Gravity compensation of an intraocular surgery robot based on computed torque method
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摘要:
为了提高一种具有远程运动中心（RCM）机构的眼内手术机器人的定位精度和稳定性，在建立机器人坐标系的基础上，通过动力学等效，对机器人各构件质心瞬态位置进行分析。根据拉格朗日方程建立机器人动力学模型。提出基于计算力矩法的重力补偿方法。在此基础上，通过MATLAB/Simulink软件对重力补偿模型进行仿真。比较独立比例微分（PD）控制方法及重力补偿方法的各关节运动响应曲线，表明重力补偿模型可有效补偿重力项；同时，分析重力补偿模型响应曲线与期望曲线的误差，证明重力补偿模型具有较高的补偿精度和可行性。
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关键词:
- 远程运动中心(RCM)机构 /
- 眼内手术机器人 /
- 动力学 /
- 计算力矩法 /
- 重力补偿 /
- Simulink仿真
Abstract:To improve the positioning accuracy and stability of an intraocular surgery robot which has a remote center of motion (RCM) mechanism, the coordinate system of the robot is established. Based on the equivalent system model, the instantaneous centroid position of model components is analyzed. The dynamic model of the robot system is built by using the Lagrange equation. On the basis of the dynamic model, the gravity compensation model is built by using computed torque method and it is simulated by using MATLAB/Simulink. Each joint motion response curve is compared between the independent proportional plus derivative(PD) control model and the gravity compensation model. The results of simulation show that the gravity compensation model can compensate the gravity effectively. The difference between response curve and expected curve of gravity compensation model is analyzed, which prove that the gravity compensation model has high precision and feasibility.
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图 1 基于RCM机构的眼内手术机器人示意图
Figure 1. Schematic diagram of intraocular surgery robotbased on RCM mechanism
图 2 眼内手术机器人坐标系示意图
Figure 2. Schematic diagram of coordinate system ofintraocular surgery robot
图 4 等效后的RCM机构简图
si—各构件质心相对于转动关节的矢径的模；θi—关节变量；φi—与构件i质心矢径相对x′轴角度有关的参数。
Figure 4. Equivalent diagram of RCM mechanism
图 9 基于计算力矩法的重力补偿模型响应曲线
Figure 9. Response curves of gravity compensation model based on computed torque method
图 10 重力补偿模型期望曲线与响应曲线的差值
Figure 10. Difference between expected curves and response curves of gravity compensation model
表 1 机器人系统D-H参数
Table 1. D-H parameters of robot system
i 从zi-1到zi沿
xi-1距离ai-1从zi-1到zi绕
xi-1角度αi-1从xi-1到xi
沿zi距离di从xi-1到xi
绕zi角度θi1 0 0 d1 ψ1 2 a1 0 d2 ψ2 3 a2 0 d3 -90° 4 0 -90° L -90°+θ3 5 0 -90° 0 θ2 6 0 0 d6 0 
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表 2 各关节响应曲线的调节时间
Table 2. Adjusting time of response curve of each joint
误差带 关节变量 调节时间/s 计算力矩法 PD控制模型 ±2% θ1 1.9 2.0 θ2 1.9 2.1 θ3 2.4 2.6 ±5% θ1 1.4 1.7 θ2 1.5 1.6 θ3 2.3 2.4
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