The Modeling of Robots Operating on Ships To Civilian and Military

There has been a great deal of effort devoted towards modeling ship motion due to wave loadings. However, the primary focus had been directed towards ship design. Our motivation for understanding ship motion is to quantify the expected magnitude and frequency of disturbance loads for a motion and/or force controlled manipulation system. Subsequently, this section will provide an abbreviated explanation of one of the techniques presently used to model ship motion.

The motion of the ship is defined by six displacements (surge, sway, heave, roll, pitch, and yaw) at the ship’s longitudinal center of gravity, from which motions at all other locations on the ship can be developed. While there are a number of techniques to simulate ship motion, the strip theory of Salvensen et al. is one of the
more popular approaches to modeling the 6-DOF response for a ship advancing at a constant forward speed with arbitrary heading in regular sinusoidal waves. In its simplest form, a ship acts as a set of filters, called the Response Amplitude Operators (RAOs), that transforms wave motion into the six degrees of motion (surge, sway, heave, roll, pitch and yaw).

Each motion has its own characteristic RAO. As illustrated in the previous section, there is ample information for characterizing the frequency content of the waves. The challenge is to design accurate models of the ship that faithfully characterizes the behavior of the ship. Strip theory is able to provide reliable estimates of sea keeping performance for a wide range of hull forms and sea conditions. Calculations are made in the frequency domain with the warping of the excitation frequency accounting for forward speed and heading, Equation.

There are three main stages to computing the motion response of the ship. First, divide the
ship into a number of transverse sections (or strips), generally from 10 to 40, and compute the two dimensional hydrodynamic coefficients such as added mass, damping, wave excitation, and restoring force. Next, integrate these values along the length of the vessel to obtain global coefficients for the coupled motion of the vessel. Finally, the equations of motion for the ship can be solved to give the amplitudes and phases of the heave, surge, sway, yaw, pitch and roll motions.

Clearly, the motion of a ship is a complex phenomenon and the above description is merely a simplified explanation of one method used for modeling ship motion. The above description is intended to only provide insight into the problem of ship motion simulation. The interested reader is referred to the following list of articles and text for a deeper understanding of ship motion simulation. Fortunately, there are a number of commercial software packages available for the analysis and simulation of marine vessels. The level of
sophistication, as well as magnitude of cost, varies dramatically. The package used for the analysis in the paper is the Simulation Time History (STH) and Access Time History (ACTH) programs developed at the Naval Surface Warfare Center in Bethesda Maryland and are available through the National Technical Information Service.