v Sx, v Sy, v Sz represent the unknown constant force of the sensors. Q(η) R 6 4 is a regression matrix, λ R 6 6 is a strictly positive matrix related to the adaptation rate. Assuming that the underwater robot is moving near the target and only yaw angle is changing, the unknown buoyancy and the forces from the fixed sensors are constant. The equation of motion is presented as: M(η) η + C(η, η) η + D(η, η) η + g(η) + δ = J T (η)τ. (5) The control model is shown as follows: τ = J T (η) [ K P η K I ] η(t)dt K D η + g(η) + λq(η)ŵ, (6)

7 MODELING, DESIGN AND EXPERIMENT OF UNDERWATER ROBOT 1115 where K P, K I, K D R 6 6 is the symmetric positive definite matrix, η = η η d (η d is predefined position) is the position error. Supposing that ˆv is the estimate of v, the adaptive self-tuning parts are given as follow: ŵ = LQ T (η)( η + b η + ρs), (7) ṡ = η, (8) where L R 4 4 is the positive matrix, b and ρ are the positive constants. Theorem 5.1. Considering the control system (5) combines with the control law (6) and the adaptation law (7) (8), if the condition as follows: K Dm + D m K IM 2 b 2 (K DM D M C M 2M M ) ρ 2 (M M + C M + K DM + D M ) > 0, (9) bk P m b 2 K DM b 2 K IM b 2 D M b 2 C M ρ 2 M M ρ 2 K P M > 0, (10) ρk Im K IM 2 b 2 K IM ρ 2 C M ρ 2 K P M ρ 2 K DM ρ 2 D M > 0, (11) are satisfied, then the system is globally asymptotically stable except the singular point θ = ±π/2. Proof: Considering the Lyapunov function V = 1 2 ηt M(η) η ηt K P η + b η T M(η) η + ρs T M(η) η + λ 2 wt L 1 w, (12) with w = ŵ w. Differentiating V and substituting dynamics Equation (5) and control model (6) into V yields V = η T [ K P η K D η K I s D(η, η) η C(η, η) η] ηt Ṁ(η) η + η T K P η + b η T [ K P η K D η K I s D(η, η) η C(η, η) η] + b η T M(η) η + b η T Ṁ(η) η + ρṡ T M(η) η + ρs T Ṁ(η) η + ρs T [ K p η K D η K I s D(η, η) η C(η, η) η] + ( η + b η + ρs) T λq(η) w + λ w T L 1 w. (13) By using character C.2, C.3 and the Equation (7), one can get V = η T K D η η T K I s η T D(η, η) η b η T K P η b η T K D η b η T K I s b η T D(η, η) η + b η T C T (η, η) η + b η T M(η) η + ρṡ T C T (η, η) η ρs T K P η ρs T K D η ρs T K I s ρs T D(η, η) η. (14) Considering the following inequalities holds: η T K I s 1 2 ( ηt K I η + s T K I s) 1 2 K IM η K IM s 2,. ρs T D(η, η) η ρ 2 [st D M s + η T D M η] ρ 2 [D M s 2 + D M η 2 ]

8 1116 X. SONG, Z.-J. ZOU AND J.-W. YE Then, one obtains: V (K Dm + D m K IM b 2 2 (K DM D M C M 2M M ) ρ 2 (M M + C M + K DM + D M ) η 2 (bk P m b 2 K DM b 2 K IM b 2 D M b 2 C M ρ 2 M M ρ 2 K P M) η 2 (15) (ρk Im K IM 2 b 2 K IM ρ 2 C M ρ 2 K P M ρ 2 K DM ρ 2 D M) s 2 Finally, considering conditions (9) (10) (11), V is negative and vanishes if and only if ( η, η, s) = (0, 0, 0). The theorem is proved. 6. Experiment of Super-mini Underwater Robot. The super-mini underwater robot experiment was carried out in the pool of South China University of Technology. The experiment situation is presented in Figure 4. The parameters of this super-mini robot in this research are given as follows: The size is 31 cm 22.5 cm 21 cm; The weight in the air is 60 kg; The max navigation speed is 2.6 knot; The max diving depth is 152 cm. Figure 4. Experiment of the super-mini underwater robot Considering the underwater robot is working closely to the target, the dimension of the controller is reduced to four. The parameters K P, K I, K D are defined as follows: K P = diag(10, 10, 100, 5), K I = diag(1, 1, 2, 0.4) and K D = diag(2, 2, 5, 0.04). Let L = 12I, b = 0.62, ρ = 0.3, these parameters satisfy the constraint condition. The underwater robot is moving from the beginning position [x 0, y 0, z 0, ψ 0 ] T = [0.1, 0.1, 0.75, 100] T to the destination position [x, y, z, ψ] T = [0, 0, 0.75, 20] T. Introducing the equation ŵ(t + T ) = ŵ(t) + ŵ(t) T, where ŵ(0) = 0. The adaptive self-tuning parameter ŵ is calculated by Euler equation. In the experiment, the yaw angle command is changed from 100 degrees 56 degrees 20 degrees. To evaluate performance of the proposed control system, three types of experiments have been done with respect to the algorithms including traditional PID controller, new self-tuning PID controller and sliding mode control (SMC) with smooth control. SMC controller is presented in [19] and the parameters are defined as λ = 0.75, ρ = 9.2.

