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Model-based adaptive control system for autonomous underwater vehicles a

Osama Hassanein , Sreenatha G. Anavatti

b,⁎

c

b

, Hyungbo Shim , Tapabrata Ray

a

ASD, Abu Dhabi Polytechnic, Abu Dhabi, UAE b SEIT, UNSW Canberra, Australia c Department of Electrical and Computer Engineering, Seoul National University, South Korea

A R T I C L E I N F O

A BS T RAC T

Keywords: Hybrid Neuro-Fuzzy Network AUV M odel-based adaptive controlSystem identiﬁcation Auto generating mechanism

The paper deals with the development of indirect adaptive controllers based on Hybrid Neuro-Fuzzy Network (HNFN) approach for Autonomous Underwater Vehicles (AUVs). The non-linear, coupled and time-varying dynamics of AUVs necessitates the development of adaptive controllers. The on-line identiﬁcation and adaptation of the controller is carried out using the HNFN approach. The methodology uses the input-output data to come up with a structure for the controller and optimal adaptation of the parameters to achieve the required accuracy. The Semi-Serial-Parallel-Model is employed both for identiﬁcation and control. Initial validation of the identiﬁcation results are carried out numerically using a mathematical model. Hardware-inloop (HIL) simulations are presented to validate the controller before carrying out the experiments. Experimental results show that the proposed controller is capable of suitably controlling the AUV in real environment and demonstrate its robust characteristics.

1. Introduction Autonomous Underwater Vehicles (AUVs) are ideal platforms for aquatic search and rescue operations and exploration, some of which necessitate very strict positioning and path control. This is a challenging task since the AUV's dynamics is inherently nonlinear and time variant, i.e., its mass and buoyancy change according to its working conditions. In addition, AUVs are also subjected to uncertain external disturbances that alter the hydrodynamic forces and moments as they depend on the environmental conditions as well as their velocities, shapes and sizes (Fossen, 1994). The control accuracy provided by guidance and control system is the basis for the successful completion of AUV missions. Conventional controllers with ﬁxed gains fail to guarantee highquality responses of the overall system when signiﬁcant changes occur in the vehicle dynamics and its environment (Zaho and Yuh, 2005). However, intelligent adaptive control has proven to be successful in several industrial nonlinear applications (Medsker and Jain, 1999). In addition, adaptive control provides an ability to re-adjust the controller parameters on-line to achieve the required performance when the process parameters are unknown and vary over time (Puttige, 2008). Adaptive control is also useful because AUVs are usually re-ﬁtted with new equipment and adapted for diﬀerent missions that change their static and dynamic characteristics. There are two diﬀerent approaches of adaptive control (Astrom and

⁎

Wittenmark, 1994), direct and indirect adaptive control. In the former, which is implicit, the controller parameters are calculated based on the error between the reference and actual output values. In indirect adaptive control, the plant and its parameters are identiﬁed online and used to adjust the controller parameters (Wang et al., 2002). In this scheme, the identiﬁed model is assumed to be the true plant and used to calculate the controller parameters and is called explicit adaptive control. In the direct adaptive control category, Model Reference Adaptive Control (MRAC) is the most appropriate technique for compensating the nonlinearities and uncertainties of underwater vehicles (Santhakumar and Kim, 2011). However, the MRAC technique may have reduced performance due to modelling errors when the plant is under the inﬂuence of input disturbance (Datta and Ioannou, 1994). As this technique has no direct mechanism for validating the adapted controller prior to its use on the plant, for complex nonlinear systems, this may lead to results with inferior responses. In an indirect adaptive control method, an identiﬁer model of the plant is used to aid the parameter adaptation process of the controller (Wang et al., 2002). Indirect adaptive control is deﬁned as a technique for applying some system identiﬁcation method to obtain a model of the process and its environment from input-output experiments and use it to design a controller. It uses a model of the process where the error between the model and process outputs is used to adjust the identiﬁcation model parameters and both the plant output and

Corresponding author. E-mail addresses: [email protected] (O. Hassanein), [email protected] (S.G. Anavatti), [email protected] (H. Shim), [email protected] (T. Ray).

http://dx.doi.org/10.1016/j.oceaneng.2016.09.034 Received 30 June 2015; Received in revised form 29 July 2016; Accepted 18 September 2016 0029-8018/ © 2016 Elsevier Ltd. All rights reserved.

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HNFN along with numerical results. Next, Section 4 presents the AUV control system design. The numerical results and experimental results are also discussed. Section 5 concludes the paper.

identiﬁcation model output are used to tune the gains of the controller. To build an eﬃcient controller, it is essential to capture the dynamics of the operating vehicle as accurately as possible. When the dynamics are nonlinear and the parameters time varying, indirect adaptive control is the most suitable approach. Hence, the system identiﬁcation is the ﬁrst stage in indirect adaptive control design. The development of a dynamic positioning system for ROVs is described by Bessa et al. (2010). The adapted approach was primarily based on the SMC strategy and enhanced by an adaptive fuzzy algorithm for uncertainty compensation. An Adaptive Fuzzy SMC (AFSMC) based on the decomposition method, using expert knowledge for Underwater Flight Vehicle (UFV) depth control, a Fuzzy Basis Function Expansion (FBFE) and a PI-augmented sliding signal, has been proposed in Kim and Shin (2005). In addition, Kim and Shin (2007) developed an Expanded Adaptive Fuzzy SMC (EAFSMC) using expert knowledge and the fuzzy basis function expansion. The proposed EAFSMC, PID and AFSMC controllers were compared, with the simulation results. Using an adaptive NN control scheme as a controller for controlling a UUV in 6-DOF is presented by Kodogiannis (2006), the performance of the adaptive controller is evaluated via computer simulation. Shi et al. (2007) described the design and application of a NN-based adaptive control scheme for an AUV’s depth control system. The unknown nonlinearity is approximated by a feed-forward NN, the parameters of which were adaptively adjusted on-line for driving the AUV to cruise at a pre-set depth. An adaptive NN (Brandt and Lin, 1999; Saikalis and Lin, 2001) is applied to control an AUV with three NNs adapted by Adaptive Interaction (ANNAI) and developed to control the heading, depth and advance speed of the vehicle in a decoupled control scheme (Phung-Hung and Yun-Chul, 2009). The Naval Postgraduate School (NPS) AUV is selected as a case study under controlling of NN in (Kuljača et al., 2009; Amin et al., 2010). Kuljača et al. (2009) presented an adaptive multi-layer NN controller for the high-precision manoeuvring of underwater vehicles in which the Neuro-control system worked with the conventional controllers LQG and PID. An on-line Multi-layer Perceptron NN (OMLPNN) which calculates forces and moments in the Earth's ﬁxed frame to eliminate the tracking errors of AUVs has been developed (Amin et al., 2010). Intelligent adaptive controllers that can learn from the input-output data of the system are desirable to make them platform free tools. The design of adaptive controllers for unknown dynamics requires the existence of suitable system identiﬁcation models of the AUV. Hence, the main objective of this research is to design an indirect adaptive controller for the AUV based on the input-output data of the identiﬁed model in order to demonstrate its real-time application for AUVs to achieve autonomous manoeuvre. A universal mechanism for identifying nonlinear physical systems with disturbances and uncertainties using the HNFN technique is proposed in Osama et al. (2013a, 2013b). It is an auto-generating mechanism with entropy-based DE modelling developed to generate a system model with an on-line tuning capability. This mechanism oﬀers a universal black-box tool for generating the system identiﬁcation and it is used in this research in order to design the indirect adaptive controller for Canberra AUV. The controller design is based on the same procedure and follows similar steps as discussed in the identiﬁcation process (Osama et al., 2013a, 2013b). Since one of the important objectives is to demonstrate the realtime implementability of the proposed indirect adaptive control scheme, validations using Hardware-In-Loop (HIL) simulations are carried out. The HIL simulations show that the scheme is feasible in real-time. Finally, experiments using the proposed algorithm to control the 6-DOF UNSW Canberra AUV's dynamics are discussed. The experimental results show that the identiﬁcation mechanism and adaptive controller are capable of suitably controlling the AUV in a real environment and demonstrate its robust characteristics. Section 2 describes the proposed model based adaptive control system. Section 3 presents the identiﬁcation for the AUV using the

