Recurrent transformation of the dynamics model for autonomous underwater vehicle in the inertial coordinate system
We considered the motion equation for an autonomous underwater vehicle (AUV) with a manipulator onboard in the inertial coordinate system (ICS). A nonlinear system of differential equations takes into account in the form of attached mass coefficients the impact of infiltration effects and dissymmetry of the outer shell of the body. The work of manipulator and fixing elements is accounted for by additional forces and moments that occur as a consequence of their relative motion. The expressions of forces and moments are presented for the given kinematic schemes. A recurrent approximation method is applied, as result of which we transformed a solution for the system of nonlinear differential equations to the recurrent sequence of analytical expressions. The constructed sequence describes the dynamics of AUV with regard to the angular position and kinematic parameters without simplifications in the kinematic matrix. The algorithm that was synthesized based on this model is presented, which provides for presenting, in the form of recurrent sequence of actions and calculations, the expressions for analytical representation of solution for the direct problem on the AUV dynamics. Based on the analytical approximations of the model, we present expressions for an error that occurs as a consequence of angular deviations and simplifications in the kinematic matrices. The dynamics of AUV was modeled and quantitative values of error were obtained as a function of operating and kinematic parameters of AUV in ICS. The derived models of dynamics and expressions for errors are important for decision support systems because they allow the representation of information about the motion of AUV and manipulator aboard in a uniform ICS. The possibilities obtained have eliminated obstacles to comprehensive modeling of technological AUV and creation of ACS. Using the results of modeling the impact of manipulator's work aboard AUV, we established factors that influence the magnitude of error when calculating by the simplified kinematic matrices.