Accurate measurement of six Degree Of Freedom small-scale ship motion through analysis of one camera images A. Benetazzo n Protecno S.r.l., Via Risorgimento 9, 35027 Noventa Padovana (PD), Italy article info Article history: Received 16 October 2010 Accepted 21 August 2011 Editor-in-Chief: A.I. Incecik Available online 7 September 2011 Keywords: 6DOF motion 3-D rigid motion Physical modeling Image analysis Planar homography abstract A new six Degree Of Freedom (6DOF) motion measurement technique for small-scale physical models of floating bodies is presented, based on analysis of image sequence from one camera. The proposed system consists of one camera and one target: the method estimates the 3-D rigid motion following the time evolution of the target of known pattern fixed to the moving body and framed by the camera. In particular, the rotation matrix and the translation vector of the 3-D rigid motion between initial still position and a generic moved position are calculated by assuming the existence of a planar homography between the camera CCD plane and the plane passing through the flat target surface. Geometrical relationship allows one the calculation of wanted 6DOFs for every point of the modeled body. In the paper, the method is mathematically presented in terms of equations of rigid motion with its associate accuracies. The image-based technique is illustrated on some tests carried out in an experimental multipurpose wave basin. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction Small-scale physical models of vessels or floating bodies are an invaluable tool to test the behavior of moored ships, sea-keeping, and towing of offshore structures on station or in transit. In fact, physical models allow testing with different environmental con- ditions (waves and currents) and design parameters (shape of structures, mass distribution, and mooring layout) in safe condition and appreciable accuracy with respect to real phenom- ena scaled, provided that appropriate scale laws are applied (Chakrabarti, 1998). Among measurements that must be taken during the scaled experiments, complete motion of the bodies under inspection (vessels, offshore platforms) is a main task to define parameters related to operational and security conditions in port terminals and open sea. This motion is 3-D, with six possible Degrees Of Freedom (6DOFs), three translations along orthogonal axes, and three rotations about the same axes. The motion of a 3-D body in space is defined by a set of independent displacements and rotations that completely specify the displaced position and orientation of a reference system constrained to the body. The 6DOF motion of a moving floating ship on the water surface are the three translations of surge, sway, and heave, and the three rotations of roll, pitch, and yaw. A ship typically rotates about the center of gravity (CG), located on the longitudinal centerline approximately amidships. Traditionally, the 3-D motion has been accomplished with potentiometer systems attached to a model or with acceler- ometers and gyroscopes (ITTC, 1999). In this context, the MOTAN Motion Analysis System (Briggs and Melito, 2008) was used to record the 6DOF vessel motions of model ships. In the MOTAN System, the inertial motion sensor unit contains three linear servo accelerometers and three micro-machined quartz angular rate sensors. The accelerometers measure the total acceleration along X, Y, and Z orthogonal axes of the ship model. The angular rate sensors measure angular rotation vectors of the model. Nowadays, optical (i.e., images based) motion measurements of ship models, floater models, or rigid bodies have become the standard in most towing tanks and model basins (ITTC, 2008). The systems developed range from the use of markers such that the three-dimensional position of the markers is calculated by combining two-dimensional data from several cameras (Xin et al., 2006), to cameras with three CCD units used to measure the position of one or more infrared LED markers on the model (Kim et al., 2006). Recently named image-based systems were introduced. The Council for Scientific and Industrial Research (CSIR) developed the Keoship system (van der Molen and Hough, 2009; van der Molen et al., 2010) to monitor ship motions with a multiple camera system. In this application, two light metal strips are placed on the deck of the model ship together with two mirrors placed at 451. Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/oceaneng Ocean Engineering 0029-8018/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2011.08.006 n Present address: Consiglio Nazionale delle Ricerche CNR – ISMAR, Castello 2737/F, 30122 Venice, Italy. Tel.: þ39 041 2407952. E-mail addresses: alvise.benetazzo@ve.ismar.cnr.it, alvise.benetazzo@gmail.com Ocean Engineering 38 (2011) 1755–1762