Smooth transition of AUV motion control: From fully-actuated to under-actuated configuration

https://doi.org/10.1016/j.robot.2014.09.024Get rights and content

Highlights

  • Steering AUV through the whole low-speed and high-speed profiles is considered.

  • Evolution of the side-slip angle is clearly treated in the motion control design.

  • Smooth control transition between fully/under-actuated configurations is enabled.

  • Simulation results explicitly show the transition behaviors of the control efforts.

Abstract

This paper addresses the problem of steering autonomous underwater vehicle (AUV) along a desired horizontal path throughout the full-range low-speed and high-speed profiles, experiencing both fully-actuated and under-actuated configurations. First, a nonlinear controller adopting Lyapunov’s direct method and backstepping technique is proposed for under-actuated AUV, based on the Line-of-Sight guidance built in a moving Frenet–Serret frame. And then, the controller is adapted to fully-actuated AUV except that the control computation for the evolution of the side-slip angle is different from the case of under-actuated one. Hence, both the fully-actuated and under-actuated configurations are under the same control framework, which enables a smooth continuous transition between two configurations in a synthesized controller. Finally, simulation results illustrate the performance of the proposed control design, where the varied control efforts in the sway direction clearly show the transitions from fully-actuated to under-actuated configuration.

Introduction

Over the past two decades, a remarkable growth regarding the operation of autonomous underwater vehicle (AUV) has been witnessed in the wide range of commercial, scientific and military applications  [1], [2], [3], [4], such as offshore oil and gas exploration and exploitation, underwater survey and observation, mine reconnaissance and neutralization, etc. In order to meet these miscellaneous goals, it is desirable to automatically control the AUV through all the feasible speed profiles from low-speed starting to high-speed maneuvering. Traditionally, fully actuated AUV with independent actuators in all degrees of freedom (DOF) simultaneously are suitable for low-speed maneuvering in confined water and easily docking in harbor, whereas under-actuated AUV possessing more DOF than the control inputs, which are not able to command independent accelerations in all DOF simultaneously, are assumed for high-speed maneuvering in long-range and long-duration missions due to cost-effective and weight considerations. In practice, lots of AUVs are inherently under-actuated without thrusters and/or rudders in the sway, heave or roll directions, as described in  [5], [6], [7], [8], [9], to name but a few. In addition, a fully-actuated AUV equipped with lateral actuators in sway and heave directions to assist at low-speed maneuvering, dramatically decreases its efficiency in these lateral directions at high-speed forward movement due to the relative perpendicular water flow passing the outlets, which implies that the sway and heave movements are not independently controlled, and leads a fully-actuated AUV to behave like an under-actuated one as the rest. It results in the development of structurally different controllers for both the fully-actuated and under-actuated configurations, and an intelligent supervisor is generally required to perform a heuristics and hybrid switch between two controllers. On the other hand, fully actuated underwater vehicles might be exposed to actuator failures, rendering themselves into under-actuated cases. Hence, it is also required for a critical solution to have control redundancy to guarantee the vehicle safety as much as possible, by allowing the vehicle to be controlled with the remained actuator capability, and enabling the control algorithm to switch between fully-actuated and under-actuated configurations to ensure system reliability. Moreover, from both a theoretical and practical point of view, it is desirable to have a smooth transition between these two actuated configurations covering the full-range speed profile in a single synthesized controller, in order to avoid the possible oscillation and even destabilization problem coming from hard switching, reduce the complexity of the controller and render easy implementation in practice.

To the best knowledge of the authors, there are few research work reported in this specific control topic to deal with the under-actuated and fully-actuated AUV configurations together. In  [10], a hybrid switching design combining a dynamic positioning controller in low-speed and a track-keeping controller in high-speed is proposed for minehunters. In [11], an automatic navigation and track-keeping system (ANTS) dealing with tight heading control are separated from a harbor mode with high-precision position and heading control. In [12], a simple logic is used to switch algorithms when the operation changes. Reinitialization of control parameter is required and discontinuity occurs at the point of switching operation. In  [13], simultaneously global asymptotic stabilization and tracking is only solved in the case of under-actuated underwater vehicle, without the consideration from fully-actuated to under-actuated configurations. In [14], a unified control structure for AUV is proposed where the transition factor relies on the composite speed; however, the derivative evolution of side-slip angle is not thoroughly analyzed in the dynamics stage, which implies different control treatments due to the directly or indirectly controlled transverse (sway) movement in fully-actuated and under-actuated modes respectively. On the other hand, while developing advanced methods for AUV motion control, it should be noticed that kinematic and dynamic models of AUVs are highly nonlinear and coupled  [15], making the motion control design a challenging task. The complex hydrodynamics effects, which must be taken into account during the control design, excludes any attempt to design a steering system for the AUV relying on its kinematic model only as stated in [7]. In addition, underactuation rules out the use of trivial control schemes, e.g., full state-feedback linearization  [16]. Furthermore, the indirectly controlled sway and heave velocities due to underactuations, which generate non-zero angles of side-slip and attack respectively, should be carefully considered as well  [17].

