力反馈主手机构设计若干关键问题研究
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摘要
主从式手术机器人系统可以把人和机器人结合起来，以力反馈主手作为交互界面控制手术机器人进入体内进行手术操作，既能利用人类具有的高级思维和决策能力，又能够利用机器人具有的高精密度和准确度。力反馈主手是主从式手术机器人系统的重要组成部分，本文对力反馈主手机构设计的工作空间分析、位姿误差建模、重力平衡等关键问题进行了深入研究，论文主要内容和成果如下：
编写了n自由度机器人机构运动学模型和雅可比矩阵的计算程序，建立了主从运动学映射的数学模型。
提出了一种计算n自由度正交机器人机构工作空间的数值方法，先求出机器人机构末端两个关节对应子工作空间的边界曲面，在前一个关节建立参考坐标系，将已知子工作空间的边界曲面分成若干层，求出每一层上的截交线，定义截交线的两个端点、半径坐标值最大点和最小点等为特征点，根据这些特征点可生成前一级子工作空间的边界曲线和边界曲面，由此递推可生成工作空间的边界曲面，并计算出工作空间的体积值。以三自由度正交机器人机构和PHANTOM力反馈主手机构为例进行了仿真分析，结果表明该算法具有运动学计算量小、结果精确等优点，并且能适用于平行关节机构。
根据机器人机构位姿误差模型的连续性、等价性、比例性要求，以加入Hayati参数的运动学模型为基础，运用Paul提出的机器人微分运动理论，提出了一种基于坐标系分组的机器人机构位姿误差矢量的计算方法，简化了Veitschegger和Chi-haur Wu提出的基于杆件的位姿误差矢量计算方法。建立了主从式手术机器人系统的位姿误差模型，开发了基于MATLAB平台的仿真程序，分析了由PHANTOM力反馈主手和Da Vinci手术机器人组成的主从式手术机器人系统的位姿误差在其工作空间截面内的分布状况。根据PHANTOM力反馈主手机构的位置误差模型，采用正交试验设计的方法，以各杆件运动学参数误差作为试验因素，以位置误差作为响应变量，进行了精度设计的仿真分析。
提出了一种弹簧重力平衡系统的能量分析方法，以具有平行四边形辅助杆件的2自由度机构为研究对象，进行了单关节弹簧重力平衡系统的方案设计。根据Kane方法推导了PHANTOM力反馈主手机构的动力学模型，进行了反向可驱动性的分析，最后对样机刚度进行了实验测试。
The master-slave surgical robotic system is a more effective surgical robotic system，theslave robot is the actual robot manipulator that performs the surgery within the patient’s bodywhile the master is an interface device that allows the surgeons to control the slave. Themaster-slave surgical robot system allows the human to provide high-level thinking and decisionmaking and allows the robot using its high precision and accuracy. The force feedback mastermanipulator is an important component of the master-slave surgical robotic system, the key issuessuch as workspace analysis, error modeling, gravity compensation have been studied, thefollowing aspects in the dissertation have been achieved：
A computer program to calculate the kinematic model and the jacobian matrix of n dof robotmanipulator has been developed in MATLAB. The linear mapping relationship between the forcefeedback master manipulator workspace and the surgical robot workspace has been built.
An algorithm for the workspace boundary of the n-R orthogonal manipulators has beendeveloped, sub workspace boundary surface of the last two joints is generated as initial subworkspace boundary，the cross sections of the initial sub workspace boundary are created withrespect to the preceding joint coordinate, the two end points, the point with maximum radius andthe point with minimum radius of each cross sections curve are defined as the feature points, theboundary curves and the boundary surfaces of the former sub workspace are determined by thesefeature points, then the workspace is computed by this iterative process, and the volume of theworkspace is calculated. A simulation has been performed on a3-R orthogonal manipulator.Simulation results show that the proposed algorithm has advantages of small amount of kinematiccalculations and high precision, and it can be used for the manipulators with parallel joints.
In order to obtain a parametrically continuous model in the case of two adjacent paralleljoints or nearly parallel joints, an additional rotation term about the y-axis known as a Hayatiparameter is introduced as the fifth parameter. According to the differential theory, a new methodto calculate the differential vector of the end-effector is proposed to simplify the expressionsderived by Veitschegger and Wu. A linear error model that described the end-effector position andorientation errors of the master salve surgical robot system due to kinematics parameters errors has been presented. A computer program to perform the accuracy analysis is developed inMATLAB. This methodology and software has been applied to the accuracy analysis of amaster-slave surgical robot system which consists of PHANTOM force feedback device and DaVinci robotic arm. The position error in its workspace cross section (XOZ) has been plotted as3Dsurface graph and discussed. The orthogonal experimental design method is adopted for accuracydesign of the haptic manipulator. The kinematic parameter errors are considered as the factors andthe pose errors are considered as the response variable, simulation analysis for the accuracydesign has been performed.
