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Realization of a Ship Autopilot using Fuzzy Logic Rahul Barman Roll number 03NA1013 Department of Ocean Engineering & Naval architecture Indian Institute of Technology, Kharagpur -721302, India Email: [email protected] Abstract Automatic steering of ships has been a goal of seafarers for many years. It was not until after the industrial revolution that methods for automatically steering of ships were first contemplated, and the first ship autopilots came into use during the first part of the twentieth century. Till date, for ship control, the Proportional plus Integral plus Derivative (PID) controllers remain common-place. However, increasingly new autopilot strategies, promising higher levels of robustness and adaptive qualities, are being proposed as possible successors to the PID. Imperatives such as reduced manning and increasing fuel costs also call for innovative designs from the classic PID controller to adaptive and robust control and latterly to intelligent control. This paper aims at addressing the possibilities of fabricating an autopilot structure for a ship using fuzzy logic. The paper describes crudely the procedure that can be used to design such a control system. An attempt is made to show how fuzzy logic can be used to tackle a problem as complex and non-linear as navigation control. Problem Definition As in any other control problems, the design of an autonomous navigation system for a ship (such as an autopilot) asks for reliable and appropriate mathematical model(s) of ship dynamics in quite different operating conditions .The particular challenges presented by ship autopilot designs relate to uncertainties in their operating environment which is inherently non-linear and time variant . Any changes in speed, water depth, mass loading, the severity of the weather, etc. change the dynamic characteristics of a ship. Modeling ship dynamics considering all real phenomena is a very complex task. In such a scenario where a concrete model is absent, fuzzy logic can be used as a tool for describing the system for design purposes. One of the main advantages of fuzzy logic autopilots is that the rules may be formulated without a precise definition of the ship’s dynamics. The control actions can normally be decided such that the required output is determined from knowledge of the expected ship’s response to the input. The use of fuzzy set theory as a method for replicating the nonlinear behaviour of an experienced helmsman is demonstrated in this paper. The process is based on the principle of subjecting the imprecise information through fuzzy arithmetic and finally obtaining a crisp value of the desired output parameter which is used in control mechanism. At any stage of the process, ship dynamics is done away with, which is good news because the dynamical model is simply not available for use. Details about the Problem The course-keeping fuzzy autopilot developed in this paper contains two control inputs: 1. Heading error 2. Yaw rate (Rate of change of heading error) The control action generated by the autopilot is the command rudder angle (δc), which is related to the maneuvering of a ship. Before the problem is presented in further detail, the above stated points need a bit of introduction which follows. A marine vehicle has 6 degrees-of-freedom (DOF) since six independent coordinates are necessary to determine the spatial position and orientation of a rigid body. The six different motion components are shown in figure 1a. For the course-keeping and the track-keeping problems only the horizontal-plane ship motion is used. Due to that 6DOF model is simplified and reduced to 3DOF model as shown in figure 1b.

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Figure 1. (a)Definition of ship motion in 6 Degrees of Freedom, (b) Ship’s horizontal plane coordinate system. The basic turning concept used in this paper is as follows. The desired route can be most easily specified by way points (P1, P2,…,Pn) with coordinates Pi = (xi, yi) (Holzhueter & Schultze, 1995). It is assumed that ship moves on a straight line between the way points. During the maneuver, the ship crosses from one to another line along a circular arc. Here, the tuning concept where the ship is circularly moving with a way point outside the circle is used. This is shown in figure 2. (The coordinates of the points Pi are obtained using GPS.)

Figure 2. Turning concept for track keeping. The ship enters maneuver by crossing from one to another line along a circular arc around a particular way point. At the end of this maneuver the next desired heading must be known for the next segment of the straight line. Let the ship move on the segment Pi−1Pi. The current ship position, denoted by the couple (x(t), y(t)), is calculated from kinematics ship equations. The desired way point is (xd, yd) = (xi, yi). Hence, the desired heading angle is obtained from the expression: ψ d = arctan

y d - y (t ) x d - x (t )

(1)

The ‘heading error’ and the ‘yaw rate’ mentioned above are defined as: HeadingError (e ) = ψ d - ψ YawRate ( r ) =

dψ dt

(2) (3)

The above inputs are fuzzy, and they are represented by using linguistic variables and appropriate membership functions. The basic block diagram of the analysis is shown in figure 3.

