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Experimental Validation of Longitudinal Control of a Platoon of Vessels Established via the V-REP Simulator

Myoung-Sung Kim1, Kwang-Kook Lee2, and Dong Hun Kim3

1Department of Mechatronics Engineering, Kyungnam University, Changwon, Korea
2Department of Naval Architecture & Ocean System Engineering, Kyungnam University, Changwon, Korea
3Department of Electrical Engineering, Kyungnam University, Changwon, Korea
Correspondence to: Dong Hun Kim (dhkim@kyungnam.ac.kr)
Received October 29, 2019; Revised November 30, 2019; Accepted December 3, 2019.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract

This study experimentally validates longitudinal control of a platoon of vessels established via the virtual robot experimentation platform (V-REP) simulator. For inter-vessel platooning, vessel positions are verified through GPS and the azimuth between vessels. A safety distance between the preceding and trailing vessels moving at variable speeds is proposed. The proposed method enables all the vessels to move, maintaining a compact formation, even when another vessel crosses the platoon of vessels because preceding vessels wait for trailing vessels. Results of extensive V-REP-based simulations indicate that the proposed approach is viable and effective in establishing longitudinal control of a platoon of vessels.

Keywords : Platooning, Vessel, Following, V-REP
1. Introduction

Lately, a variety of unmanned surface vessels are being developed globally, having numerous applications and progressively demonstrating increased industrial and military use. For autonomous unmanned surface vessel propulsion and navigation, accurate positioning and obstacle avoidance data is required.

Currently, as the economy progresses, total manned small vessel volume is continuously declining due to relatively high operating costs. These problems have led to a steady expansion of autonomous navigation study [1, 2]. Although automation technologies in the United States, Germany, and Japan have led the way until now, many other countries such as China, Israel, and South Korea are also investing in technology development. Based on these technical skills, research related to track keeping control [35], dynamic ship position [68], and automatic movement control [9] is underway; with application research also proceeding for actual vessels.

Meanwhile, to reduce land-based labor costs, platoon technology was developed for maintaining the distance between a platoon of vehicles. A representative example is the recent development of autonomous driving trucks in The Netherlands, where two or three trucks connected by Wi-Fi are driven at a constant distance. Additionally, numerous platooning systems based on vehicle-to-vehicle (V2V) communication have been studied [10, 11].

Similarly, to reduce the labor costs at sea, related studies on platooning have been conducted [12]; land-based studies have been conducted extensively; however, considerable sea-based research is yet to be conducted. Although vehicle platooning has been studied, no way of maintaining the vessel spacing at sea has been specified. Therefore, this study introduces vessel platooning.

This study experimentally validates the longitudinal control of a platoon of vessels established via the virtual robot experimentation platform (V-REP) [13, 14]. Presently, there are several robot branch simulators both at home and abroad; for example, Gazebo, We-bots, V-REP, etc. Among these, V-REP, as an open-source application also free to researchers, is one of the most widely used simulators. In the platooning framework, the safety distance between a preceding and a trailing vessel moving at a variable speed is proposed. This method enables all vessels to move, maintaining a compact formation, even when another vessel crosses their track because the preceding vessel waits for the trailing vessel. There is no intention to tackle all possible navigational problems related to the longitudinal control of a platoon of vessels.

The remainder of the paper is organized as follows. Section 2 shows vessel composition in the V-REP environment. Section 3 explains a vessel model and controller design. In Section 4, the vessel platooning using preceding vessel variable safe distance and speed control is proposed. The V-REP simulation results are presented and discussed in Section 5. Finally, the paper is concluded in Section 6.

2. Composition in V-REP Environment

Here, a platoon of unmanned vessels is designed through V-REP as shown in Figure 1. Unmanned vessels are equally equipped with GPS [15] and LiDAR [16, 17] sensors because they must always be aware of their current and final coordinates to reach the intended destination. To this end, vessels are equipped with these sensors for avoiding obstacles during autonomous driving. Figure 2 shows a platoon of vessels.

