Method for solving the inverse kinematics problem for a mechatronic device under the concept of separation between measurement space and physical motion space

The issue of improving control accuracy for complex mechatronic systems in robotics and precision engineering is examined. The problem of misalignment between the measurement and physical spaces of mechatronic objects has been resolved. This misalignment arises due to manufacturing inaccuracies in mechatronic systems and instability in the sensor characteristics of mechanical actuation systems, among other systematic factors. A method of solving the inverse kinematics problem is proposed that is based on piecewise linear transformation and determining the orientation of the physical space axes using the concept of space separation (i.e. measurement, physical and generalised spaces). The transformation matrix was constructed using the direction cosines of the physical space axes, thereby reducing positioning errors under real-world conditions. An algorithm for correcting the direction cosine matrix, which links coordinates across different spaces, is also presented. Experimental validation was conducted on a monorail tripetron system (“STANKIN”, Russia). A Leica LTD800 laser tracker (Leica Geosystems AG, Switzerland) was used to evaluate positioning errors for both the traditional method (based on an ideal model) and the modified approach that accounts for distortions. The results showed a reduction in total positioning error from 5.69 mm to 3.41 mm (40.1%) across 11 control points. The key advantage of the proposed inverse kinematics solution is its ability to compensate for systematic errors without requiring precise measurement of the mechatronic system’s geometric parameters. These findings can be applied to industrial and collaborative robotics, medical manipulators and other systems where spatial control accuracy is critical. These results contribute to advancing calibration methods for mechatronic systems with non-ideal geometry.