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Research Papers

Nonsingular Serret–Frenet Based Path Following Control for an Underactuated Surface Vessel

[+] Author and Article Information
Jawhar Ghommam

Research Unit on Mechatronics and Autonomous Systems, Ecole Nationale d’Ingenieurs de Sfax, Tunisia; Laboratoire de Vision et Robotique (LVR),  Université d’Orléans, 63, Avenue, De Lattre de Tassigny, 18000 Bourges, France

Faïçal Mnif

 Sultan Qaboos University, P.O. Box 33, Muscat 123, Oman; Research Unit on Mechatronics and Autonomous Systems, Ecole Nationale d’Ingenieurs de Sfax, 3038 Sfax, Tunisia

Abederraouf Benali

Laboratoire de Vision et Robotique (LVR), Université d’Orléans, 63, Avenue De Lattre de Tassigny, 18000 Bourges, France

Nabil Derbel

Research Unit on Mechatronics and Autonomous Systems, Ecole Nationale d’Ingenieurs de Sfax, 3038 Sfax, Tunisia

For any a and b in Rn, and for any positive real number ε, we have ab(1/4ε)aa+εbb.

J. Dyn. Sys., Meas., Control 131(2), 021006 (Feb 04, 2009) (8 pages) doi:10.1115/1.3023139 History: Received April 04, 2007; Revised August 31, 2008; Published February 04, 2009

In this paper we develop a new control law to steer an underactuated surface vessel along a predefined path at a constant forward speed controlled by the main thruster system. The methodology is based on the Serret–Frenet formulation to represent the ship kinematics in terms of path parameters, which allows for convenient definition of cross and along track error. Furthermore, our approach for path following overcomes the stringent initial condition constraints. This paper also addresses the path following with environmental disturbances induced by wave, wind, and ocean-current. The proposed controller is designed based on the Lyapunov direct method and backstepping technique. The closed loop path following errors is proven to be uniform ultimate bounded. Results are demonstrated by high fidelity simulation.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Surface ship and frame definitions

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Figure 2

Path following control effort τr: without disturbances

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Figure 3

Ship position and orientation in the (x,y) plane

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Figure 4

Positions errors xe and ye

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Figure 5

Orientation error ψe

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Figure 6

Velocity in the sway direction

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Figure 7

Ship position and orientation in the (x,y) plane under environmental disturbance

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Figure 8

Positions errors xe and ye under environmental disturbance

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Figure 9

Orientation error ψe under environmental disturbance

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Figure 10

Velocity in the sway direction under environmental disturbance

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Figure 11

Path following control effort τr: with disturbances

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