3. Vessel Model and Controller Design

An environmental unmanned vessel kinematic formula as shown in Figure 2 is expressed below in Eq. (1) [18, 19],

$Δxpi=cos θpi×(vLi+vRi)2=cos θpi·vi,Δypi=sin θpi×(vLi+vRi)2=sin θpi·vi,Δθpi=vLi+vRi2=wi,$

where θpi is the unmanned vessel rotation angle with respect to the x-axis. vi and wi is linear and angular velocity, respectively, and are defined by Eq. (5). vLi and vRi is the left and right propeller speed value, respectively.

Both propeller speeds of vLi and vRi are equal when driving straight. However, vLi is greater than vRi when the vessel turns right, and vRi is zero during a sharp right turn. The opposite is true when the vessel turns left.

Eq. (1) summarization is expressed in Eq. (2),

$Q˙i=[x˙piy˙piθ˙pi]=[cos θpi0sin θpi001] [viwi].$

The unmanned vessel has three degrees of freedom, xpi, ypi, and θpi, around the z-axis and is expressed as three vectors $Qi=[xpiypiθpi]T$, where x and y are the x- and y-axis positions.

The linear velocity vi and angular velocity wi are described in discrete time as follows:

$vi(k)=vLi(k)+vRi(k)2,wi(k)=vLi(k)-vRi(k)2.$

In Figure 3, (xt1(k), yt1(k)) is the first vessel goal position. (xti(k), yti(k)), i = 2, ..., n is a vessel Qi goal position, which is designed according to Sdi,

$xti(k)=xp i-1(k)-Sdi(k)·cos(θti(k),yti(k)=yp i-1(k)-Sdi(k)·sin(θti(k)),$

where compares the corresponding vessel starting point coordinates with the goal point coordinates. For a vessel Qi, the current coordinates are xpi(k) and ypi(k). Figure 3 shows safety distance between 1st and 2nd vessels.

The vessel and goal point coordinate difference is xdi and ydi as follows:

$xdi(k)=xti(k)-xpi(k),ydi(k)=yti(k)-ypi(k).$

The destination distance, edi(k) is shown in Eq. (6),

$edi(k)=xdi2(k)+ydi2(k).$

The direction angle for the vessel goal position is θti(k),

$θti (k)=atan (ydi(k)xdi(k)).$

The vessel direction angle and goal position difference is,

$θdi(k)=θti(k)-θpi(k),$

where the i-th vessel direction angle is θpi(k).

The unmanned vessel control performs autonomous operation by comparing the current coordinates with the destination coordinates through the GPS and compass sensors. PD control is used because only azimuth direction and straight motion control are required [20, 21]. PD control is a control technique that uses derivative control to generate an error signal that produces a proportional control signal.

For a vessel Qi, the left and right motor speed to a vessel goal point is as follows:

$vLi(k)= c-kpθθdi(k)-kdθ×θdi(k)-θdi(k-1)Δt +kpeedi(k)+kde×edi(k)-edi(k-1)Δt,vRi(k)= c+kpθθdi(k)+kdθ×θdi(k)-θdi(k-1)Δt +kpeedi(k)+kde×edi(k)-edi(k-1)Δt,$

where $kpθ$ and $kdθ$ represent the proportional and differential gains for the direction angle, respectively; with $kpe$ and $kde$ representing distance proportional and differential gains, respectively. c is the minimum value required for the motor to turn.

The size of vL and vR is constrained using a saturation function due to vessel rotational radius.

The proportional terms use current steps of θdi(k) and edi(k). The differential terms use variations of θdi(k) and edi(k) for sampling time Δt.

4. Vessel Platooning

To enable autonomous vessel platooning, a trailing vessel must secure a safe distance from its preceding vessel. The preferred safety distance must be as small as possible. The minimum safety distance can be defined in different forms when considering safety factors for tides, waves, or other external environmental factors.