2. Model-based adaptive control system An adaptive control system can be deﬁned as a feedback system with the capability to adapt its characteristics in a dynamic environment in accordance with a speciﬁc criterion (Puttige, 2008). Adaptive controllers learn to improve their performance through observations of the process under control. Direct adaptive controllers use the error between the reference input and the process output to adjust the controller parameters. Indirect adaptive controllers use a model of the process where the error between the model output and the process output is used to adjust the identiﬁcation model parameters and the controller parameters are mainly based on the identiﬁed model. 2.1. Proposed controller design Fig. 1 shows the general block diagram of the process (AUV) with the controller. From the controller point of view, its input is the error between the actual and desired response, while its output, control action, is the input to the system. Three types of data should be available to apply the mechanism, input and output data of the process and the desired action supplied to the system. Then, the output data is subtracted from the desired action to calculate the error, e , caused by the system. This error, its derivative and the input data are fed to the proposed algorithm to generate the controller parameters required for controlling the system, Fig. 2. The proposed mechanism is a combination of two stages, oﬀ-line and on-line procedures. The former comprises a structure-generating phase based on an entropy measure used to adjust the controller's accuracy and a parameter-learning phase which is executed in two steps, the ﬁrst during the structure-generating phase based on supervised learning algorithms using the BP algorithm and the second, after the controller structure is generated, which uses the DE algorithm to adjust its parameters based on a diﬀerent inputoutput training data set. The second stage converts the generated controller into an adaptive controller equipped with a training algorithm... 2.2. Adaptive control system In the present research, an indirect adaptive control system is applied to the AUV control problem where the controller parameters are adjusted based not only on the error between the reference input and the process output but also on the process sensitivity which can be approximately derived from the identiﬁcation model of the process, Fig. 3. The proposed control design is based on HNFN techniques.. Generally, the sampling times required to acquire and manipulate data from the sensors are higher than that for the controller to send the control action to the system. It is important to highlight that, in the online controller; adaptation of the controller parameters is performed in parallel with the normal operation of the system. A new architecture for representing the system identiﬁcation structure, a combination of the well-known parallel model and serialparallel model architecture, the “Semi-Serial-Parallel Model” (SSPM), is presented in Osama et al. (2013a, 2013b). This model is considered as a modiﬁed nonlinear moving average model (NMA) which combines the advantaged of both parallel and serial-parallel model techniques. In Ref

e

Controller

Input data

Process

Fig. 1. Controller block diagram.

59

Output data

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Input-data Output-data

Ref-data

+

+

Controller parameters

e ∂ ∂t

Δe

Black-box tool

Fig. 2. Controller generating scheme. Fig. 4. On-line tuning of system identiﬁcation.

the SSPM, the system actual output is passed to the identiﬁer for one sample time and then the identiﬁcation model output is fed back to the identiﬁer for the next few consecutive samples. When the actual output is passed to the identiﬁer, SSPM is considered as serial-parallel model and when the output of the identiﬁcation model is fed back to the model, the system is parallel model. The advantages of this structure in overcoming noisy sensor data or unavailability of sensor data due to the sampling limitations of the sensor are shown to be minimal loss of accuracy with just one past input and one past output for identifying the system. As shown in Fig. 4, the generated model is placed in parallel with the process to be identiﬁed on-line using the actual input-output measurements of the process. A back propagation, BP, method adapts the model parameters on-line based on the error between the identiﬁed model and actual output of the process..

will be denoted by the uppercase letters X, Y and Z. u, v and w represent the forward, lateral and vertical speeds along x, y and z axes respectively. Similarly, the hydrodynamic moments on AUV will be denoted by L, M and N acting around x, y and z axis respectively. The angular rates will be denoted by p, q and r the components. The common notations for underwater vehicles according to Fossen (1994) are listed in Table 1. 3.1. AUV mathematical modelling Dynamics of AUVs, including hydrodynamic parameters uncertainties, are highly nonlinear, coupled and time varying. The rigid body dynamics can be written in component form as

X = m [u ̇ − vr + wq − xG (q 2 + r 2 ) + yG ( pq − r )̇ + zG ( pr + q )̇ ] Y = m [v ̇ − wp + ur − yG (r 2 + p 2 ) + zG (qr − p ̇ ) + xG (qp + r )̇ ]

3. AUV system identiﬁcation

Z = m [ẇ − uq + vp − zG ( p 2 + q 2 ) + xG (rp − q )̇ + yG (rq + p ̇ ) ] K = Ix p ̇ + (Iz − Iy ) qr − (r ̇ + pq ) Ixz + (r 2 − q 2 ) Iyz + ( pr − q )̇ Ixy + m [ yG (ẇ − uq + vp ) − zG (v ̇ − wp + ur )]

The modelling of the AUVs involves the study of statics and dynamics. The former is concerned with the equilibrium of a body at rest or moving at a constant velocity and the latter with a body experiencing accelerated motion (Fossen, 1994). In order to derive a 6DOF nonlinear mathematical model of the AUV, the coordinate system and deﬁnitions of the motion parameters should be provided ﬁrst. There are two reference frames for describing the position, orientation, and linear and angular velocities of an underwater vehicle. The ﬁrst is the body-ﬁxed frame, XO YO ZO , which is usually chosen to coincide with the CG of the body and is described relative to an inertial reference or Earth-ﬁxed frame, E-xyz, as shown in Fig. 5. As, for underwater vehicles, it is assumed that the acceleration of a point on the surface of the Earth can be neglected (Fossen, 1994), in this research, the Earth-ﬁxed frame is considered inertial. In this context, the position and orientation of the vehicle are described relative to the inertial reference frame and its linear and angular velocities to the body reference frame. For more details regarding to AUV mathematical model, readers refer to Osama et al. (2011, 2013a, 2013b).. Fig. 5 shows a typical underwater vehicle model. One electrical thrusters power the AUV for forward motion. Two electrical pumps used for manoeuvring in the horizontal plane. In addition, two electrical pumps help the AUV to navigate in the vertical plane. The inner box is used for carrying the sensors, battery and the electronic accessories. The hydrodynamic forces per unit mass acting on each axis

