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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 $a⊤b≤(1/4ε)a⊤a+εb⊤b$.

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

Abstract

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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Figures

Figure 2

Path following control effort τr: without disturbances

Figure 5

Orientation error ψe

Figure 6

Velocity in the sway direction

Figure 7

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

Figure 8

Positions errors xe and ye under environmental disturbance

Figure 9

Orientation error ψe under environmental disturbance

Figure 10

Velocity in the sway direction under environmental disturbance

Figure 1

Surface ship and frame definitions

Figure 3

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

Figure 4

Positions errors xe and ye

Figure 11

Path following control effort τr: with disturbances

Errata

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