9 MODELING, DESIGN AND EXPERIMENT OF UNDERWATER ROBOT 1117 Each type of experiment includes two different situations. One chooses the experiment without drift disturbance. The other one considers the drift disturbance. The timevarying drift speed is predefined as V Drift = 0.15(sin(4πt)+1)m/s and the wave disturbance is ignored. The yaw angle results in the experiment are recorded, shown in Figure 5 and Figure 6. Figure 5 shows the experimental results between self-tuning PID and PID. Figure 6 shows the results between self-tuning PID and SMC with smooth control. Figure 5. Controller results comparison between self-tuning PID and PID Figure 6. Controller results comparison between self-tuning PID and sliding mode controller with smooth control

10 1118 X. SONG, Z.-J. ZOU AND J.-W. YE From the results without drift disturbance, all controllers can reach relatively steady status. The stable time grows up when the command angle reduces. At 100 degrees and 56 degrees, these three algorithms can control the yaw angle to the command angle. However, at 20 degrees, the underwater robot cannot keep the posture at command angle. It swings in a short range and becomes relatively steady. In the experiment with drift disturbance, the tendency of yaw angle is similar to the former results. However, the vibration in this experiment is larger as the angle errors grow up and the stable time becomes longer. The weight of this super-mini underwater robot is small. The disturbance from the cables and others are relatively large. When the yaw angle is at 180 degrees, the cable is rightly behind the underwater robot. Thus, the smallest disturbance is attached to the yaw motion. However, when the underwater robot reduces angle, its front part is moving toward the cable. The angle errors increase and the vibration becomes bigger as the resistance and its moment of the cable grow up. When the command angle is at 20 degrees, the disturbances are beyond the controllers abilities of regulation. Thus, the underwater robot keeps a small range of swing in a relatively stable state, rather than the other two situations that the underwater robot can finally stabilize and keep the yaw angle after a period of adjustment. From the results, comparing with other two algorithms, the new self-tuning PID control algorithm shows obvious advantages as the errors are smallest and the stable times are shortest. The results of SMC with smooth control are better than PID control. Though the self-tuning algorithm cannot keep the angle at 20 degrees, the vibrations and the angle errors are the smallest. Thus, the robustness is the best among these algorithms. These results can demonstrate the performance and effectiveness of this new algorithm. Comparing with the original underwater robot, the whole improvement scheme can largely enhance its working abilities. The operation becomes easy and the steady observation can be realized quickly. This new design can help the underwater robot meet higher working requirement, such as the observation task in these experiments. Unfortunately, the original design can hardly satisfies them. For the shortcomings in current work, the mathematic models of the cable are important. A prediction and compensation algorithm of the cable and other disturbance are necessary to be considered in future. A fast station-keeping algorithm and the parameters optimization algorithm should also be further studied considering more complex nonlinear disturbance. 7. Conclusion. In this paper, the modeling, design, control algorithms and data processing algorithm of super-mini underwater robot are discussed in detail. The main advantages of these new improvements are summarized in two categories. One is the mechanical part. The other is the software part. An improvement scheme of mechanical structure is proposed. The main features are to reduce the radius of gyration and increase the capabilities of anti-risk. This design can make the underwater robot become more applicable in the complex environment. A closeloop control software is proposed. The easy commands that are instead of the complex manual operations reduce the risk of low response of pilots and help the underwater robot easy to handle. A new self-tuning PID controller is proposed for the dynamic yaw angle control. This new algorithm is aimed to estimate the unknown constant forces, etc. This control algorithm also realizes a simple disturbance estimation and compensation. The way of measurement and calculation of hydrodynamic coefficients, etc are presented. The results of coefficients in this research are given.