M = Iy q ̇ + (Ix − Iz ) rp − (q ̇ + qr ) Iyz + ( p 2 − r 2 ) Izx + (qp − r )̇ Iyz + m [zG (u ̇ − vr + wq ) − xG (ẇ − uq + vp )] N = Iz r ̇ + (Iy − Ix ) pq − (q ̇ + rp ) Iyz + (q 2 − p 2 ) Ixy + (rq − p ̇ ) Izx + m [xG (v ̇ − wp + ur ) − yG (u ̇ − vr + wq )]

(1)

The ﬁrst three equations represent the translational motion and the last three are the rotational motions. The general equations of motion for the AUV are derived from Newton's second law of motion. The equations of motion for underwater vehicle can be written as follows (Fossen, 1994):

MRB v ̇ + CRB (v ) v + MA v ̇ + CA (v ) v + D (v ) v + g (η) = τ

(2)

where M is a 6×6 inertia matrix as a sum of the rigid body inertia matrix, MRB and the hydrodynamic virtual inertia (added mass) MA. C (q )̇ is a 6×6 Coriolis and centripetal matrix including rigid body terms CRB (q )̇ and terms CA (q )̇ due to added mass. D (q )̇ is a 6×6 damping matrix including terms due to drag forces. G(q) is a 6×1 vector containing the restoring terms formed by the vehicle's buoyancy and gravitational terms. τ is a 6×1 vector including the control forces and moments. The rigid-body terms represent the equations of motion of the rigid body in an empty space. However, as ships and underwater vehicles require the presence of forces and moments caused by ﬂuid to

Fig. 3. Indirect adaptive controller scheme.

60

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Fig. 5. Body-ﬁxed and earth-ﬁxed coordinate system.

Table 1 Notations used for underwater vehicles. DOF

Description

Forces and moments

Linear and angular velocities

Position and euler angles

1 2 3 4 5 6

Motion in x-direction (SURGE) Motion in y-direction (SWAY) Motion in z-direction (HEAVE) Rotation about x-direction (ROLL) Rotation about y-direction (PITCH) Rotation about z-direction (YAW)

X Y Z K M N

u v w p q r

x y z Φ θ ψ

3.2.1. Added mass and inertia When a rigid body is submerged and moving in a ﬂuid, the additional inertia of the ﬂuid surrounding it is accelerated by the movement of the body and has to be considered in the equations of motion. As stated in (Antonelli et al., 2008), the eﬀect of the added mass and inertia can be neglected in industrial robotics since the density of the air is much lower than that of the moving mechanical system. However, in an underwater vehicle application, the densities of the water and vehicle are comparable; for example, at 0 °C, the density of fresh water is 1002.68 kg/m3 and, of seawater with 3.5% salinity, 1028.48 kg/m3. As a moving body accelerates the ﬂuid surrounding it, the ﬂuid exerts a reaction force which is equal in magnitude and opposite in direction. This is the added mass contribution which consists of the added mass inertia and Coriolis and Centripetal matrices, MA andCA , respectively. According to the body's symmetry in XZ-plane, MA can be represented as;

be considered, hydrodynamic terms are added to the equation while the hydrostatic terms represent the gravitational force and buoyancy that occur when a rigid body is completely or partially submerged in a ﬂuid.

MRB

⎡m ⎢ ⎢0 ⎢0 =⎢ ⎢0 ⎢ mzG ⎢ ⎣− myG

0 m 0 − mzG 0 mxG

0 0 m myG − mxG 0

0 − mzG myG Ix − Iyx − Izx

mzG 0 − mxG − Iyx Iy − Izy

− myG ⎤ ⎥ mxG ⎥ ⎥ 0 ⎥ − Ixz ⎥ − Iyz ⎥ ⎥ Iz ⎦

(3)

CRB = ⎡ 0 0 0 ⎢ 0 0 0 ⎢ 0 0 0 ⎢ m ( yG p + w ) m (z G p − v ) ⎢− m ( yG q + zG r ) ⎢ m (x G q − w ) − m ( yG q + zG r ) − m ( yG q + zG r ) ⎢ m y q z r − ( + ) − m ( yG q + zG r ) − m ( yG q + zG r ) ⎣ G G − m ( yG q + zG r ) − m ( yG q + zG r ) − m ( yG q + zG r ) 0 Iyz q + Ixz p − Iz r Iyz q + Ixz p − Iz r

− m ( yG q + zG r ) − m ( yG q + zG r ) − m ( yG q + zG r ) Iyz q + Ixz p − Iz r 0 Iyz q + Ixz p − Iz r

− m ( yG q + zG r ) − m ( yG q + zG r ) − m ( yG q + zG r ) Iyz q + Ixz p − Iz r Iyz q + Ixz p − Iz r 0

⎡ Xu ̇ ⎢ ⎢0 ⎢ Z u̇ MA = ⎢ ⎢0 ⎢ Mu ̇ ⎢ ⎣0 (4)

0 Yv ̇ 0 Kv ̇ 0 Nv ̇

Xẇ 0 Z ẇ 0 Mẇ 0

0 Yp ̇ 0 K ṗ 0 Nṗ

Xq ̇ 0 Z q̇ 0 Mq ̇ 0

0 ⎤ ⎥ Yr ̇ ⎥ 0 ⎥ ⎥ Kr ̇⎥ 0 ⎥ ⎥ Nr ̇ ⎦

(5)

The Coriolis and Centripetal matrix, CA is given by;

⎡0 ⎢ ⎢0 ⎢0 CA = ⎢ 0 ⎢ ⎢ a3 ⎢⎣− a2

3.2. Hydrodynamic forces and moments The hydrodynamic terms are composed of the added mass and inertia and damping eﬀects. 61

0 0 0 − a3 0 a1

0 0 0 a2 − a1 0

0 a3 − a2 0 b3 − b2

− a3 0 a1 − b3 0 b1

a2 ⎤ ⎥ − a1 ⎥ 0 ⎥ b2 ⎥ ⎥ − b1⎥ 0 ⎥⎦

(6)

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where

a1 = Xu ̇ u + Xv ̇ v + Xẇ w + X p ̇ p a2 = Yu ̇ u + Yv ̇ v + Yẇ w + Yp ̇ p + Yq ̇ q + Yr ̇ r + X q ̇ q + Xr ̇ r a3 = Z u ̇ u + Z v ̇ v + Z ẇ w + Z p ̇ p a4 = Ku ̇ u + Kv ̇ v + Kẇ w + K p ̇ p + Kq ̇ q + Z q̇ q + Zr ̇ r a5 = Mu ̇ u + Mv ̇ v + Mẇ w

