### 1. Introduction

### 2. System design

### 2.1 Communication network

### 2.2 Route planning algorithms

*p*) between two specific points is equal to the arc length of the meridians of the two points at the middle latitude(

*L*).”. If the middle latitude is less than 60 ° and the sailing distance(

_{m}*D*) is within 600 nautical miles, the error range is less than 1%.(Yoon et al., 2013).

*A*(

*L*

_{1},

*λ*

_{1}) and the arriving point is

*Z*(

*L*

_{2},

*λ*

_{2}) , the course(

*C*) and the sailing distance (

*D*) between the two points are calculated by Eq. (1) and Eq. (2).

*DL*, difference of latitude

_{o}*l*, middle latitude

*L*and departure

_{m}*p*are obtained by the following equations.

### 2.3 Automatic steering controller

#### (a) Ship manoeuvring motion model

*G*-

*xyz*) with the coordinate origin at the ship’s center of gravity(

*G*) as shown in Fig. 2.

*δ*is rudder angle,

*β*is drift angle,

*r*is turning rate,

*u*and

*υ*are

*x*-axis speed and

*y*-axis speed, and

*V*is the sum of

*u*and

*υ*. And the ship manoeuvring motion can be formulated as a combined motion by the inertia, propulsion and external forces. On the other hand, the mathematical model proposed by Nomoto et al.(1957) is relatively simple and has the advantage that the slave ship manoeuvring motion could be expressed as a relationship between input(rudder angle) and output(turning rate), not in terms of fluid force. Nomoto model has limitations in representing the motion of the ship accurately. However, the purpose of this paper is to find out the effectiveness of the proposed system using RC boats, so simple Nomoto model was adopted that can predict the manoeuvring motion model of ship with minimal information. And the autoregressive with exogenous variables(ARX) model(Ljung, 1987) was used to estimate the manoeuvring indices

*K*and

*T*, unknown coefficients of Nomoto model. The ARX model generates a transfer function from input-output data, and then estimates the parameters of the transfer function. This method has been used in a study by Kim(2011) to build the USV manoeuvring motion model.

#### (b) Nomoto model

*δ*), turning rate(

*r*) and manoeuvring indices(

*T*

_{1},

*T*

_{2},

*T*

_{3},

*K*) shown as Eq. (7).

#### (c) ARX model

*z*is time delay operator,

*n*is time delay in the system,

_{k}*e*(

*t*) is random noise and coefficient terms

*A*(

*z*) and

*B*(

*z*) can be expressed by Eq. (11) and Eq. (12). Where

*n*and

_{a}*n*are the orders of the ARX model,

_{b}*R*

^{2}). The coefficient of determination has a value between 0 and 1, and the closer the value is to 1, the higher the reliability of the ARX model.

#### (d) PD controller

*K*is proportional gain,

_{P}*T*is derivative time,

_{D}*T*is derivative time constant and

_{f}*T*is sampling time.

_{s}*e*(

*z*)) by comparing the target course(

*ψ*) and the current course(

_{r}*ψ*). Then, control variable(

*u*(

*z*)) is calculated by the proportional-derivative actions. The control variable(

*u*(

*z*)) is limited to -35 to 35 degrees(

*u*(

_{s}*z*)) by the saturator and entered into the ship manoeuvring motion model. Finally, the ship manoeuvring motion model outputs the turning rate(

*r*), which changes the current course(

*ψ*).

*N*is a coefficient for adjusting the bandwidth of the filter, and usually has a value between 8 and 20(Åström & Hägglund, 1995). It was set to 10 in this study.

*K*and

_{P}*T*of the digital PD controller, the relay feedback tuning method(Åström & Hägglund, 1984) was used. This method generates critical oscillation using a transport delay and a relay with an amplitude of

_{D}*d*. Fig. 4 shows the process of the relay feedback tuning method.

*T*) and amplitude(

_{c}*a*) could be found, and then the critical gain (

*K*) is calculated by Eq. (15).

_{c}*K*and

_{P}*T*of the PD controller is calculated by Eq. (16) and Eq. (17) using the Ziegler-Nichols tuning method(Ziegler & Nichols, 1942).

_{D}### 2.4 Speed controller

*D*) is calculated by the positions of the master ship(

_{s}*L*

_{1},

*λ*

_{1}) and the slave ship(

*L*

_{2},

*λ*

_{2}) using middle latitude sailing method. Then, the controller changes the motor pulse width(

*P*) according to the distance(

_{m}*D*). The pulse width controls the motor RPM of the slave ship.

_{s}### 3. Experiments and results

### 3.1 Experimental setup

### 3.2 System identification results

*n*,

_{a}*n*) and parameters(

_{b}*δ*) and turning rates(

*r*). During the experiments, the Beaufort scale was 2 and the average wind speed was 2.2 m/s. But small wavelets on the surface were occurred due to the current to the south. Fig. 8 and Fig. 9 shows the experimental scene and the trajectory of the slave boat. The average speed of the slave boat was 6.0 kn(3.1 m/s).

*n*= 6 and

_{a}*n*= 6 using FPE criterion, and the corresponding parameters

_{b}*r*) and calculated by the ARX model(

*r*). The coefficient of determination

_{A}*R*

^{2}of the obtained ARX model is about 0.9387, which means that the ARX model and the slave ship manoeuvring motion have a significance of about 94%.

*K*and

_{P}*T*, the relay feedback tuning method was used. Adding a relay with an amplitude(

_{D}*d*) of 10 and a transport delay of 1 second to the slave ship manoeuvring motion model, a critical oscillation graph with an amplitude(

*a*) of 16.60 and a critical period(

*T*) of 8 is generated as shown in Fig. 11.

_{c}