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The problem of coordinated control for multiple marine vessels in the presence of external disturbances is considered in this paper. A robust coordinated control algorithm is proposed for multiple marine vessels. The proposed robust coordinated control algorithm is divided into two parts. The first part develops an extended state observer to estimate the disturbances of marine vessels. The second part presents a robust coordinated control algorithm based on the output of the extended state observer. Furthermore, the robust coordinated control algorithm is designed using the dynamic surface control method. In light of the leader-follower strategy, the trajectory for each vessel is defined according to the desired trajectory of the assigned leader and the relative distance with respect to the leader. The effectiveness of the proposed coordination algorithm is demonstrated by the simulation results.

In recent years, coordinated control of multiple vehicles has received increasing attention as an emerging technology [

The problem of coordinated formation control has been reported in a large number of recent publications. Basic approaches of the coordinated control include leader-follower approach [

Some advanced approaches including graph theory [

In this paper, we consider the problem of coordinated formation control of multiple surface vessels in the presence of exogenous disturbances. The coordinated formation controller is proposed by combining the extended state observer and dynamic surface control using the leader-follower strategy. The extended state observer is developed to estimate the external disturbances of the surface vessels. The coordinated control algorithm is accomplished based on the output of the extended state observer. Furthermore, the trajectory of each vessel is defined using the desired trajectory of the assigned leader and the relative distance with respect to the leader. This paper is organized as follows. In Section

The vessel model can be divided into two parts: the kinematics and nonlinear dynamics. Generally, only the motion in the horizontal plane is considered for the surface vessel. The elements corresponding to heave, roll, and pitch are neglected. The dynamic model for the

In order to design the backstepping sliding mode controller, we transform the vessel model as follows:

In this section, the controller is designed from two inspects. One is the extended state observer design for each vessel, and the other is the coordinated controller for multiple vessels based on the output of the extended state observer.

In this section, we design the extended state observer for each vessel to estimate the disturbances.

Let

Let

The extended state observer is designed as

Set

The following assumptions are presumed.

The possibly unknown function

Let

The stability for the extended state observer is analyzed in [

This paper considers a fleet of n vessels to perform the desired coordination formation task. Each vessel in the formation is identified by the index set

The formation of these vessels.

Define the first dynamic surface as

The control input of the vessel is

Consider the vessel with the nonlinear model as in (

With the definition of the second surface, (

In this section, experimental simulations are carried out to evaluate the effectiveness of the proposed coordinated formation control algorithm. The detailed parameters of the vessel are presented in the literature [

The simulation results are shown in Figures

The movement of the vessel in the plane.

The practical value and estimated value of the positions.

The practical value and estimated value of the velocities.

The estimated value of the disturbances.

Then we evaluate the effectiveness of the proposed robust coordinated formation control algorithm. Three surface vessels are considered to perform the coordinated tracking task. The initial positions of the three vessels are

The simulation results are shown in Figures

Coordinated trajectory tracking of the vessels.

Heading change of the vessels.

Surge velocity change of the vessels.

Sway velocity change of the vessels.

Angular velocity change of the vessels.

This paper has proposed a new robust coordinated formation control algorithm for multiple surface vessels in the presence of external environmental disturbances. The proposed coordinated formation controller for these vessels is designed by combining the extended state observer and the dynamic surface control together. The extended state observer is designed to estimate the external disturbances of the surface vessels. The coordinated formation is realized based on the leader-follower strategy. The desired trajectory of each vessel is defined using the desired trajectory of the assigned leader and relative distance with respect to the leader. The controller is designed based on the output of the extended state observer and using the dynamic surface control method. The proposed coordinated controller is robust to the external disturbances. Finally, the effectiveness of the proposed robust coordination control algorithm is demonstrated by the simulation results.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors would like to acknowledge the support of the Natural Science Grant of Liaoning Province (2013020002).