Derivatives of quaternion spline interpolation function for multibody dynamics

Abstract

Interpolation plays an important role in nowadays world. By interpolating data, we save time and money in general. The main areas where interpolation is applied are robotics, automotive, medicine and biology. One of the possible basis splines for interpolation are B-splines, which are also used in Computer Aided Geometric Design (CAGD) due to their smoothness and locality properties. In the extended abstract, we consider problems of kinematics, which are, in many cases, characterized by a set of non-linear algebraic equations that have to be assembled and solved at each time step. The computational procedure could be time-consuming; therefore it is reasonable to develop suitable methods to overcome such difficulties. Moreover, the parametrization of finite rotations is an essential issue in multi-body kinematics and dynamics and therefore the concept of quaternions is employed to describe body rotations in this work. In other words, the main idea is to solve the kinematics prior to the dynamics, pre-compute the rotation parameters of a car wheel support, and then use the interpolation of rotations in the framework of more complex computational tasks. The pre-computation of the rotation parameters leads to a look-up table.