Motivated by the above considerations, this paper proposes a synthesized path following controller which enables smooth transition between fully-actuated and under-actuated AUV configurations throughout the full-range feasible speed profile. For sake of simplicity, 3-DOF horizontal motion control of AUVs is considered herein, and it can be extended to 6-DOF motion control in full space if the heave speed in the decoupled vertical plane and resulted attack angle are included, besides the side-slip angle in the sway direction. The control system proposed in this paper is derived via two steps. First, by adopting Lyapunov’s direct method and backstepping technique, a nonlinear path following control law for fully-actuated AUV is proposed based on Line-of-Sight guidance built-in Frenet–Serret frame, which is adapted from the control law for under-actuated AUV originally proposed in  [18]. Thus, both the under-actuated and fully-actuated cases under the same control framework, except that the control computation for the derivatives of the side-slip angle of AUV is different, through completely considering the difference of the indirectly or directly controlled side-slip angle in these two cases. And then, a smooth transition but not hard switch between two controllers is designed from low-speed starting in fully-actuated pattern to high-speed maneuvering in under-actuated pattern, where the transition factor covering the full-range speed profile is a smooth function of the instantaneous surge speed of the AUV. Consequently, the desired control design is completed for AUV traveling from low speed (fully-actuated configuration) to high speed (under-actuated configuration).

The rest of the paper is organized as follows. Problem statement is presented in the next section, including the kinematics and dynamics model of AUV and the control objective. In Section  3, a nonlinear path following controller is designed for under-actuated AUV, and then extended to fully-actuated AUV in order to keep the same control framework for both actuation configurations. Subsequently, a synthesized controller with smooth continuous transition in terms of the instantaneous surge speed of AUV is proposed. Numerical simulation results are given in Section  4 to illustrate the performance of the proposed controller. Section  5 contains some concluding remarks and discusses problems that warrant further research.

Section snippets

Problem statement

This section describes the kinematic and dynamic model of the AUV in the horizontal plane and formulates the motion control problem of the path following through the full-range feasible speed profiles. The notation used in the paper is standard  [19].

Path following error dynamics

Let the position and course angle of the AUV denoted by Q=(x,y,ψW)T in the inertial frame {I} as illustrated in Fig. 1, and let the position and heading of the moving virtual target on the path denoted by P=(xF,yF,ψF)T in the inertial frame {I}. The path following error vector peF=(xe,ye,ψe)T built in the Frenet–Serret frame {F} can be written as [xeyeψe]=[cosψFsinψF0sinψFcosψF0001][xxFyyFψWψF] where the course angle ψW=ψB+β and yaw rate r=ψ̇B.

Differentiating the error vector (4) and

Numerical simulations

In order to illustrate the performance of the proposed control scheme in Section  3, numerical simulations are carried out with the AUV dynamics model in [30], [16]. The hydrodynamic parameters are shown in Table 1.

Conclusions

This paper addresses the problems of nonlinear motion control of path following for fully-actuated/under-actuated AUV in the horizontal plane, based on Lyapunov theory and backstepping technique. Traditional LOS guidance for tracking straight-line path is trimmed to follow curved path by building LOS in the moving Frenet–Serret frame. Smooth transition between fully-actuated and under-actuated AUV configurations is achieved in a single synthesized controller, which enables an AUV travels

Acknowledgments

This work was partially supported by the EU FP6 FreeSubNet project under Grant 036186, the National Natural Science Foundation (NNSF) of China under Grant 51209100, the Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20120142120045, and the Fundamental Research Funds for the Central Universities (HUST: 2013TS090). The first author was supported by the European Marie Curie ESR Fellowship of the FP6 project Freesubnet.

The authors would like to thank the

Xianbo Xiang received the Ph.D. degree in robotics from the University of Montpellier 2, Montpellier, France, in 2011. He received his Bachelor and Master degrees in Automatic Control and Marine Engineering, from Huazhong university of science and technology, China, in 2000 and 2003 respectively. And then, he joined the same university as a Lecturer. From Sept. 2006 to Dec. 2006, he was an EU Erasmus Mundus visiting scholar in the SpaceMaster project. From February 2008 to March 2011, he worked

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    Xianbo Xiang received the Ph.D. degree in robotics from the University of Montpellier 2, Montpellier, France, in 2011. He received his Bachelor and Master degrees in Automatic Control and Marine Engineering, from Huazhong university of science and technology, China, in 2000 and 2003 respectively. And then, he joined the same university as a Lecturer. From Sept. 2006 to Dec. 2006, he was an EU Erasmus Mundus visiting scholar in the SpaceMaster project. From February 2008 to March 2011, he worked for the European Project FreeSubNet as a EC Marie Curie ESR Fellow at LIRMM, CNRS UMR 5506, France. Currently, he is an Associate Professor at the School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology.

    Lionel Lapierre received the Ph.D. degree in robotics from the University of Montpellier 2, Montpellier, France, in 1999. Then, he joined the team of Prof. A. Pascoal within the European project FreeSub for three years in Instituto Superior Técnico(IST), Portugal. Since 2003, he has been with the Robotics Department, the Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier (LIRMM), CNRS UMR 5506, Montpellier, France. He is currently a Maître de conférences (eq. Associate Professor) at University of Montpellier 2, Montpellier, France.

    Bruno Jouvencel was born on February 3, 1955, in Paris, France. He graduated from the Electronical Engineering Department, Ecole Normale Suprieure, Cachan, France, in 1981. He received the Ph.D. degree in perception systems for robotic manipulators in automatic control from Montpellier University, Montpellier, France, in 1984. Currently, he is a Full Professor at Montpellier University II and Researcher at LIRMM. For ten years, he has worked on the design, the command, and the perception of autonomous underwater vehicles. A first prototype Taipan1 has been developed in 1998, and a second vehicle Taipan2(H160) was conceived and realized in partnership with an industrial company. He was recipient of the first prize of the EURON/EUnited Robotics “Technology Transfer Award” in 2006 due to the contribution to Taipan AUVs.

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