Tian Heqiang, Zhang Mengke, Tan Jiezhong, Chen Zhuo, Chen Guangqing
College of Mechanical and Electronic Engineering, Shandong University of Science and Technology, Qingdao 266590, China.
Biomimetics (Basel). 2025 Jun 8;10(6):383. doi: 10.3390/biomimetics10060383.
This study presents an integrated stiffness modeling and evaluation framework for an orthopedic surgical robot, aiming to enhance cutting accuracy and operational stability. A comprehensive stiffness model is developed, incorporating the stiffness of the end-effector, cutting tool, and force sensor. End-effector stiffness is computed using the virtual joint method based on the Jacobian matrix, enabling accurate analysis of stiffness distribution within the robot's workspace. Joint stiffness is experimentally identified through laser tracker-based displacement measurements under controlled loads and calculated using a least-squares method. The results show displacement errors below 0.3 mm and joint stiffness estimation errors under 1.5%, with values more consistent and stable than those reported for typical surgical robots. Simulation studies reveal spatial variations in operational stiffness, identifying zones of low stiffness and excessive stiffness. Compared to prior studies where stiffness varied over 50%, the proposed model exhibits superior uniformity. Experimental validation confirms model fidelity, with prediction errors generally below 5%. Cutting experiments on porcine femurs demonstrate real-world applicability, achieving average stiffness prediction errors below 3%, and under 1% in key directions. The model supports stiffness-aware trajectory planning and control, reducing cutting deviation by up to 10% and improving workspace stiffness stability by 30%. This research offers a validated, high-accuracy approach to stiffness modeling for surgical robots, bridging the gap between simulation and clinical application, and providing a foundation for safer, more precise robotic orthopedic procedures.
本研究提出了一种用于骨科手术机器人的集成刚度建模与评估框架,旨在提高切割精度和操作稳定性。开发了一个综合刚度模型,该模型纳入了末端执行器、切割工具和力传感器的刚度。基于雅可比矩阵使用虚拟关节法计算末端执行器刚度,从而能够准确分析机器人工作空间内的刚度分布。通过在受控负载下基于激光跟踪仪的位移测量对关节刚度进行实验识别,并使用最小二乘法进行计算。结果表明位移误差低于0.3毫米,关节刚度估计误差低于1.5%,其值比典型手术机器人报告的值更一致、更稳定。仿真研究揭示了操作刚度的空间变化,识别出低刚度和过高刚度区域。与先前刚度变化超过50%的研究相比,所提出的模型具有更高的均匀性。实验验证证实了模型的保真度,预测误差通常低于5%。对猪股骨进行的切割实验证明了该模型在实际中的适用性,平均刚度预测误差低于3%,在关键方向上低于1%。该模型支持基于刚度的轨迹规划和控制,可将切割偏差降低多达10%,并将工作空间刚度稳定性提高30%。本研究为手术机器人的刚度建模提供了一种经过验证的高精度方法,弥合了模拟与临床应用之间的差距,并为更安全、更精确的机器人骨科手术奠定了基础。