This paper presents fuzzy sliding mode control with region tracking control for a single autonomous underwater vehicle. The vehicle is needed to track a certain moving region whilst under the influence of wave current. The fuzzy logic is used to tune the gain and to reduce the effect of chattering effect, the signum function is replaced by saturation function. Simulation result is presented to demonstrate the performance of the proposed tracking control of the AUV

Ismail, Zool Hilmi

Mohd. Mokhar, Mohd. Bazli

Jurnal Teknologi

Universiti Teknologi Malaysia Institutional Repository

72:2 (2015) 97-101 | www.jurnalteknologi.utm.my | eISSN 2180-3722 | Full paper             Jurnal Teknologi   Fuzzy Sliding Mode with Region Tracking Control for Autonomous Underwater Vehicle  Mohd Bazli Mohd Mokhar, Zool Hilmi Ismail*  Center for Artificial Intelligence and Robotics, Universiti Teknologi Malaysia, Kuala Lumpur, Malaysia Faculty of Electrical Engineering, UniversitiTeknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia  *Corresponding author: zool@fke.utm.my     1.0  INTRODUCTION  Underwater vehicles play an important part in military, oil and gas sector nowadays. However, the environment underwater is also not very known to men, so the underwater vehicle or robot that get sent there have to be fully autonomous in order to be able to do the mission  without fail. Therefore, many research in the recent years focusing on how to improve the performance of underwater vehicle especially in regulate and tracking control system.    A lot of controllers have been proposed for the purpose of improving the control system of AUV such as PID, sliding mode control, adaptive, fuzzy logic, neural network and combination of these controllers. Proportional-Derivative (PD) control plus gravity compensation [1] is the simplest set-point technique for controlling an AUV. However, the weakness of PD control plus gravity compensation is that it is difficult to obtain the exact model of gravitational and buoyancy forces as the dynamic of AUV depend on the condition of the subsea. In addition, the wave current could easily sway away the AUV from its destination. The conventional set point method as this method required more energy so that the vehicle can stay on its point whilst being drag out with wave current. Another method called region tracking method is proposed by Li [2] to overcome this weakness. In this method, the target is a region instead of a point. By redefine the target as a region, the AUV can stay as long as needed without having to activate its controller as long as the wave current does not drag itself out of the region. This method also is applied to a swarm robot as proposed by Hou [3]. Zool proposed using boundary region instead of region in [4] because there are AUV missions that need boundary as objective such as monitoring the exterior pipeline underwater and etc.   Sliding mode control is one of controller usually used for AUV control system as it robust against uncertainty and disturbance. However, the main weakness of sliding mode is the chattering effect. So, most of research using sliding mode control focus on eliminated the chattering effect. One of the usual methods to reduce the chattering effect is by substitute the signum function with saturation function. In [5], Santhakumar and Asokan proposed combine and using best the PID and sliding mode control. In the initial phase, SMC will be operating however when the system is in reaching phase, PID controller will be used to bring the system to steady state.  Bessa [6] in the other hand, proposed an adoption of properly design boundary layer to overcome the chattering effect. Soylu [7], proposed using adaptive term instead the sign term to eliminated the chattering effect and Sun, also using the same approaches as Soylu added with backstepping technique for tracking control of an AUV in [8].   