并联机构运动学标定的参数可辨识特性研究

Accuracy performance of mechanisms plays an important role in robot manipulations. As an efficient and economical approach, kinematic calibration can significantly improve the absolute positioning accuracy of robot manipulators. Generally, robot calibration can be divided into four consequent procedures: modeling, measurement, identification and compensation, among which the identifiability analysis of geometric parameters serves as a fundamental issue. During the past decades, many researchers have made their contributions to this problem for serial robots manipulators and several systematic approaches have been proposed to determine the identifiable parameters. However, for parallel manipulators, the identifiability analysis of the geometric parameters is still far from being complete due to the complexity of their structural topology. .According to the duality between parallel manipulators and their serial counterparts, this proposal presents a hierarchical strategy for the geometrical error modeling and kinematic-parameter identifiability analysis of parallel manipulators. The concept of constraint errors is proposed for the limbs to describe the influences of the links'geometrical errors on the limbs' constraints to the moving platform. The constraint errors of different limbs are independent from each other and can be considered as the direct causes of the moving platform’s pose error due to links' geometrical ones. Hence, the pose error of the moving platform can be uniquely distributed into the limbs by taking advantage of the direct-sum decomposition of the end-effector's error space into the limbs' sub-ones. As a consequence, the identifiability analysis of the whole parallel manipulator can be transformed to the ones for determining the independent parameters that influence the constraint errors in individual limbs. Therefore, existing methods for serial robots can be employed to solve the identifiability problem of parallel manipulators. Using the proposed method, a complete and minimal error model can be obtained for the kinematic calibration of parallel manipulators, which can improve the identification accuracy of the geometric parameters.

末端定位精度是影响机构操作性能的一个重要指标，运动学标定是提高机构绝对定位精度的有效途径。通过运动学参数的可辨识性分析，可以确定影响机构末端定位精度的尺寸误差参数中的独立分量，为运动学标定建模与误差补偿控制提供理论依据。目前，对于串联机构的参数可辨识特性研究已较为成熟，而针对拓扑结构更为复杂的并联机构，由于存在被动关节的协调运动和缺乏误差参数的独立性判别准则，目前尚缺乏有效方法来分析其运动学参数的可辨识特性。.本项目依据并联机构的构型特点，从各运动支链对末端平台的约束偏差分析入手，建立从各个构件尺寸误差到各支链约束误差，再到末端位姿误差的层次化误差映射模型，借助末端位姿误差空间到各支链约束误差子空间的直和分解，在各运动支链内部实现并联机构的尺寸误差独立性判别与运动学参数可辨识性分析，为运动学标定与误差补偿控制提供准确的模型基础，提高并联构型操作装备运动学标定的参数辨识精度。

末端定位精度是影响机构操作性能的关键指标，运动学标定是提高机构绝对定位精度的有效途径。其中，误差映射模型的参数可辨识特性对机构运动学标定的计算效率、稳定性以及精度均具有重要影响。本项目围绕并联机构运动学标定的参数可辨识特性开展研究，成果如下：. 利用局部指数积公式，建立了满足连续性要求的运动支链误差映射模型；在此基础上，基于旋量系关联关系理论，通过将各构件尺寸误差向被动关节的约束旋量投影，消除了被动关节运动误差对末端平台定位精度影响，从而得到了满足完整性和连续性要求的并联机构误差映射模型。相较于传统方法，该方法具有表征形式统一，通用性好，包含所有误差影响因素等特点，可以作为并联机构误差建模的一般方法。. 通过对参数辨识矩阵零化空间的特性分析，提出了并联机构各支链误差参数的独立性判别准则；基于辨识矩阵零空间和列空间的正交分解，推导了具有解析表达形式的冗余误差消元算子，建立了同时满足完整性、连续性及独立性要求的并联机构最小误差映射模型。并进一步证明了对于一般恰约束并联机构，其最大可辨识运动学参数数目与其具体构型无关，仅取决于组成它的运动副类型和数目，具体为N=4r+2p+6，其中，r、p分别表示等效转动关节与移动关节数目。. 以3-PRRU机构为对象，开展了并联机构运动学标定的实验研究，验证了本项目理论研究成果的有效性，并进一步在航天大部件对接装配中开展应用研究。分别与航天一院天津航天长征火箭制造有限公司和航天八院上海航天设备制造总厂开展合作，协助其成功实现了长征三号和长征五号两型运载火箭贮箱部段装配的自动化对接实验，初步验证了本项目研究成果的可行性，为后续我国大型运载火箭全箭总装工艺向柔性自动化转型的提供有效技术支撑。. 项目执行期间，共发表/录用学术论文12篇，其中SCI源期刊11篇（第一作者8篇），课题组参与人员共参加国际学术会议6人次。授权国家发明专利5项，公开/申请3项。毕业博士研究生1名、硕士研究生2名。