+ Kr ̇ r a6 = Nu ̇ u + Nv ̇ v + Nẇ w + N p ̇ p + Nq ̇ q

+ M p ̇ p + Mq ̇ q + Mr ̇ r

+ Nr ̇ r

3.2.2. Damping eﬀects In general, the damping of an underwater vehicle moving in 6DOFs at high speed will be highly nonlinear and coupled. Nevertheless, one rough approximation that could be assumed due to the symmetry of the vehicle is that terms higher than the second order are negligible which suggests a diagonal structure with only linear and quadratic damping terms on the diagonal (Antonelli et al., 2008) as; ⎡ Xu + Xu | u| u ⎢ ⎢0 ⎢0 D (v ) = ⎢ 0 ⎢ ⎢0 ⎢ ⎣0

0 Yv + Yv | v| v 0 0 0 0

0 0 Z w + Z w | w| w 0 0 0

0 0 0 Kp + Kp | p| P 0 0

0 0 0 0 Mq + Mq | q| q 0

⎤ 0 ⎥ 0 ⎥ ⎥ 0 ⎥ 0 ⎥ ⎥ 0 ⎥ Nr + Nr | r| r ⎦

Fig. 6. Conﬁguration of coupled dynamics of the AUV.

The HNFN model realises a fuzzy if–then rule in the following form (Osama et al., 2013a, 2013b);

(7)

R(l ) : IF (x1 is F1l and ....................... and xn is FNl ) THEN M

yˆj = ∑i =1 wij φi (x ) = w1j φ1 + w2j φ2 + .......... +wjM φM

3.2.3. Restoring forces and moments In hydrodynamics terminology, the gravitational and buoyant forces are called restoring forces which act on the CG of the vehicle and have components along the body axes. The z-axis is taken to be positive downwards while the restoring force and moment vector in the body-ﬁxed coordinate system is deﬁned as

⎡ ⎤ (W −B ) sinθ ⎢ ⎥ −( W − B ) cosθsin ∅ ⎢ ⎥ ⎢ ⎥ − (W −B ) cosθcos∅ ⎥ gRB (η)=⎢ −( y W − y B ) cosθcos ∅+( z W − z B ) cosθsin ∅ G B G B ⎢ ⎥ ⎢ (zG W −zB B ) sinθ +(xG W −zB B ) cosθcos∅ ⎥ ⎢ ⎥ ⎣ −(xG W −xB B ) cosθsin∅−( yG W − yB B) sinθ ⎦

(9)

where xi and yˆi are the input and local output variables, respectively, FNl is the linguistic term of the precondition part with the Gaussian membership function, N is the number of input variables, wij is the link weight of the local output, φM is the basis trigonometric function of the input variables, M is the number of basis functions and j, the j th fuzzy rule. Fig. 7 shows the structure of the proposed HNFN identiﬁer for each of the sub-systems. The nodes in layer 3 receive one-dimensional (1-D) membership degrees of the associated rules from the nodes of a set in layer 2. The calculated membership value in layer 2 is;

⎛ (xi − cji )2 ⎞ ⎟ Lji(2) = exp ⎜ −0.5 (σji )2 + ε ⎠ ⎝

(8)

where W = m g is the submerged weight of the body, B = ρ∇ g the buoyancy, ρ the ﬂuid density, ∇ the volume of the body and g = [ 0 0 9.81]T the acceleration of gravity. The AUV's modelling is constructed based upon the input-output data characterised from the open-loop system results for the mathematical model described in Osama et al. (2011). As shown in Fig. 4, the outputs from the system, y, and identiﬁcation model Yr | r are fed back into the selector switch based on the sampling time of the system identiﬁcation. The output data is considered as the resulting linear or angular velocities of the vehicle taking into account the coupling eﬀect of the other degrees of freedom in that direction.

(10)

where cji andσji represent the centre and width of the Gaussian membership for the input variable xi , respectively, and ε > 0 is a small constant, the purpose of adding this to the fuzzy membership functions is that, even if σji 's=0, these functions are still well deﬁned. This modiﬁcation will make the adaptive law simpler because we do not require σji ’s≠0. As the network nodes in layer 3 receive the membership degree of the associated rule in layer 2, the output function of each is N

Lj(3) =

∏ Lji(2) i =1

(11)

where the of each rule represents the ﬁring strength the corresponding rule.. The input to a node in layer 4 is the output from layer 3 and the other inputs are calculated from the FLNN part presented in Fig. 6. Therefore, the output from that layer is calculated as

3.3. HNFN system identiﬁcation of AUV

Lj(3)

The conﬁguration of the system identiﬁcation of the AUV model shown in Fig. 6 consists of six systems that include the surge, pitch and yaw motions. The ﬁrst input to the HNFN model in the surge motion is the force required for the thruster, X, to produce the desired forward motion of the AUV corresponding to the desired pose. The second and third inputs represent the coupling eﬀect on this forward motion from the yaw and pitch motions. The last input is considered as a combination of the system or plant and identiﬁcation model outputs that represent the previous state of the model. The output from the HNFN model is the linear velocity in the x-direction, u..

M

Lj(4) = Lj(3) ∑ wij φi i =1

(12)

where wij is the corresponding link weight of the Functional Link Neural Network (FLNN) and ϕi is the Function Expansion (FE) of the input variables. The output is in the form of 62

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Fig. 7. Structure of proposed HNFN identiﬁer. R

yˆ (k + 1) =

∑ j =1 Lj(4) R ∑ j =1 Lj(3)

R

=

ENTMAX = max ENTj

M

∑ j =1 Lj(3) (∑i =1 wij ϕi ) R ∑ j =1 Lj(3)

1≤ X ≤ R (t )

(13)

where R (t ) is the number of existing rules at time t . If ENTMax ≤ ENT , where ENT is a pre-speciﬁed threshold, a new rule is generated and added to the model, otherwise, the current input-output pair belongs to the corresponding cluster. In the structure-generating phase, ENT is an important parameter as, if it is low, there are fewer rules whereas, if it is high, it leads to the learning of ﬁne clusters (i.e., more rules are generated). Therefore, its selection critically aﬀects modelling accuracy. When the membership function of a fuzzy set is equal to 0.5 for all j , the fuzzy entropy of the fuzzy set attains the maximum. It means that the threshold value belongs to the range [0, 0.5].

where R is the number of fuzzy rules and y is the output from the HNFN identiﬁer. As shown in Fig. 7, no computation is performed in layer 1 as each node in it transmits only input values to the next layer. Each fuzzy set is described by a Gaussian membership and the output function is;

⎛ ⎛ (xi − cji )2 ⎞ ⎞ R M N ∑ j =1 (∑i =1 wij φi ) ∏i =1 ⎜exp ⎜ −0.5 2 ⎟ ⎟ (σji ) + ε ⎠ ⎠ ⎝ ⎝ yˆ (k + 1) = . ⎞ ⎛ ⎛ 2 ⎛ (xi − cji ) ⎞ ⎞ R N ∑ j =1 ⎜⎜∏i =1 ⎜exp ⎜ −0.5 2 ⎟ ⎟ ⎟⎟ (σji ) + ε ⎠ ⎠ ⎝ ⎝ ⎠ ⎝

(14)

3.5. Numerical simulation results

where cji and σji represent the centre and width of the Gaussian membership for the input variable xi , respectively, and ε > 0 is the small constant deﬁned earlier. R is the number of fuzzy rules and y is the output from the HNFN identiﬁer. Following a similar procedure, sway, heave, pitch and yaw fuzzy models are developed. For sway HNFN modelling, the coupling eﬀects on the sway direction from the forward and yaw motions are considered. Similarly, for heave modelling, the coupling eﬀects on the heave direction from the forward and pitch motions are taken into account. For pitch and yaw modelling, there is one output for each HNFN model, the angular velocities in the y-direction, q, and zdirection, r, respectively.