Fuzzy logic has been extensively used in the recent years compared when it was first introduced by Zadeh around forty years ago[9]. The application of fuzzy logic is range from consumer product to control application. For control purposes, fuzzy logic has been designed as a tuning gain algorithm for control method such as PID and sliding mode control. The use of fuzzy logic to tune the gains in PID controller is reported in [10, 11] and sliding mode gain in [12]. In [13], fuzzy logic is used to model the equation switching term in sliding mode controller instead using signum function.    In this paper, we presented fuzzy sliding mode control with region tracking control for a single AUV. Simulation results on AUV with 6 degrees of freedom are presented to demonstrate the effectiveness of the proposed controller. The rest of the paper is organized as follow: Section 2 describes the kinematic and dynamic properties of an AUV. In Section 3, the fuzzy sliding model control with region function formulation is briefly explained. In Section 4, numerical simulation results are provided to demonstrate the performance of the proposed controllers compared with conventional sliding mode control. Finally, the paper is closed with Article history  Received :15 June 2014 Received in revised form :  15 September 2014 Accepted :15 October 2014  Graphical abstract t = t0t = t1 (t1 >t0) t = t2 (t2 > t1 > t0) XiZiYiAUV   Abstract  This paper presents fuzzy sliding mode control with region tracking control for a single autonomous underwater vehicle. The vehicle is needed to track a certain moving region whilst under the influence of wave current. The fuzzy logic is used to tune the gain and to reduce the effect of chattering effect, the signum function is replaced by saturation function. Simulation result is presented to demonstrate the performance of the proposed tracking control of the AUV.   Keywords: Underwater vehicle; sliding mode control; fuzzy logic; region tracking  © 2015 Penerbit UTM Press. All rights reserved.  98                                      Mohd Bazli Mokhar & Zool Hilmi Ismail / JurnalTeknologi (Sciences & Engineering) 72:2 (2015) 97-101   some concluding remarks in Section 5. Figure 1 shows illustration of region tracking control for a single AUV. t = t0t = t1 (t1 >t0) t = t2 (t2 > t1 > t0) XiZiYiAUV Figure 1  Region tracking control for a single AUV   2.0  KINEMATIC AND DYNAMIC MODEL OF AN AUV  2.1  Kinematic Model  The relationship between inertial and body-fixed vehicle velocity can be described using the Jacobian matrix 𝐽(𝜂2) in the following form [6].    [?̇?1?̇?2] = [𝐽1(𝜂2) 03×303×3 𝐽2(𝜂2)] [𝑣1 𝑣2] ⟺ ?̇? = 𝐽(𝜂2)𝑣 (1)  where 𝜂1 = [𝑥 𝑦 𝑧]𝑇 ∈ ℝ3 and  𝜂2 = [𝜙 𝜃 𝜓]𝑇 ∈ ℝ3 denote the position and the orientation of the vehicle, respectively, expressed in the inertial-fixed frame. 𝐽1 and 𝐽2 are the transformation matrices expressed in terms of the Euler angles. The linear and angular velocity vectors,[𝑢 𝑣 𝑤]𝑇 ∈ ℝ3  and 𝑣2 = [𝑝 𝑞 𝑟]𝑇 ∈ ℝ3 , respectively, are described in terms of the body-fixed frame.   2.2  Dynamic Model  The investigation of dynamic equation of motion for an underwater vehicle has been previously reported in [14]. The underwater vehicle dynamic equation can be expressed in closed form as  𝜏 =  𝑀?̇? + 𝐶(𝑣)𝑣 + 𝐷(𝑣)𝑣 + 𝑔(𝜂)  (2)  where 𝑣 ∈ ℝ6 is the velocity state vector with respect to the body-fixed frame, 𝑀 is the inertia matrix including the added mass term, 𝐶(𝑣) represents the matrix of the Coriolis and centripetal forces including the added mass term, 𝐷(𝑣) denotes the hydrodynamic damping and lift force, 𝑔(𝜂) is the restoring force and 𝜏 is the vector of generalized forces acting on the vehicle. The dynamic equation in (2) preserves the following properties [14]: Property 1: The inertia matrix 𝑀 is symmetric and positive definite such that 𝑀 = 𝑀𝑇 > 0. Property 2: 𝐶(𝑣) is the skew-symmetric matrix such that 𝐶(𝑣) =−𝐶𝑇(𝑣).     