Elsevier

Information Sciences

Volume 486, June 2019, Pages 359-378
Information Sciences

Velocity free leader-follower formation control for autonomous underwater vehicles with line-of-sight range and angle constraints

https://doi.org/10.1016/j.ins.2019.02.050Get rights and content

Abstract

This paper investigates the problem of leader-follower formation control of underactuated autonomous underwater vehicles (AUVs), where the Line-of-sight (LOS) range and angle are constrained. An observer is involved to estimate the leader velocity in finite time with zero error, alleviating the need of communications between the AUVs. Based on the finite time observer, the formation controllers of the AUVs are designed using time-varying ln-type barrier Lyapunov function (BLF) method, which can guarantee that the resulting AUVs formation control system is uniformly ultimately bounded. To deal with the problem of explosion of differentiation terms in backstepping control, we introduce a command filter to realize the derivative of virtual variables. At the same time, a compensating signal is constructed (based on the auxiliary system technique) to compensate for the errors of the command filter. Simulation results have demonstrated the effectiveness of the proposed method.

Introduction

In the past decades, autonomous underwater vehicles (AUVs) have been widely used to perform various underwater tasks for civilian and military purposes like search, exploration, surveillance, reconnaissance, rescue missions, seabed mapping, ocean floor survey, mine-sweeping, environmental monitoring, natural resource detection, marine biology exploration, and deep sea archeology and so on [2], [3], [26], [29], [31]. Such tasks usually cannot be performed by a single vehicle with satisfactory performance and within reasonable time and cost, since any vehicle (even those with sophisticated equipment) has limited energy and coverage. Cooperation of multiple vehicles is thus a good choice to accomplish such missions, which has attracted great research interests, especially in formation control of AUVs. Among the various formation control methods, the leader-follower strategy is preferred in many applications due to its simplicity and scalability. Some outstanding works within this framework can be seen in the literature [13], [21], [28], [30], [34], [35].

What are the challenging problems associated with the leader-follower formation control of autonomous underwater vehicles? The first fundamental issue is the limitation of information exchange between the AUVs. The acoustic communication devices in AUVs has low propagation speed, limited bandwidth, and high energy consumption. Moreover, since sound energy is attenuated by the water very rapidly as the frequency increases, relatively low frequencies are desirable for long-range communications. This means that the data rate is very low and, hence, data transmissions between AUVs should be kept to a minimum amount [4]. Most of the results on AUVs formation control so far assume continuous information exchanging between AUVs [13], [23], [28], [30], [34], [35]. This implies that a large amount of redundant (and noisy) data should be transmitted, which is clearly impractical due to unbearable communication burden, energy consumption, and large delay. A practical control method should be less demanding for communications between AUVs. To this end, some new schemes have been proposed in [5], [16], [21] aiming at reducing data communications between neighbouring AUVs and the leader. For example, an impulsive system approach to AUV formation control was given in [21], which reduces data transmission by using an impulsive signal sequence to control the communications between nodes. Some other research works suggested to use position feedback only, introducing speed projection algorithm [5] or velocity observer [16] to eliminate transmission of the leader velocity. In [24], a coordination error observer is involved to estimate the leader state which is usually transmitted via acoustic communication. Velocity-free AUV formation control methods were presented, using a filter for each follower AUV to estimate the velocity of the leader in [1], [6]. Aperiodic sampling [17], especially, event-triggered communication [18], are of great use for eliminate communication cost. This paper will use a finite-time observer to estimate the leader velocity, which is the first effort of its type in AUV formation control.