In order to understand and analyse the identiﬁcation strategy, the inputs and outputs from the mathematical model of UNSW Canberra AUV that includes the model of the actuators are used. This mathematical model is simulated using Matlab/Simulink (Osama et al., 2011) as the baseline model for comparison with the HNFN model. The hydrodynamic coeﬃcients calculated using the CFD analysis are listed in Table 2. The inputs in Fig. 8 were applied to the AUV actuators. The HNFN identiﬁcation algorithm is used to identify and compare the performance of the AUV.. The HFNF identiﬁer of coupled 6-DOF of the AUV are developed based upon the open-loop characteristics of its dynamics captured from mathematical model. The results of the oﬀ-line and on-line HNFN identiﬁer of the AUV are presented in the following paragraphs. The model is said to be oﬀ-line trained if the entire training process is completed prior to its use. In contrast, an on-line model is progressively trained during its use.

3.4. Entropy measurement The entropy measure is used as the criterion for accuracy while determining the structure and its value between each data point and each current membership function is calculated to determine whether a new rule should be added. For each incoming pattern, input-output pair, a rule's ﬁring strength is considered as the degree to which the incoming pair belongs to the corresponding cluster. The entropy measure calculation, which is based on the ﬁring strength of each rule (Wang and Dong, 2009), is given by

3.5.1. Oﬀ-line HNFN model The identiﬁcation and prediction responses of the HNFN model and the actual responses of the mathematical model of the linear and angular velocities of the AUV are shown in Fig. 9. The input is represented by ﬁve Gaussian membership functions. In the consequent part, the output is generated by FLNN. The function expansion in FLNN uses trigonometric functions. It leads to the weight variables matrix, w(m xR ), that depends on the number of inputs to the FLNN.. For a 1-D input, [x1], as in Roll model, the enhanced input is obtained

N

ENTj =

∑ Lij(2) (1 − Lij(2) ) i =1

(16)

(15)

where gmax , as described in Eq. (15), is the ﬁring strength of each rule and the maximum entropy measure is determined as 63

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Table 2 Hydrodynamic coefficient of UNSW Canberra AUV model. Parameter

Calculated value

Unit

Parameter

Calculated value

Unit

Xu | u Xv | v Xw | w Xq | q

−7.365 −0.737 −0.737 −1.065 −1.065 −112.2 0.250 −112.2 −0.250 −0.5975 2.244 −119.5 −2.244 −59.75 −1.17 −34.834 1.042 −34.834 −1.042

kg/m kg/m kg/m kg m/rad kg m/rad kg/m kg m/rad kg/m kg m/rad kg m2/rad2 kg m/rad kg m2/rad2 kg m/rad kg m2/rad2 kg kg kg m/rad kg kg m/rad

Xu Xv Xw Xq Xr Yv Yr Zw Zq Kp

−2.12 −0.31 −0.31 −0.51 −0.51 −62.45 0.12 −62.45 0.12 −0.3125 1.2 −59.75 1.2 −31.25 0 −1.042 −2.659 −1.042 −2.659

kg/s kg/s kg/s kg m/s kg m/s kg/s kg m/s kg/s kg m/s kg m2/s kg m/s kg m2/s kg m/s kg m2/s Kg m/rad Kg m/rad Kg m/rad kg m/rad kg m/rad

Xr | r Yv | v Yr | r Z w|w Zq | q Kp | p Mw | w Mq | q Nv | v Nr | r Xu̇ Yv̇ Yr ̇

Yaw force, Pitch force, N.m N.m

Surge force, N.m

Z ẇ Z q̇

Mw Mq Nv Nr K ṗ Mẇ Mq̇ Nv̇ Nr ̇

10 5 0

Fig. 9. AUV oﬀ-line HNFN model: Linear and Angular velocities. 0

20

40

60

80

100

5

Table 3 AUV off-line HNFN model RMSE values: Coupled dynamics.

0

Statistics -5

0

20

40

60

80

100

5

RMSE

Linear velocities

Angular velocities

u

v

w

p

q

r

0.0024

2.09e–04

0.0007

0

0.0204

0.0315

0 -5

0

20

40

60

80

3.5.2. On-line HNFN model In the case of on-line identiﬁcation and prediction, the responses of the HNFN model and the actual responses of the mathematical model of the linear and rotational velocities of the AUV are plotted in Fig. 11. The total number of rules used is ﬁve for each HNFN identiﬁer. The learning rates used to learn the parameters of the fuzzy system αc, α w are based on the convergence limit for the identiﬁer and the RMSE values are tabulated in Table 4 for the linear and angular velocities of the vehicle. The RMSE values indicate that the model of the AUV is captured accurately by the HNFN model... In order to appreciate the robustness of the HNFN model, parameter variations and external noise and disturbance are considered. The model system response is investigated when external noise as sensor noise (5%) is applied on all linear and angular velocities on the actual system. In addition, the hydrodynamic coeﬃcients are increased by 25% as added mass variation and the data is utilized to capture the dynamics using HNFN. It can be seen from Table 5 that the model is capable of capturing the dynamics accurately even in the presence of noisy data and variations in parameters. Numerical simulations with 50% increase in the added mass, Coriolis and Centripetal forces and damping matrix are presented in Fig. 10 to highlight the robustness of the on-line HNFN Model.

100

Time Fig. 8. Input signal for the AUV.

using the trigonometric functions in [1, x1, sin(πx1), cos(πx1)], for a 2-D input [x1, x2], as in pitch and yaw modelling, the trigonometric functions are those in [1, x1, sin(πx1), cos(πx1), x2 , sin(πx2 ), cos(πx2 ), x1 x2]. These lead to weight variables, x = (x1, .......... ,xn )T ∈ U and y ∈ R , dimensioned by (4 × 5) and (8 × 5), respectively. In sway and heave modelling, the input to the FLNN is three, so trigonometric functions is given by Eq. (17) and the weight matrix is (12 × 5). In the case of surge model, there are four inputs. The trigonometric functions for that model is given by Eq. (18) and weight variables, i = 1, 2, ... ,M , is having the dimension of (16 × 5).

