基于刚软耦合模型和粒子群优化的手术机器人骨钻削力控制

脊柱椎体的多层复合结构和易热损伤特性要求手术机器人在对椎弓根进行骨钻孔时需精确控制其轴向钻削力。然而人的个体差异和脊柱-软组织构成的刚软耦合结构会使得通用型力控制器的控制精度不足，手术安全性降低。本文旨在提高轴向钻削力控制的精度。首先建立了基于质量、弹簧和Maxwell黏弹性单元的脊柱-软组织系统的刚软耦合模型。然后在离体羊脊柱上进行了应力松弛实验，并基于实测力数据对模型参数进行了标定。采用PID（比例-积分-微分）控制器来调整骨钻的轴向进给速度，并基于标定后的刚软耦合模型的传递函数，使用动态权重的标准粒子群算法整定控制器参数。最后，仿真证明闭环控制系统具有较好的动态性能和鲁棒性。离体羊脊柱骨钻孔力控制实验结果表明，轴向钻削力的阶跃力响应稳态误差小于0.15 N，相对力控制误差小于3%，且无明显超调；正弦力响应幅度在频率为3.49 rad/s时衰减到-3 d B，闭环控制系统具有较好的控制带宽。所提方法的力控制精度和控制带宽能够满足手术机器人执行骨钻削时的力跟踪要求，提高了机器人自动骨钻削过程的安全性。

Bone Drilling Force Control of Surgical Robot Based on Rigid-Soft Coupling Model and Particle Swarm Optimization

The spine vertebral body is of multi-layer composite structure and is prone to thermal damage, so the surgical robot should accurately control its axial drilling force when drilling the bone tissue of the pedicle. However, the control precision of general-purpose force controllers is insufficient for surgical safety due to the individual differences among different persons and the rigid-soft coupling structure composed of spine and soft tissue. This paper aims to improve the accuracy of the axial drilling force control. Firstly, a rigid-soft coupling model of the spine-soft-tissue system is established based on mass, spring, and Maxwell viscoelastic element. Then, the model parameters are calibrated based on the measured force data from a stress relaxation experiment on the isolated sheep spine. The axial feed rate of the bone drilling is adjusted by a PID (proportional-integral-derivative) controller. And the controller parameters are tuned by the standard particle swarm algorithm with dynamic weights, based on the transfer function of the calibrated rigid-soft coupling model. Finally, the simulation proves that the closed-loop control system is of good dynamic performance and robustness. Results of the drilling force control experiment on the isolated sheep spine show that, the steady-state error of the step force response of the axial drilling force is less than 0.15 N, the relative force control error is less than 3%, and in fact without any noticeable overshoot. The sinusoidal force response amplitude is attenuated to -3 dB at a frequency of 3.49 rad/s, which means that the closed-loop control system has a wide enough control bandwidth. The force control accuracy and control bandwidth of the proposed method can meet the force tracking requirements of the surgical robot when performing bone drilling, and the safety of the automatic bone drilling process is improved.