Property 3: The hydrodynamic damping matrix 𝐷(𝑣)is positive definite, i.e.: 𝐷(𝑣) = 𝐷𝑇(𝑣) > 0.  3.0  FUZZY SLIDING MODE CONTROL WITH REGION TRACKING CONTROL  In region-based control law, the desired moving target is specified by a region instead of a point. First, a dynamic region of specific shape is defined and this can be viewed as a global objective of the proposed control law. Let us define a desired region as the following inequality equation functions as follow:  ℱ(𝛿𝜂) ≤   0 (3)  where 𝛿𝜂 = (𝜂 − 𝜂𝑑) ∈ ℝ6 are the continuous first partial derivatives of the dynamic region; 𝜂𝑑(𝑡) is the time-varying reference point inside the region shape. It is assumed that 𝜂𝑑(𝑡) is bounded functions of time.    The potential energy function for the desired regions is as follows:  𝑃𝑝(𝛿𝜂)  =𝑘𝑝2[max(0, ℱ(𝛿𝜂))]2  (4) or   𝑃𝑝(𝛿𝜂) ≜ { 0,                                ℱ(𝛿𝜂) ≤ 0 𝑘𝑝2ℱ2(𝛿𝜂),               ℱ(𝛿𝜂) > 0   (5)   Partially differentiate the equation (5) with respect to 𝜕𝜂 gives  (𝜕𝑃𝑝(𝜕𝜂) 𝜕𝜂)𝑇= 𝑘𝑝 max(0, ℱ(𝛿𝜂)) (𝜕ℱ(𝛿𝜂) 𝜕𝜂)𝑇 (6)  Now, let (6) be represented as a region error 𝛥𝜉 in the following form  𝛥𝜉 = max(0, ℱ(𝛿𝜂)) (𝜕ℱ(𝛿𝜂) 𝜕𝜂)𝑇 (7)  When the AUV are outside the desired region, the control force 𝛥𝜉 described by (10) is activated to attract the AUV toward the desired region. When the AUV is inside the desired region, then the control force is zero or 𝛥𝜉 = 0. The sliding mode can be define as follows:  𝜏 =  𝜏𝑒𝑞  +  𝜏𝑠𝑤 (8)  where 𝜏 corresponds to a generalized force acting at the centre of mass of the AUV. 𝜏𝑒𝑞  and 𝜏𝑠𝑤 symbolize the equivalent control law and the switching control law. It is well-known that the switching term 𝜏𝑠𝑤 is defined as follows  𝜏𝑠𝑤 =  − 𝐾𝑠gn(𝑠)  (9) 𝐾 is the positive definite diagonal gain matrix that is defined based on the upper bounds on the system parameter uncertainties, and 𝑠gn(∙) is the nonlinear signum function. Sliding mode control design involves two step, first is to get the sliding manifold, 𝑠 and second is to get equivalent control,. The sliding manifold is defines as  𝑠 = 𝑣 − 𝑣𝑟 (10)  𝑣𝑟 in equation 10 can be define as  99                                      Mohd Bazli Mokhar & Zool Hilmi Ismail / JurnalTeknologi (Sciences & Engineering) 72:2 (2015) 97-101   𝑣𝑟 = 𝐽−1(?̇?𝑑 − 𝑆−1?̇?𝛿𝜂) − 𝐽−1Δ𝜉  (11)  Differentiate the sliding manifold to get  ?̇? =  ?̇? − ?̇?𝑟 (12)  Multiply both side of (12) by inertia matrix ?̂? and substituting (2) into resulting equation yields  ?̂??̇?  =  𝜏𝑒𝑞 − (?̂??̇?𝑟  + ?̂?(𝑣)𝑣 + ?̂?(𝑣)𝑣 +  ?̂?(𝜂)) (13)  Let 𝑠 = 0, yield an equivalent control   𝜏𝑒𝑞  =  ?̂??̇?𝑟  + ?̂?(𝑣)𝑣 + ?̂?(𝑣)𝑣 +  ?̂?(𝜂) (14)  Membership functions for s and ?̇? are presented in Figure 2 and 3 respectively. In order to reduce the chattering effect in proposed controller, the signum function in the switching term, 𝜏𝑠𝑤 with saturation function and gain, is tune using fuzzy yield  𝜏𝑠𝑤 =  − 𝐾𝑓𝑢𝑧𝑧𝑦𝑠𝑎𝑡(𝑠/𝛿)  (15) where 𝛿 is the boundary layer and the membership function of output 𝐾𝑓𝑢𝑧𝑧𝑦 is shown in Figure 4.    When the value of gain, k is decreased its value near the sliding surface can damp the chattering amplitude, while if the value of gain is choose to be as large as allowed can reduce the reaching time [15]. So, to maintain the facts mention before, a fuzzy controller is designed for the purpose of tuning the suitable gain accordingly. The figures below show the membership function for the inputs and output.   Figure 2  Membership function of input s   Figure 3  Membership function of input ?̇?   