⎡1, x1, sin(πx1), cos(πx1), x2 , ⎤ ⎢ ⎥ ⎢ sin(πx2 ), cos(πx2 ), x1 x2 , ⎥ ⎣ x3, sin(πx3), cos(πx3), x1 x2 x3 ⎦

(17)

⎡1, x1, sin(πx1), cos(πx1), x2 , ⎤ ⎢ ⎥ sin( ), cos( ), , πx πx x x 2 2 1 2 ⎢ ⎥ ⎢ x3, sin(πx3), cos(πx3), x1 x2 x3 ⎥ ⎢⎣ x4 , sin(πx4 ), cos(πx4 ), x1 x2 x3 x4 ⎥⎦

(18)

4. AUV control system design

A statistical interpretation in terms of RMSE is presented in Table 3. The results from the table indicate that the proposed HNFN model is capable of capturing the coupled dynamics of the AUV pretty accurately (Fig. 10).

As the AUV's dynamics have six degrees of freedom, are highly nonlinear and time-varying, designing its path controller is a challenging problem. Thus, its controller should be suﬃciently adaptive to enable it to handle variations in the dynamics of the AUV under 64

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u, m/sec

1 0 -1 0 20 -3 x 10 5 0 -5 0 20

40

40

HNFN Output

60

60

80

80

100

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System Output

100

2 0 System Output

-2 5

AHNFN Output

0 -3 x 10

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100

0

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O. Hassanein et al.

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q, deg/sec

x 10 5 0 -5 0 20

40

60

80

100

2 1 0 0

20

40

60

80

5 0 -5 0

r, deg/sec

q, deg/sec

w, m/sec

-3

5 0 -5 0

100

Time (Sec)

r, deg/sec

5

Fig. 11. AUV on-line HNFN model: Linear and Angular velocities.

0 -5

0

20

40

60

80

Table 4 AUV on-line HNFN model RMSE and learning rates values: Coupled dynamics.

100

Time

Statistics

Fig. 10. AUV on-line HNFN model with parameter variation: Linear and Angular velocities. RMSE αw αc

diﬀerent manoeuvring regimes and disturbances arising from both internal and external sources. The AUV's HNFN control is constructed based on the input-output data and generated according to the SSPM control and identiﬁcation scheme. The main tasks of its control system (autopilot) are to guide, control and navigate the AUV through a certain manoeuvre scenario. The sensors include gyros, accelerometers, magnetometers and pressure sensors, and an onboard processor PC104. The conﬁguration of the AUV control system shown in Fig. 12 consists of three control loops that represent its surge, pitch and yaw motions. Each controller has two inputs, the error and error diﬀerence, while the output from the system ( e (k + 1) = e (k )[1 − ασ PσT (k ) Pσ (k )] ≤ e (k ) • 1 − ασ PσT (k ) Pσ (k ) ) is the control action required by the thrusters and pumps. Generally, the depth of an AUV can be maintained by controlling its pitch and forward motions while directing it to the right and left by controlling its yaw angle. Therefore, controlling its surge, pitch and yaw motions are suﬃcient for determining its orientation in three dimensions. The simulation results presented in the next section demonstrate the beneﬁts of the chosen control scheme..

Linear velocities

Angular velocities

u

v

w

p

q

r

0.0061 0.009 0.1

1.22e−05 0.009 0.1

1.38e−07 0.009 0.1

0 0.03 0.05

3.56e−04 0.45 0.3

1.11e−04 0.1 0.05

Table 5 AUV on-line HNFN model RMSE values: Robustness. Statistics RMSE

Normal Noise Mass Var.

Linear velocities

Angular velocities

u

v

w

p

q

r

0.0061 0.0061 0.0061

1.22e−05 4.36e−05 4.34e−05

1.38e−07 1.59e−07 1.59e−07

0 0 0

3.56e−04 3.57e−04 3.53e−04

1.11e−04 0.0012 0.0012

4.1.1. HNFN control system The total number of rules generated is four, with two inputs and one output, and the selected value of ENT is 0.123. The fuzzy sets of the ﬁrst input variables are deﬁned as zero (ZZ), small error (SE), medium error (ME), and big error (BE). The second input variables are deﬁned as zero (ZZ), small rate change (SRC), medium rate change (MRC), and large rate change (LRC). The generated centres of the adaptive HNFN sets are −0.055, 0.29, 0.58, and −1.1 for ex (k ) and −0.055, 0.29, 0.58, 1.13 for Δ ex (k ). The function expansion used in the FLNN for a two-dimensional [ex , Δex ] input is the trigonometric functions [1, ex , sin(πex ), cos(πex ), Δex , sin(πΔex ), cos(πΔex ), ex × Δex ]. Therefore, the ﬁnal output from the HNFN controller is given by;

4.1. AUV surge control loop For the surge motion, the inputs to the controller are the error,ex and its error diﬀerence,Δ ex and its output is the force required by the thrusters to power the vehicle in a forward motion. 65

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O. Hassanein et al. Measured x

Desired x

Trajectory Planing

SURGE Controller

Desired Pitch Angle

AUV DYNAMICS

PITCH Controller

Desired Yaw Angle

YAW Controller

Measured Yaw Angle Measured Pitch Angle

Fig. 12. Block diagram of AUV control system.

⎤ M R ⎡ N ∑l =1 ⎢∏ j =1 (μe (e (k )) × μΔe (Δe (k ))) ⎥ (∑i =1 wij φi ) ⎣ ⎦ u (k ) = ⎡ ⎤ R N ∑l =1 ⎢∏ j =1 (μe (e (k )) × μΔe (Δe (k ))) ⎥ ⎣ ⎦ where Δσij is the number of fuzzy rules and

∂e (k ) ∂σij

=

∂e (k ) ∂y ∂y ∂σij

Table 6 Generated values of surge HNFN control parameters. Δex(k)

ex (k)

(19) ZZ=−0.95

SE=0.9

ME=3.22

BE=5.3

y1 y2 y3 y4 0.95 0.136

y2 y3 y4 y3 0.8 0.151

y3 y4 y3 y2 0.95 0.135

y4 .y3 y2 y1 0.75 0.132

= Pσ (k ) the

output of the adaptive HNFN controller. Table 6 shows the generated values of the HNFN controller parameters. The link weight variables, ⎛ ⎛ ⎛ ⎞2 ⎞ ⎛ ⎞2 ⎞ ⎜x1j − cx1, ji⎟ ⎟ ⎜x j2 − cx 2, ji⎟ ⎟ ⎜ ⎜ ⎝ ⎠ ⎝ ⎠ μ yl (x1 (k )) = exp ⎜−0.5 ⎟ ; μ yjl (x2 (k )) = exp ⎜−0.5 (σ )2 + ε ⎟ ;, of (σx1, ji )2 + ε j x 2, ji ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ the HNFN controller are generated by the proposed algorithm in the range [−1,1].

ZZ=0.05 SRC=0.29 MRC=0.59 LRC=0.89 σex (k ) σΔ ex (k )

Table 7 Generated values of pitch adaptive HNFN control parameters.

4.2. AUV pitch control loop

Δeθ (k)

For the pitch motion, the inputs to the controller are the position error, eθ , and its error diﬀerence, Δ eθ and its output is the force required by the up and down pumps to power the AUV in the pitching motion for generating the required pitching moment.

