On the modeling of robots operating on ships

The decrease in manpower and increase in material handling needs on many naval vessels provides the motivation to explore the modeling and control of naval robotic and robotic assistive devices. This paper presents a simple methodology to symbolically compute the dynamic equations of motion of a serial link manipulation system operating on the moving deck of a ship. First we provide background information that quantifies the motion of the ship, both in terms of frequency and amplitude. We then formulate the motion of the ship in terms of homogeneous transforms. Likewise, the kinematics of a manipulator is considered as a serial extension of the ship motion. We then show how to use these transforms to formulate the kinetic and potential energy of the arm moving on a ship. As a demonstration, we consider two examples: a one degree-of-freedom system experiencing three sea states operating in a plane to verify the methodology and a 3 degree of freedom system experiencing all six degrees of ship motion to illustrate the ease of computation and complexity of the solution. We provide a preliminary comparison between conventional linear control and repetitive learning control (RLC) and show how fixed time delay RLC breaks down due to the varying wave disturbance frequency.