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Figure 3. Basic block diagram of the process. Details about the set applied For fuzzy analysis, the range of possible values for the input and output variables need to be determined. The real world measurements are then mapped into fuzzy membership functions, on which fuzzy operations are to be done. In this paper, analysis is done on normalized data (The range of values for a given autopilot inputs and output are normalized to the interval [−3 3]).After the operation, the output is obtained in normalized fuzzy form and has to be defuzzified to obtain a crisp value for use in control operations. Membership functions of input and output variables are shown in figure 4.The triangular-shaped membership function for input variables is used because the triangular-shaped fuzzy sets require the least amount of storage capacity and generate a far smoother fuzzification over the given input range, then trapezoidal or Gaussian sets (Polkinghorne, Roberts, Burns, & Winwood, 1994). Labels for the membership functions are given in Table 1.

Figure 4. (a) Membership functions for inputs (Heading-Error and Yaw-Rate) [Normalized].

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Figure 4. (b) Membership function for the output (Control-Radar-Angle) [Normalized]. Table 1. Labels for the membership functions.

The decision which the fuzzy controller makes is derived from the rules which are stored in the database. The fuzzy rules are extracted from fundamental knowledge and human experience about the process. These rules contain the input/output relationships that define the control strategy. This controller consists of if-then rules of the form: ‘IF heading error is positive small AND heading error rate is positive big THEN rudder angle is positive medium.’ The fuzzy autopilot uses 49 rules, corresponding to 7×7 different combinations of the two input fuzzy sets which are presented in a tabular matrix form .They are shown in table 2. Table 2. Rulebase of the course-keeping autopilot. (connection between the inputs is AND)

δc

Results and discussion With all the ingredients for fuzzy analysis defined, the response of the fuzzy system can be found out. For this paper, the response surface of the input-output relations has been determined using the Fuzzy Logic Toolbox of MATLAB, and is shown in figure 5. The response output is also normalized in form. The command rudder angle (δc ), has to be defuzzified to obtain the crisp value for use. For majority of cargo ships the rudder angle and the rudder rate are confined to be in the range δ max = 35 degrees and maximum rate of change of δ is between 2.33 degree/sec to 7degree/sec. The surface shows for a big Heading error and a big Yaw rate, the command rudder angle is also big, etc. which makes absolute sense.

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Figure 5. Input/output response surface Summary In the paper, we have been able to obtain the command-rudder angle from the very fuzzy inputs such as heading-angle and rate of change of heading error. In other words the controller has been presented with a situation analysis capability. What comes as a major advantage of the method is that at any stage of the analysis, we do not require the knowledge of ship dynamics in complex ocean environment. In the process the control mechanism becomes much more automatic and user friendly. To curtail the complexity of the problem only two input parameters were used in the paper. In a real sea state, the application of the method will require more number of relevant input parameters to sufficiently represent the sea characteristics which control the output parameter. Future directions Improvement of the track-keeping performance may be achieved by using a method of automatic tuning of parameters of an already existing standard fuzzy autopilot. A fuzzy gain controller (FGC) may be used that adjusts the inputs and output variables of fuzzy autopilot. This makes the process more automatic and real in taking care of the heavily complex and confused structure of sea. Future developments in more automatic and intelligent autopilots will undoubtedly evolve in a similar way in which the intelligent control community is evolving where incorporation of new ideas and methodologies based on learning control and intelligent decision making are gaining increasing popularity. References Roberts, G. N., Sutton, R., Tiano, A., Zirilli, A. (2003). ‘’Intelligent ship autopilots – a historical perspective’’, Mechatronics 13, 1091-1103. Velagic, J., Vukic, Z. (2003). ‘’Adaptive fuzzy ship autopilot for track-keeping’’, Control engineering Practice 11, 433-443. Polkinghorne, M.N., Roberts, G.N., Winwood, D. (1995). ‘’The implementation of fixed rulebase fuzzy logic to the control of small surface ships’’, Control engineering Practice Volume 3, Issue 3, 321-328. Abril, J., Salom, J. (1997). ’’Fuzzy control of a sailboat’’, International Journal of Approximate Reasoning, Volume 16, Issues 3-4, 359-375.