Method for solving the inverse kinematic problem for a mechatronic device within the framework of the concept separation of measurement and physical spaces of motion

We study the problem of improving the accuracy of control over complicated mechatronic systems in robotics and precision engineering. The problem of misalignment between the measurement and physical spaces of mechatronic objects is resolved. The indicated misalignment arises due to the presence of inaccuracies in the process of manufacturing of mechatronic systems, the instability of the characteristics of sensors in mechanical actuation systems, and other systematic factors. We propose a method for solving the inverse kinematic problem that is based on a piecewise linear transformation and determination of the orientations of the axes of physical space by using the concept of space separation (namely, of the measurement, physical, and generalized spaces).

The transformation matrix was constructed by using the direction cosines of axes of the physical space. This enabled us to decrease positioning errors under the real-world conditions. We also propose an algorithm aimed at correcting the matrix of direction cosine, which links the coordinates in different spaces. The experimental verification was carried out on a monorail tripteron system (produced by the “STANKIN” MGTU, Russia). A Leica LTD800 laser tracker (Leica Geosystems AG, Switzerland) was used to evaluate the positioning errors with the help both of the traditional method (based on the ideal model) and of the modified approach that takes into account distortions. The accumulated results revealed a decrease in the total positioning errors from 5.69 mm down to 3.41 mm (40.1%) at 11 control points. The key advantage of the proposed method for solving the inverse kinematic problem is its ability to compensate systematic errors without precise measuring of the geometric parameters of mechatronic objects. The accumulated results can be applied in the commercial and collaborative robotics, as well as in the medical manipulators and other systems where the accuracy of spatial control is critical. These results contribute to the development of the methods of calibration for mechatronic systems with nonideal geometry.