Figure 4  Membership function of output, 𝐾𝑓𝑢𝑧𝑧𝑦  Table 1  Fuzzy rule base   s  s_dot NB NS ZE PS PB N B B M S B Z B M S M B P B S M B B     Table 1 shows fuzzy rule base for tuning 𝐾 where N indicate Negative, ZE indicate Zero, P Indicate Positive, B indicate Big, M indicate Medium and B Indicate Big. Therefore, a proposed sliding-mode adaptive control law with region formulation can be written as follows:  𝜏 =  𝜏𝑒𝑞  −  𝐾𝑓𝑢𝑧𝑧𝑦𝑠𝑎𝑡(𝑠/𝛿) −  𝐽𝑇(𝜂)∆𝜉 (16)      -15 -10 -5 0 5 10 1500.20.40.60.81sDegree of membershipNB NS ZE PS PB-10 -8 -6 -4 -2 0 2 4 6 8 1000.20.40.60.81sdotDegree of membershipN Z P0 50 100 150 200 250 300 350 400 450 50000.20.40.60.81output1Degree of membershipS M B100                                      Mohd Bazli Mokhar & Zool Hilmi Ismail / JurnalTeknologi (Sciences & Engineering) 72:2 (2015) 97-101   4.0  SIMULATION RESULTS  In this section, a simulation studies is carried out to test the efficiency of the proposed fuzzy sliding mode controller under the influence of wave current. The vehicle is required to track a certain region in this simulation. An ODIN with full 6-DOF [16] is chosen as autonomous underwater vehicle model for numerical simulation. The numerical values for the matrices of the vehicle dynamic equations are available in [16]. In simulation, the following inequality functions are defined for a spherical region  ℱ(𝛿𝜂1) = (𝑥 − 𝑥0)2 + (𝑦 − 𝑦0)2 + (𝑧 − 𝑧0)2 ≤ 𝜅𝑟2 (17)  where (30) represents the inequality equation of a region with 𝜅𝑟 is defined as a scalar tolerance. An underwater vehicle is required to track a straight-line trajectory with green (cross-section lines) trajectory is the horizontal basis position initialized at [1.5  0 −1.2]𝑇m. The solid blue lines represent the position of an AUV at various time instances.    A constant and unidirectional current velocity designated with the arrows in figures below is set to 𝑣𝑑 = [0  0.04 0]𝑇 𝑚/𝑠. For both simulation, the region radius is set to, 𝜅𝑟 = 0.2. The orientation is kept constant with the allowable errors are set to 0.1 rad, and the initial values are  𝜂2(0) = [0   0   0]𝑇 rad.     From Figure 5 and Figure 6, it has been shown that the proposed controller effectiveness under the influence of constant wave current.   Figure 5  A 3-dimension view of simulation study; 𝐱 marks the initial position of an AUV    (a)  (b) Figure 6  Planar trajectories of an AUV for simulation study that are illustrated in (a) XY-plane and (b) YZ-plane   5.0  CONCLUSION  In this paper, a new region based tracking control method has been proposed for an autonomous underwater vehicle. This control technique enables an AUV to perform a specific underwater tracking task. It has been shown that AUV is able to track a desired moving region. Moreover, an AUV is capable to navigate into a moving region under constant external disturbance. Simulation results have been presented to demonstrate the performance of the proposed tracking controller.    Acknowledgement   This work was supported in part by the Ministry of Higher Education, Malaysia and Universiti Teknologi Malaysia under Grant no Q.J130000.2509.05H54.       -8-6-4-202-0.4-0.200.20.4-1.4-1.3-1.2-1.1-1-0.9xX-axis position [m]Y-axis position [m]Z-axis position [m]-7 -6 -5 -4 -3 -2 -1 0 1 2-0.25-0.2-0.15-0.1-0.0500.050.10.150.2xX-axis position [m]Y-axis position [m]-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-1.4-1.35-1.3-1.25-1.2-1.15-1.1-1.05-1-0.95xY-axis position [m]Z-axis position [m]𝑣𝑑 𝑣𝑑 𝑣𝑑 101                                      Mohd Bazli Mokhar & Zool Hilmi Ismail / JurnalTeknologi (Sciences & Engineering) 72:2 (2015) 97-101   References  [1] Takegaki, M. and Arimoto, S. 1981. A New Feedback Method for Dynamic Control of Manipulators. ASME Journal of Dynamic Systems, Measurement and Control. 103(2): 119–125. [2] Li, X., Hou, S. P.  and Cheah, C. C. 2010. Adaptive Region Tracking Control for Autonomous Underwater Vehicle. In Proc of the 11th Int. 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Fuzzy sliding mode with region tracking control for autonomous underwater vehicle

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Fuzzy sliding mode with region tracking control for autonomous underwater vehicle

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