POE-Based Error Modeling and Multiple Plane Constraint-Based Parameter Identification for the Kinematic Calibration of a 4-UPS/SPR Parallel External Fixator

Abstract

Limb deformity is a common complaint in orthopedic surgery. Currently, gradual treatment using parallel external fixator (PEF) has become the preferred option for deformity correction. As the key medical apparatus with the special application properties of temporary assembly and direct utilization, the geometric errors generated during the manufacturing and assembly process of the PEF contribute to the post-correction residual and iatrogenic deformities. However, considering the complexity of clinical scenarios, there is a lack of an applicable solution to reduce the effect of the above error source of PEF. To overcome these problems, taking a 4-UPS/SPR PEF as the research object, this paper proposes a novel kinematic calibration method. First, the error model with the features of completeness, continuity, and minimality is first established based on the product of exponentials (POE) formula. Then, the identifiability analysis is conducted to eliminate the redundant error parameters and ensure the stability and accuracy of the iterative calculation in the process of parameter identification. Furthermore, a multiple plane constraint (MPC)-based parameter identification approach is introduced to the calibration task of the PEF to effectively reduce the difficulty of the pose information measurement in the current cost-effective constraint calibration method. Finally, the simulation and prototype experiments validate that the proposed calibration method (i.e., the combination of the POE-based error model and the MPC-based parameter identification approach) can accomplish the calibration tasks in clinical applications and meet the cost-effectiveness and efficiency requirements.