The i-th unmanned vessel preferred safety distance rule is known as the California rule in Eq. (10) as follows [22]:

$Sdi(k)=ρvi(k)+L, i=2,…,n,$

where vi is the i-th vessel speed, ρ is the minimum deceleration of the vessels and L is the minimum distance, considerably larger than the vessel’s length.

Based on the California rule, this study proposes a method that restricts the speed of the preceding vessel when its trailing vessel stops or encounters another vessel. According to Eq. (10), the vessel destination point is given by Eq. (4).

Eq. (10) is called a constant time headway policy for a certain time period; utilized for safety distance maintenance between preceding and trailing vessels at varying speeds. It also maintains a minimum distance of L when the preceding vessel stops. When the constant ρ is large, a significant preceding vessel speed percentage is used to establish safety distance rules. Sd1(k) is not needed, since the first vessel is going for the goal position. The vessel speed is expressed as the unit 1 kn = 0.514 m/s.

Figure 4 shows an example of safety distance between the preceding and trailing vessels according to the preceding-ship speed when ρ = 0.5 and L = 1.3 m in Eq. (10).

Eq. (11) is the compactness index and also represents the total safe distance between vessels. If the distance between vessels is small, a compact straight formation exists,

$∑i=1n-1(xpi-xp i+1)2+(ypi-yp i+1)2.$

Maintaining a safe distance between the preceding and trailing vessels means that the faster the preceding vessel speed, the larger the safety distance, and the slower the preceding vessel speed, the smaller the safety distance.

However, if the trailing vessel encounters another vessel interrupting its track, it stops until the interrupting vessel is away from its path. In this case, the distance between the trailing and preceding vessels increases further; as a result, the trailing vessel takes a long time to return to the preceding-vessel minimum safety distance.

To prevent this phenomenon, when the trailing vessel stops or reduces speed, we consider varying Gaussian speed as in Figure 5(a) for the preceding vessel, as shown in Eq. (12),

$vi(k)=exp(-(edi(k)-μ)2σ2),$

where σ means the width and μ means the time to reach the maximum value.

Finally, we adopt a variable speed as in Figure 4(b) for the preceding vessel, where μ = 0, σ = 7.

This paper presents experimental validation for platoon of vessels longitudinal control. Latitudinal control issues related to Collision regulations (COLREGs) is out of scope for the paper [23, 24]. If the trailing vessel encounters another vessel that interrupts the track, it stops until the interrupting vessel is out of the pathway; then, the trailing vessel follows the preceding vessel without changing direction. Thus, only a COLREGs crossing maneuver from right or left is considered.

5. Simulation

In this section, platoon of vessels longitudinal control is presented. The proposed method is demonstrated for three unmanned vessels through a V-REP simulator [9, 10]. The parameter values are ρ = 0.5, L = 1.3 m, $kpθ=0.01,kdθ=0.037,kpe=1$, and $kde=0.1$, equally applied to three unmanned vessels.

Figures 6 and 7 show the V-REP simulation snap shots and vessels position coordinates, respectively. At 52 seconds, another vessel crosses between the first and second vessels. The second vessel waits while the intervening vessel passes the platoon. The first vessel waits for the second vessel, maintaining the gap between the two vessels.

For the scenario, linear velocity, angular velocity, and safety distance between the vessels are illustrated in Figures 8 and 9; showing a platoon of vessels based on a constant safety distance method and the proposed method, respectively. In Figure 9(a) the first vessel is waiting for the second vessel between 55 seconds and 70 seconds unlike

In the proposed method, safety distance changes linearly based on preceding vessel speed. At 75 seconds in Figure 9(c), the actual distance becomes smaller than the safety distance. This is caused by the drastic preceding vessel speed change; however, since the actual distance is still larger than minimum distance L, no collision occurs.

Figure 10 shows the total safe distance between vessels described in Equation (11). The constant safety distance method and the proposed method are used for vessel platooning in Figure 10(a) and 10(b), respectively. As a result, the proposed method shown in Figure 10(b) shows a more compact formation than the general method with constant safety distance defined by L = 2 m as seen in Figure 10(a). Therefore, the proposed method shows it is better suited for maintaining distance compactness between vessels.

