When the spinal surgery robot assists the surgeon perform the surgery, the patient is prone on the operating table. However, due to the force of the surgical instruments on the spine, there is a corresponding deformation in the surgical field, which affects the accuracy of the operation. In order to improve the accuracy and safety of the operation, this paper reconstructs the three-dimensional model of the lumbar spine which includes the vertebral body and the intervertebral disc based on the CT scan data, and then the lumbar spine is analyzed by the finite element method. The mathematical model of the relationship between force and displacement is established by using response surface methodology based on the simulation results. After that, the position control system is constructed based on the mathematical model. Through the simulation of the control system, the trajectory curve of the end of the manipulator is compared and the validity of the mathematical model is verified.

当脊柱外科手术机器人协助外科医生进行手术时，患者容易卧在手术台上。但是，由于手术器械在脊柱上的作用力，手术区域会发生相应的变形，这会影响手术的准确性。为了提高手术的准确性和安全性，本文基于CT扫描数据重建了包括椎体和椎间盘的腰椎三维模型，然后通过有限元分析。元素方法。基于响应结果，利用响应面法建立了力与位移关系的数学模型。之后，基于数学模型构建位置控制系统。