Error modeling and accuracy improvement of the cylindrical coordinate mechanism for a mobile machining robot

Cylindrical coordinate mobile machining robots offer an efficient solution for milling curved panels in large rotating components. However, achieving high-accuracy positioning of long-travel robotic equipment presents significant challenges in industrial applications. The development of a physically meaningful and numerically stable error model for the cylindrical coordinate mechanism remains a critical problem to be solved. In this paper, the kinematic model with the non-ideal inter-axial relationship is derived. Thereafter, an accuracy improvement scheme is proposed to simultaneously identify and adjust the base coordinate system pose and geometric parameters. Initially, under the condition of explicitly defined geometric relationships, a well-conditioned error model for kinematic calibration that comprehensively considers the error relationship between the base coordinate system and geometric parameters is established. The error model maintains the physical significance of the base coordinate system while reducing the complexity of error compensation. Subsequently, after establishing single-axis error models for linear and rotary axes and developing a multi-axis synergistic compensation strategy, parameter identification and comprehensive error compensation are conducted. The identification can be treated as a nonlinear least squares problem with constraints, and is solved by the Levenberg-Marquardt algorithm. Finally, an accuracy verification experiment and a machining experiment for comparison were conducted on the prototype. The experimental results show 79%/77% reduction in maximum/mean positioning error. The machining experiment confirms the effectiveness in practical applications. The study improves the positioning accuracy of the cylindrical coordinate mechanism and has reference significance for other positioning mechanisms with the rotary axis.