D=−3

S=0

U=3.2

y1 y1 y1 1.2 0.009

y2 y2 y3 0.9 0.01

y3 y3 y3 1.3 0.01

L=−3.9

S=0

R=3.65

L=−0.035 S=0.01 R=0.033 σeψ (k )

y1 y1 y1 1.48

y2 y2 y3 1

y3 y3 y3 1.39

σΔ eψ (k )

0.016

0.01

0.015

D=−0.035 S=0.009 U=0.032 σeθ (k ) σΔ eθ (k )

4.2.1. HNFN control system The total number of rules generated is three, with two inputs and one output, and the selected value of ENT is 0.153. The fuzzy sets of input variables are deﬁned as down (D), stop (S) and up (U) and the function’s expansion is [1, eθ , sin(πeθ ), cos(πeθ ), Δeθ , sin(πΔeθ ), cos(πΔeθ ), eθ × Δeθ ] and its weight matrix is (8 × 3). Table 7 shows the generated values of the HNFN controller parameters.

eθ (k)

Table 8 Generated values of yaw HNFN control parameters. Δeѱ (k)

4.3. AUV yaw control loop Similar to the pitch controller, for the yaw motion, the inputs to its controller are the (eψ ) position error and its error diﬀerence ( Δeψ ), while its output is the force required by the left and right pumps to power the AUV in the yaw motion (for generating the required yaw moment).

eѱ (k)

controller when applied to the 6-DOF coupled AUV mathematical model as the vehicle was subjected to a square motion in XY-plane and a straight line in XZ-plane as shown in Fig. 13. It should be noticed that the square motion is a diﬃcult path for an AUV to follow.. The learning rates α w ’s, for the controller were initially set to 0.05 for all HNFN parameters. Then the convergence conditions were veriﬁed at every sampling time. It was found that the 0.1 value was always within the limit of convergence for the antecedent part of the controller, and was 0.04 for the consequent part. Fig. 14 shows that

4.3.1. Adaptive HNFN control system The total number of rules generated is three, with two inputs and one output, and the selected value of ENT is 0.083. Its fuzzy sets of input variables are deﬁned as left (L), stop (S) and right (R), and its function expansion is [1, eψ , sin(πeψ ), cos(πeψ ), Δeψ , sin(πΔeψ ), cos(πΔeψ ), eψ × Δeψ ]. Table 8 shows the generated values of the HNFN controller parameters. The HIL simulation results of the proposed adaptive HNFN 66

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Desired Action

Y – Direction, m

5

Y – Direction, m Z – Direction, m

5

AUV Response

0

-5

0

100

200

300

400

500

600

2.5 0 -2.5 Desired Path PID Controller HNFN Controller

0

-5 0

-50 -100

Desired

0

100

200

300

400

500

Pitch error deg

10

20 0 -20 0

0

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400

600

800

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800

100 100

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300

400

500

600

700

800

Yaw error, deg

Pitch, deg

800

PID Controller HNFN Controller

40

20

100

Yaw, deg

600

600

Fig. 13. AUV motion in XYZ plane: HNFN control.

0

50 0 -50 -100

-100 0

400 X – Direction, m

Actual

X – Direction, m

0

200

100

200

300

400

500

600

700

800

0

200

Time (Sec)

Time (Sec) Fig. 14. AUV HNFN controller: angles response.

Fig. 15. -A The AUV square motion in XY plane with HNFN and PID. B: AUV motion in XY Z plane: HNFN and PID control and angles error.

HNFN controller tracked successfully the pitch and yaw angles. The robustness of the controller is investigated via increasing the hydrodynamic coeﬃcients parameters by 10% and applying an external noise as sensor noise and sea currents.. In order to evaluate and validate performance capabilities of the proposed HNFN controller, a numerical simulation of the HNFN controller and conventional PID controller with the mathematical model of the AUV is carried out. Fig. 15-A and Fig. 15-B show the simulation result of the motion of the AUV in square trajectory in XY plane, which means the yaw angle control when HNFN and PID are applied to the AUV mathematical model. In addition, the corresponding angle error between the desired and the actual trajectory in yaw angle and pitch angle, are also shown. The RMSE values of the pitch angle error of the system are 4.61 and 0.572 and 10.35 and 5.1 for yaw angle for PID and HNFN controllers, respectively. Generally, it is clear that the performance of the AUV with HNFN controller is more accurate and more eﬀective.. Table 9 shows the RMSE values of the errors in the angles of the actual response of the HNFN controller. As shown from the RMSE values, it is clear that the performance of the AUV with HNFN controller is accurate and acceptable. In addition, the real time implementation can be carried out due to HIL successful demonstration.

Table 9 AUV HNFN control RMSE values: Coupled dynamics. RMSE

Original With Parameter Variation With noise

Angles Pitch, θ , deg

Yaw, ψ , deg

0.0592 0.0632 0.0893

4.2594 5.1872 6.2881

1. The real-time manoeuvre excites the desired dynamics very well, and 2. High quality data with least or acceptable measurement noise is collected. These data sets are used for the identiﬁcation algorithm to generate, tune and identify. Several experiments were carried out at UNSW Canberra to collect a range of data for diﬀerent operating conditions. The swimming pool at UNSW, shallow water branch from Molonglo River and Gungahlin Lake in Canberra are chosen as test environments for the AUV to validate the robustness of the proposed algorithm. For coupled dynamics, a suitable manoeuvre is conducted such that all the control inputs are used and the coupled dynamics are excited over a period of time. Fig. 16 shows the real-time manoeuvring of the AUV during the data collection phase in diﬀerent environments.. The real-time input-output data set collected from swimming pool test is used in the ﬁrst stage of our algorithm to generate a coupled 6DOF AUV model. The data sets collected from the other environments are used in the second stage for tuning the generated model to improve the accuracy and its generalisation capabilities. Finally, diﬀerent

4.4. Real-time test data collection The UNSW Canberra AUV is used to validate the identiﬁcation and control algorithm. To model its dynamic system, separate real-tests are conducted exclusively, to excite its corresponding dynamics. Before actual real-time experiments, the following factors are taken into consideration;. 67

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Fig. 16. UNSW Canberra AUV during experimental test data collection.

dynamics while achieving the training within the available training time. It can be concluded that the identiﬁcation model is able to predict the dynamics in real-time successfully. The blue line represents the identiﬁed model and the red line represents the actual measured data. The RMSE values of the real-time identiﬁcation results of the coupled 6-DOF AUV are listed in Table 10. Results indicate that the model adapts itself with changes in the test regime very well.

Table 10 Real-time AUV modelling RMSE values: Coupled dynamics. RMSE

HNFN test

Linear velocities

Angular velocities

u

v

w

φ

θ

ψ

0.0017

0.0029

0.0110

0.0157

0.0157

0.0053

batches of the real-time input-output data are used to validate the identiﬁcation technique on the ground using HIL before implementation in real-time test.