11 MODELING, DESIGN AND EXPERIMENT OF UNDERWATER ROBOT 1119 To evaluate the effectiveness and feasibility of the improvement scheme, several experiments with and without the time-varying drift disturbance have been carried out. The experimental results are discussed and also demonstrate the performance of the new control algorithm. Finally, shortcomings in current work and further research works are pointed out. Acknowledgment. This work is partially supported by the National Natural Science Foundation of China (Grant No ) and National 863 High-Tech R & D Program of China (Grant No. 2007AA11Z250). The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation. REFERENCES [1] J. Yuh, Learning control for underwater robotic vehicles, IEEE Control Systems Magazine, vol.14, no.2, pp.39-46, [2] J. Yuh, Underwater Robotic Vehicles Design and Control, TSI Press, Albuquerque, [3] T. I. Fossen, Guidance and Control of Ocean Vehicles, John Wiley & Sons, [4] K. Goheen, Techniques for URV modeling, in Underwater Robotic Vehicles Design and Control, J. Yuh (ed.), Albuquerque, TSI Press, [5] H. Suzuki, N. Kato and T. Katayama, Motion simulation of an underwater vehicle with mechanical pectoral fins using a CFD-based motion simulator, Proc. of the International Symposium on Underwater Technology, Tokyo, Japan, pp , [6] T. Sunlin, N. Takeshi, T. Blair et al., Estimation of the hydrodynamic coefficients of the complexshaped autonomous underwater vehicle TUNA-SAND, Journal of Marine Science and Technology, vol.14, no.3, pp , [7] P. V. D. Ven, T. Johansen, A. Sorensen et al., Neural network augmented identification of underwater vehicle models, Control Engineering Practice, vol.15, no.6, pp , [8] P. V. D. Ven, C. Flanagan and D. Toal, Identification of underwater vehicle dynamics with neural networks, Proc. of Conference on OCEANS 04 MTS/IEEE, vol.3, pp , [9] L. H. Jiang, M. C. Deng and A. Inoue, Obstacle avoidance and motion control of a two wheeled mobile robot using SVR technique, International Journal of Innovative Computing, Information and Control, vol.5, no.2, pp , [10] D. A. Smallwood and L. W. Louis, Model-based dynamic positioning of underwater robotic vehicles: Theory and experiment, IEEE Journal of Oceanic Engineering, vol.29, no.1, pp , [11] T. Fossen, Marine Control Systems Guidance Navigation and Control of Ships Rigs and Underwater Vehicles, Marine Cybernetics, Norway, [12] J. N. Newman, Marine Hydrodynamics, MIT Press, [13] X. Song, J. Ye and W. L. Min, Application of the integral sliding mode controller with fuzzy logic to submersible vehicle, International Journal of Innovative Computing, Information and Control, vol.3, no.4, pp , [14] Y. H. Cheng, X. S. Wang and R. H. Lei, A fuzzy control system for path following of mobile robots, ICIC Express Letters, vol.3, no.3(a), pp , [15] J. Guo, F. C. Chiu and C. C. Huang, Design of a sliding mode fuzzy controller for the guidance and control of an autonomous underwater vehicle, Ocean Engineering, vol.30, no.16, pp , [16] M. M. Fateh and A. Azarfar, Improving fuzzy control of robot manipulators by increasing scaling factors, ICIC Express Letters, vol.3, no.3(a), pp , [17] G. Capi, Application of recurrent neural controllers for robot complex task performance, International Journal of Innovative Computing, Information and Control, vol.5, no.5, pp , [18] W. M. Bessa, M. S. Dutra and E. Kreuzer, Thruster dynamics compensation for the positioning of underwater robotic vehicles through a fuzzy sliding mode based approach, Proc. of the 18th International Congress of Mechanical Engineering, Ouro Preto, Brazil, [19] T. Chatchanayuenyong and M. Parnickkun, Neural network based-time optimal sliding mode control for an autonomous underwater robot, Mechatronics, vol.16, no.8, pp , 2005.