用矩阵微分建立股骨颈手术导航机器人位姿误差模型的方法

Construction of the position and orientation error model of navigation robots for femoral neck surgery using matrix differential

应用矩阵微分建立了股骨颈手术导航机器人的位姿误差模型。依次做了以下主要工作:设计股骨颈手术导航机器人的三维形体结构,即串、并联混合机构;基于结构与运动特征,采用传递矩阵建立手术导航模型;提取特征参数作为微分变元,通过矩阵微分建立手术导航的位姿误差模型;应用仿真软件matlab7.0,以导航机器人的设计尺寸与容差值为变量,对特征参数引起的导航位姿误差分布进行仿真,其结果位姿误差呈平面分布,极大误差在边界线上获得。应用矩阵微分建立的手术导航误差分析模型的工程含义明确,结构规范,适用于将机器人的精度校核穿插到形体设计的前期阶段进行,在并行设计中的精度校验上有实用性。

This paper proposes a position and orientation error model of the femoral neck surgery navigation robots through matrix differential. The study consists of the following four steps： firstly, design of a three-dimension serial-parallel hybrid mechanical structure for the robots; secondly, construction of a navigation model through the transfer matrix based on the physical structure and the motion characteristics; thirdly, extraction of the characteristic parameters as the differential variables and establishing the position and orientation error model of surgery navigation by means of the matrix differential; finally, simulation of the navigation error distributions of the two structural variables in Matlab 7.0 with the actual sizes and tolerance values of the robots as variables, which results in an error distribution as the planar and the maximum error presentation at the boundary of the plane. The proposed explicit and normatively structured error analysis model for the surgery navigation, is suitable＇ for checking robot precision in the earlier mechanism structure design stage and is also applicable to accuracy calibration in parallel designs.