An energy approach to analysis the spring balancing mechanisms has been proposed, themono-articular spring balancing mechanism with auxiliary link for a2-DOF manipulator has beendesigned. The dynamic model of the PHANTOM force feedback device has been built, and thebackdrivability has been analyzed. The stiffness of a prototype force feedback master manipulatorhas been tested by experiment.
编写了n自由度机器人机构运动学模型和雅可比矩阵的计算程序，建立了主从运动学映射的数学模型。
提出了一种计算n自由度正交机器人机构工作空间的数值方法，先求出机器人机构末端两个关节对应子工作空间的边界曲面，在前一个关节建立参考坐标系，将已知子工作空间的边界曲面分成若干层，求出每一层上的截交线，定义截交线的两个端点、半径坐标值最大点和最小点等为特征点，根据这些特征点可生成前一级子工作空间的边界曲线和边界曲面，由此递推可生成工作空间的边界曲面，并计算出工作空间的体积值。以三自由度正交机器人机构和PHANTOM力反馈主手机构为例进行了仿真分析，结果表明该算法具有运动学计算量小、结果精确等优点，并且能适用于平行关节机构。
根据机器人机构位姿误差模型的连续性、等价性、比例性要求，以加入Hayati参数的运动学模型为基础，运用Paul提出的机器人微分运动理论，提出了一种基于坐标系分组的机器人机构位姿误差矢量的计算方法，简化了Veitschegger和Chi-haur Wu提出的基于杆件的位姿误差矢量计算方法。建立了主从式手术机器人系统的位姿误差模型，开发了基于MATLAB平台的仿真程序，分析了由PHANTOM力反馈主手和Da Vinci手术机器人组成的主从式手术机器人系统的位姿误差在其工作空间截面内的分布状况。根据PHANTOM力反馈主手机构的位置误差模型，采用正交试验设计的方法，以各杆件运动学参数误差作为试验因素，以位置误差作为响应变量，进行了精度设计的仿真分析。
提出了一种弹簧重力平衡系统的能量分析方法，以具有平行四边形辅助杆件的2自由度机构为研究对象，进行了单关节弹簧重力平衡系统的方案设计。根据Kane方法推导了PHANTOM力反馈主手机构的动力学模型，进行了反向可驱动性的分析，最后对样机刚度进行了实验测试。
The master-slave surgical robotic system is a more effective surgical robotic system，theslave robot is the actual robot manipulator that performs the surgery within the patient’s bodywhile the master is an interface device that allows the surgeons to control the slave. Themaster-slave surgical robot system allows the human to provide high-level thinking and decisionmaking and allows the robot using its high precision and accuracy. The force feedback mastermanipulator is an important component of the master-slave surgical robotic system, the key issuessuch as workspace analysis, error modeling, gravity compensation have been studied, thefollowing aspects in the dissertation have been achieved：
A computer program to calculate the kinematic model and the jacobian matrix of n dof robotmanipulator has been developed in MATLAB. The linear mapping relationship between the forcefeedback master manipulator workspace and the surgical robot workspace has been built.
An algorithm for the workspace boundary of the n-R orthogonal manipulators has beendeveloped, sub workspace boundary surface of the last two joints is generated as initial subworkspace boundary，the cross sections of the initial sub workspace boundary are created withrespect to the preceding joint coordinate, the two end points, the point with maximum radius andthe point with minimum radius of each cross sections curve are defined as the feature points, theboundary curves and the boundary surfaces of the former sub workspace are determined by thesefeature points, then the workspace is computed by this iterative process, and the volume of theworkspace is calculated. A simulation has been performed on a3-R orthogonal manipulator.Simulation results show that the proposed algorithm has advantages of small amount of kinematiccalculations and high precision, and it can be used for the manipulators with parallel joints.
In order to obtain a parametrically continuous model in the case of two adjacent paralleljoints or nearly parallel joints, an additional rotation term about the y-axis known as a Hayatiparameter is introduced as the fifth parameter. According to the differential theory, a new methodto calculate the differential vector of the end-effector is proposed to simplify the expressionsderived by Veitschegger and Wu. A linear error model that described the end-effector position andorientation errors of the master salve surgical robot system due to kinematics parameters errors has been presented. A computer program to perform the accuracy analysis is developed inMATLAB. This methodology and software has been applied to the accuracy analysis of amaster-slave surgical robot system which consists of PHANTOM force feedback device and DaVinci robotic arm. The position error in its workspace cross section (XOZ) has been plotted as3Dsurface graph and discussed. The orthogonal experimental design method is adopted for accuracydesign of the haptic manipulator. The kinematic parameter errors are considered as the factors andthe pose errors are considered as the response variable, simulation analysis for the accuracydesign has been performed.
An energy approach to analysis the spring balancing mechanisms has been proposed, themono-articular spring balancing mechanism with auxiliary link for a2-DOF manipulator has beendesigned. The dynamic model of the PHANTOM force feedback device has been built, and thebackdrivability has been analyzed. The stiffness of a prototype force feedback master manipulatorhas been tested by experiment.
引文
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