6. Conclusions

In this paper, a platoon of vessels longitudinal control method using a V-REP simulator is presented; proposing an effective platoon of vessels scheme in the V-REP environment; using a variable safe distance between preceding and trailing vessels based on the California rule. In the conventional California rule platoon scheme, the preceding vessel moves without considering its trailing vessel position. For that reason, a compact formation among vessels is not achieved. The proposed method satisfies compact formation among vessels even when another vessel cuts across the platoon. Since the preceding vessel considers its trailing vessel speed, the distance between the preceding and trailing vessels is maintained without a large gap between two vessels. Thus, the proposed method is more appropriate for variable distance maintenance than constant distance, or even using the California rule alone.

Conflict of Interest

Acknowledgements

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2017R1A2B4011329).

Figures
Fig. 1.

Vessel configuration in V-ERP.

Fig. 2.

A platoon of vessels.

Fig. 3.

Safety distance between 1st vessel and 2nd vessel.

Fig. 4.

Example of safety distance according to speed: (a) 5 kn and (b) 10 kn.

Fig. 5.

Speed of the preceding vessel in Eq. (12): (a) μ = 5and σ = 2and (b) μ = 0and σ = 7.

Fig. 6.

V-REP simulation: (a) t = 0, (b) t = 52, (c) t = 62, and (d) t = 170 seconds.

Fig. 7.

Position coordinates of vessels: (a) t = 0, (b) t = 52, (c) t = 62, and (d) t = 170 seconds.

Fig. 8.

Unmanned vessel using constant safety distance: (a) linear velocity of vi(k) in Eq. (3), (b) angular velocity wi(k) in Eq. (3), and (c) safety distance calculated as Sdi(k) = 2 in Eq. (4).

Fig. 9.

Unmanned vessel using the proposed method: (a) linear velocity of vi(k) in Eq. (3), (b) angular velocity wi(k) in Eq. (3), and (c) safety distance calculated as Sdi(k) = ρvi(k) + L in Eq. (4).

Fig. 10.

Total safe distance between vessels in Eq. (11): unmanned vessel using (a) constant safety distance and (b) the proposed method.

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Biographies

Myoung-Sung Kim received his B.S. degree from the Department of Electrical Engineering, Kyungnam University, Korea, in 2017. He is currently a M.S. candidate in the Department of Mechatronics Engineering, Kyungnam University. His research interests include platoon of vessels, mobile robots, and behavior algorithm.

E-mail: muldonge3@naver.com

Kwang-Kook Lee received his degrees from the Department of Naval Architecture& Ocean Engineering, Seoul National University, Korea, in 2008. From 2008 to 2011, he was a manager of production planning team in STX Offshore & Shipbuilding. From 2019 to 2020, he joined University of Southampton, UK, as a visiting professor. Since 2011, he has been an associate professor at the Department of Naval Architecture & Ocean System Engineering, Kyungnam University, Korea. His research interests include marine system design and control, modelling and simulation, and hardware-in-the-loop simulation.

E-mail: kklee@kyungnam.ac.kr

Dong Hun Kim received his B.S., M.S., and Ph.D. degrees from the Department of Electrical Engineering, Hanyang University, Korea, in 1995, 1997, and 2001, respectively. From 2001 to 2003, he was a research associate under several grants in the Department of Electrical and Computer Engineering, Duke University, NC, USA. In 2003, he joined Boston University, MA, USA, as a visiting assistant professor under several grants at the Department of Aerospace and Mechanical Engineering. In 2004, he was engaged in post-doctoral research at the School of Information Science and Technology, the University of Tokyo, Japan. Since 2005, he has been a professor at the Department of Electrical Engineering, Kyungnam University, Korea. His research interests include swarm robotics, mobile robots, decentralized control of autonomous vehicles, intelligent control, and adaptive nonlinear control.

E-mail: dhkim@kyungnam.ac.kr

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