Comparison Study of Different Types of Setting Reference Movements for Mechatronic Objects by Parametric Splines

The paper presents a comparative study of various ways of specifying program movements for mechatronic objects (MO) along complex spatial trajectories defined by parametric Bezier splines, B-splines and third-order Catmull-Rom splines. An expression is obtained to describe the dependence of the rate of change of the parameter setting the desired position of the MO with the program speed of its movement, taking into account information about the type of trajectory. As a result, using this expression, which is universal for all the specified parametric splines of the third order, it is ensured that the MO moves along the trajectory exactly at a given speed while simultaneously changing its orientation as desired. The application of the methods considered in this paper does not require complex iterative calculations and allows one to perform all the necessary calculations in real time, even on low-power on-board computers of various robots and robotic complexes. Numerical modeling was carried out to analyze the features of the use of these splines in solving practical problems.