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-US/SR 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.

中文翻译：

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基于 POE 的误差建模和基于多平面约束的参数识别，用于 4-UPS/SPR 并行外部固定器的运动学校准


肢体畸形是骨科手术中常见的病症。目前，平行外固定架（PEF）渐进治疗已成为畸形矫正的首选方案。作为具有临时组装和直接使用的特殊应用特性的关键医疗器械，PEF在制造和组装过程中产生的几何误差导致了矫正后的残余畸形和医源性畸形。但考虑到临床场景的复杂性，目前还缺乏适用的解决方案来降低上述PEF误差源的影响。为了克服这些问题，本文以4-US/SR PEF为研究对象，提出了一种新颖的运动学校准方法。首先，首先根据指数乘积（POE）公式建立具有完备性、连续性和极小性特征的误差模型。然后进行可辨识性分析，消除冗余误差参数，保证参数辨识过程中迭代计算的稳定性和准确性。此外，将基于多平面约束（MPC）的参数识别方法引入到PEF的标定任务中，有效降低了当前经济高效的约束标定方法中位姿信息测量的难度。最后，仿真和原型实验验证了所提出的校准方法（即基于POE的误差模型和基于MPC的参数识别方法的结合）可以完成临床应用中的校准任务，并满足成本效益和效率要求。