4.6. AUV model-based control system results The ﬁnal goal of any controller design is to prove its validity in real conditions with unknown disturbances and the associated diﬃculties with real time implementation. This is a particularly challenging task for a complex, nonlinear and time-varying system like an AUV. Realtime tests are necessary to test the ability of the controller to perform satisfactorily in the presence of unknown weather conditions and noise in the system. Several real-time tests of the proposed control system were conducted over several days in the environment mentioned previously. The experimental results are shown in Fig. 17. This test is conducted in uncontrolled environment, shallow water branch of Molonglo River. The variations from the commanded value are due to the wind conditions and a high water stream ﬂow. A dead band of ± 2.5° around the set point was used while doing the experiments to avoid vehicle ﬂuctuations on the surface. The corresponding pumps’

4.5. Experimental identiﬁcation results Real-time implementation of the proposed adaptive controller is presented in this section. This implementation is carried out in diﬀerent environments as previously mentioned. The identiﬁcation algorithm was downloaded to the computing unit including PC104. The identiﬁcation algorithm is based on HNFN technique. The sensor data from diﬀerent sensors mounted on the AUV are measured and are logged in the data logger and the ﬁnal results of the predicted model outputs at each sample time are also logged. Fig. 16 shows the identiﬁcation results from the real-time experiment with the HNFN model of the AUV. It can be seen that the HNFN model generated by the proposed mechanism is able to model the AUV

Desired Path

AUV Response

2 v, m/sec

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20 p, deg/sec

w, m/sec

0.5

-0.5

0

0

20

0 -50

40

Time (Sec)

0

Time (Sec)

Fig. 17. AUV HNFN identiﬁcation experimental results: coupled dynamics.

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Pitch, deg

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RT Yaw pump

Pitch pump

UP

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Time (Sec)

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LT

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Fig. 18. AUV control based HNFN experimental results: Coupled dynamics. Publishing Co., Inc., Longman, Boston. Bessa, W.M., et al., 2010. An adaptive fuzzy sliding mode controller for remotely operated underwater vehicles. Robot. Auton. Syst. 58 (1), 16–26. Brandt, R.D., Lin, F., 1999. Adaptive interaction and its application to neural networks. Inf. Sci. 121 (3–4), 201–215. Datta, A., Ioannou, P.A., 1994. Performance analysis and improvement in model reference adaptive control. IEEE Trans. Autom. Control 39 (12), 2370–2387. Fossen, T., 1994. Guidance and Control of Ocean Vehicles 2nd ed.. John Wiley And Sons Ltd., New York. Kim, H.S., Shin, K., 2007. Expanded adaptive fuzzy sliding mode controller using expert knowledge and fuzzy basis function expansion for ufv depth control. Ocean Eng. 34 (8), 1080–1088. Kim, H.S., Shin, Y.K., 2005. Design of adaptive fuzzy sliding mode controller based on fuzzy basis function expansion for UFV depth control. Int. J. Control Autom. Syst. 3 (2), 217–224. Kodogiannis, V.S., 2006. Neuro-control of unmanned underwater vehicles. Int. J. Syst. Sci. 37 (3), 149–162. Kuljača, O., et al., 2009. Multilayer neural net trajectory tracking control for underwater vehicle. Brodogradnja 60 (4), 388–394. Medsker, L., Jain, L.C., 1999b. Recurrent Neural Networks: Design and Applications. CRC, London. Osama, H., et al., 2013a. Hybrid neuro-fuzzy network identiﬁcation for autonomous underwater vehicles. In: Proceedings of the 4th International Conference, SEMCCO 2013, Chennai, India, December 19–21. Osama, H., et al., 2013b. Black-box tool for nonlinear system identiﬁcation based upon fuzzy system. IJCIA 12 (02). Osama, H., et al., 2011. Fuzzy modeling and control for autonomous. In: Proceedings of the 5th International Conference on Automation, Robotics and Applications (ICARA), Wellington, NZ, 6–8 Dec{C}. Phung-Hung, N.Yun-ChulJ.2009. Control of autonomous underwater vehicles using adaptive neural network. In: Proceedings of the International Conference on Advanced Technologies for Communications(ATC). Puttige, V.R., 2008. Neural Network Based Adaptive Control For Autonomous Flight of Fixed Wing Unmanned Aerial Vehicles. University of New South Wales. Saikalis, G.LinF., 2001. A neural network controller by adaptive interaction. In: Proceedings of the IEEE American Control Conference. Santhakumar, M.KimJ. 2011. modelling, simulation and model reference adaptive control of autonomous underwater vehicle-manipulator systems. In: Proceedings of the 11th International Conference Control, Automation and Systems (ICCAS). Shi, Y., et al., 2007. Adaptive depth control for autonomous underwater vehicles based on feedforward neural networks. Intell. Control Autom., 207–218. Wang, C.-H., et al., 2002. Direct adaptive fuzzy-neural control with state observer and supervisory controller for unknown nonlinear dynamical systems. IEEE Trans. Fuzzy Syst. 10 (1), 39–49. Wang, X.-Z., Dong, C.-R., 2009. Improving generalization of fuzzy if—then rules by maximizing fuzzy entropy. IEEE Trans. Fuzzy Syst. 17 (3), 556–567. Zhao, S., Yuh, J., 2005. Experimental study on advanced underwater robot control. IEEE Trans. Robotics 21 (4), 695–703.

action for pitch and yaw movements are also shown in Fig. 18. It is clearly seen that the AVU follows the commanded input. The blue line represents the actual AUV response and the red line represents the desired trajectory... 5. Concluding remarks The paper presents the real time implementation of HNFN adaptive controller. The adaptive controller uses the SSPM architecture for identiﬁcation and control. The indirect adaptive controller also uses the sensitivity as an additional input to the HNFN for improved performance. Both the identiﬁcation and control use only the input output data to identify the structure of the model, tune the parameters of the model and make them robust to handle parameter variations using the DE technique. Initially, the model is validated using mathematically simulated data from an existing mathematical model. After this validation, real time data is used to identify and design the controller. This is validated using HIL simulation. The results from numerical validation and HIL indicate that the controller is accurate and real-time implementable using the available sensors and processing unit. Finally, experimental validations are carried out to show the eﬃcacy of the proposed controller in real-time environment. AUV built at UNSW at Canberra is used for the experimental purposes. The experimental validation shows that the method is applicable for non-linear, coupled and time-varying systems. Since, the method is platform free technique, in future; the algorithm will be implemented on other AUV platforms as well as other autonomous systems like Unmanned Aerial Vehicles (UAVs) and Autonomous Ground Vehicles (AGVs). References Amin, R. et al., 2010. Neural networks control of autonomous underwater vehicle. In: Proceedings of the 2nd IEEE International Conference Mechanical and Electronics Engineering (ICMEE). Antonelli, G., Fossen, T.I., Yoerger, D., 2008. Underwater Robotics. Handbook on Robotics. Springer-Verlag, 987–1008. Astrom, K.J., Wittenmark, B., 1994. Adaptive Control. Addison-Wesley Longman

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