LINE-OF-SIGHT PATH FOLLOWING OF UNDERACTUATED MARINE CRAFT Thor I. Fossen ∗,1 Morten Breivik ∗ Roger Skjetne ∗ ∗ Centre of Ships and Ocean Structures (CESOS), Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway. E-mails: tif@itk.ntnu.no, mortebre@itk.ntnu.no, skjetne@ieee.org Abstract: A 3 degrees of freedom (surge, sway, and yaw) nonlinear controller for path following of marine craft using only two controls is derived using nonlinear control theory. Path following is achieved by a geometric assignment based on a line-of-sight projection algorithm for minimization of the cross-track error to the path. The desired speed along the path can be specified independently. The control laws in surge and yaw are derived using backstepping. This results in a dynamic feedback controller where the dynamics of the uncontrolled sway mode enters the yaw control law. UGAS is proven for the tracking error dynamics in surge and yaw while the controller dynamics is bounded. A case study involving an experiment with a model ship is included to demonstrate the performance of the controller and guidance systems. Copyright c °2003 IFAC. Keywords: Ship steering, Line-of-Sight guidance, Path following, Maneuvering, Nonlinear control, Underactuated control, Experimental results 1. INTRODUCTION In many applications offshore it is of primary impor- tance to steer a ship, a submersible or a rig along a desired path with a prescribed speed (Fossen 1994, 2002). The path is usually defined in terms of way- points using the Cartesian coordinates (x k ,y k ) ∈ R 2 . In addition, each way-point can include turning in- formation usually specified by a circle arc connecting the way-point before and after the way-point of inter- est. Desired vessel speed u d ∈ R is also associated with each way-point implying that the speed must be changed along the path between the way-points. The path following problem can be formulated as two con- trol objectives (Skjetne et al. 2002). The first objective is to reach and follow a desired path (x d ,y d ). This is referred to as the geometric assignment. In this paper a line-of-sight (LOS) projection algorithm is used for 1 Supported by the Norwegian Research Council through the Cen- tre of Ships and Ocean Structures, Centre of Excellence at NTNU. this purpose. The desired geometric path consists of straight line segments connected by way-points. The second control objective, speed assignment, is defined in terms of a prescribed speed u d along the body- fixed x-axis of the ship. This speed will be identical to the path speed once the ship has converged to the path. Hence, the desired speed profile can be assigned dynamically. 1.1 Control of Underactuated Ships For floating rigs and supply vessels, trajectory track- ing in surge, sway, and yaw (3 DOF) is easily achieved since independent control forces and moments are si- multaneously available in all degrees of freedom. For slow speed, this is referred to as dynamic positioning (DP) where the ship is controlled by means of tunnel thrusters, azimuths, and main propellers; see Fossen (2002). Conventional ships, on the other hand, are usually equipped with one or two main propellers for forward speed control and rudders for turning control.