The second fundamental problem is relevant to system output constraints. As in all practical engineering systems, we need the state of the AUVs to remain in some compact sets due to system specifications, performance or safety requirements. Any violation of these constraints may lead to misbehavior of the system’s transient response, performance degradation, or system instability. Control problems with hard constraints on the system’s outputs have not been fully handled in marine engineering. In the context of formation control of autonomous underwater vehicles, there are applications in which the line-of-sight (LOS) range and bearing angle between AUVs need to be constrained within a certain range. For example, when crossing narrow passages and passing areas crowded with obstacles, it is necessary to restrict the LOS range and bearing angle of the vehicles within a given zone. If the LOS range is too small, it may result in collision between the vehicles. Otherwise, if the LOS range is too large, the vehicles may fail to cross or pass safely. In search and rescue missions, for example, undesired LOS range and angle between AUVs may result in leaving some critical areas unsearched or making the AUVs to lose contact with each other. Although the problem is of practical importance, constrained formation control of AUVs has not been investigated. Studies along this direction have merely considered systems that are relatively easy to handle, e.g., multi-agent systems and mobile robots. For instance, a formation constrained control problem was studied in [12] for multi-agent systems by introducing a constraint function to establish the formation. Model predictive control (MPC) methods were presented for formation control of multiple agents in [7], [9], [25], [36], [38]. In [8], a geometric constrained formation control method was given for differential drive mobile robots. Notice that these results are not directly applicable to the formation control problem of underactuated autonomous underwater vehicles with constrained LOS range and bearing angle. This paper presents a constructive leader-follower formation control method for a group of underactuated autonomous underwater vehicles with LOS range and angle constraints and communication limitations. The presented framework assumes no velocity information transmission from the leader to the follower AUV. A finite-time velocity observer is designed to solve the problem of communication limitations, which can estimate the leader velocity in finite time. The control strategy is designed based on asymmetric barrier Lyapunov function (ABLF) method that accounts for the constraints on the LOS range and angle between the leader and the follower. A command filter is introduced to realize the derivative of variables, which can avoid explosion of differentiation terms in many backstepping control methods [5], [6], [30], [34], [35], that uses an approximate differentiation scheme (i.e., velocity is derived from differentiation of the position measurement). In the meanwhile, a compensator signal is constructed (based on the auxiliary system technique) to compensate for the errors of the command filter. The main contributions of this paper are summarized as follows:

  • 1)

    In contrast to the formation control of AUV systems [23], [34], [35], where the leader’s state information (i.e. position and velocity) need to be transmitted continuously to the follower, through a velocity observer, the proposed scheme only requires the leader position information in the formation process, which can greatly reduce the communication burden. Besides, the given velocity observer can guarantee that the observed values track the real one in a finite time, which is better than those proposed in [5], [6], [30].

  • 2)

    To avoid the contravention of the time-varying constraint requirements on the LOS range and angle, asymmetric BLFs are incorporated with the control scheme and formation tracking is achieved successfully.

  • 3)

    Finally, the command filter technique is integrated into the controller design, and an error compensating system is constructed. Compared to the backstepping algorithm in [34] and the dynamic surface control (DSC) algorithms in [5], [30], [35], the proposed algorithm can not only decrease the computational burden, but also can eliminate the filtering error.

The organization of this paper is as follows. Some useful preliminaries and problem formulation are presented in the next section. Section III presents the main results. Section IV demonstrates the effectiveness of the proposed control approach by simulations, and finally, we conclude this paper and propose some further work in Section V.

Section snippets

Preliminaries and problem formulation

In this section, some lemmas and definitions are given first, which are followed by the problem formulation.

Main results

In this section, a velocity observer is designed to estimate the velocity of the leader AUV with zero estimation error. Then, based on the estimated velocity we obtain a controller design method, in which the Barrier Lyapunov Function is used to avert the contravention of the constraints.

Simulation

In this section, the performances of the proposed control law for the formation controller of two autonomous underwater vehicles will be verified by simulations. The simulations are carried out using MATLAB/Simulink environment. For these simulations, the physical parameters of the leader and the follower are given by Ml=Mf, Cl(υl), Cf(υf), Dl(υl), and Df(υf) which are determined as follows [1]:Ml=Mf=[15000220002.5],Dl=Df=[250002500015]Cl(υl)=[0022vl0015ul22vl15ul0],Cf(υf)=[0022vf0015uf22vf

Conclusions

In this paper, a leader-follower formation control method has been proposed for underactuated AUVs with LOS range and angle constraints and the velocity of the leader is not available. A finite-time velocity observer is designed to estimate the velocity of leader with zero estimation error. Then, based on the estimated velocity of the leader, a nonlinear controller is designed for the follower. In the process of controller design, an asymmetric BLF is used to avert the contravention of the

Acknowledgements

This work was supported by the National Nature Science Foundation of China under Grant 61573077 and U1808205, and partially by National Key R&D Program of China under Grant 2017YFA0700300.

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