五自由度混联机器人EXE-M的关键技术研究
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摘要
本文面向新型多杆汇交式网壳节点的加工需求,在国家863示范工程的资助下,对具有我国自主知识产权的新型5自由度可重构混联机械手EXE-M的关键技术进行了初步研究,内容涉及位置逆解、雅可比矩阵求解、尺度综合、逆动力学、伺服电机参数预估和轨迹规划,主要研究成果如下:
1.位置逆解和雅可比矩阵求解:根据EXE-M混联机械手的结构组成,将其分解为3-SPR并联模块与2自由串联模块,提出一种利用Sylvester法求解以位置坐标为独立变量并具有显式解的逆解分析法。借助循环搜索法和纯轨迹理论得到串联模块的逆解模型。利用螺旋理论建立了并联模块的完整雅可比矩阵,就此构建了一般雅可比矩阵;
2.尺度综合:为了克服机构正解的复杂性,提出一种利用CAD仿真模型求取3-SPR机构可达空间的简单方法。利用机构任务空间的特点及各尺度参数之间的关系,构造了一种可均衡条件数全域均值及其极差间矛盾的综合操作性能指标,进而将尺度综合归结为一类双参数的寻优问题,该方法避免了多参数非线性规划的复杂性,并通过算例验证了该方法的有效性和简单性;
3.逆动力学和伺服电机参数预估:提出了一种借助支链动坐标系和动平台动坐标系联合求解各部件角速度、角加速度与动平台速度的解耦映射关系的方法,巧妙地得到了各驱动杆自旋角速度和角加速度。进而利用虚功率原理列出了精确的逆动力学模型。借助雅可比奇异值法预估了驱动伺服电机的参数,并通过典型轨迹验证理论模型的正确性和预估方法的有效性;
4.轨迹规划:将机器人末端执行器的运动归为空间点矢的运动,提出适合任何混联机器人的时间同步运动轨迹规划算法及空间任意曲线运动的规划方法。应用三次样条函数进一步规划了从操作空间映射到关节空间的离散控制点,可防止驱动关节的运动波动,并通过节点的加工仿真验证了各方法的有效性。
With the aid of the 863 Exemplary Project, to meet the demand for the manufacture of a novel Bars-Converging Joint used in the steel structure, the dissertation investigates into the design theory and method of the EXE-M robot—a novel 5-DOF hybrid reconfigurable robot possessing proprietary intellectual property rights. Research includes inverse position analysis, Jacobian matrix solution, dimensional synthesis, inverse dynamic analysis, servomotor parameters estimation and trajectory planning. The following work has been accomplished:
1. Inverse position analysis and Jacobian matrix solution: According to the characteristics of the EXE-M robot, it is decomposed into 3-SPR parallel module and 2-DOF serial module. With three displacement variables, the former reveal inverse kinematic model has been developed by the Sylvester method, while the latter is proposed by the method of cyclic search and pure trajectory theory. The integrated Jacobian matrix of its parallel subsystem is simply formulated by the screw theory, and then the general Jacobian is constructed.
2. Dimensional synthesis: To avoid the complexity of the forward solution, a simple solution to workspace of the 3-SPR parallel manipulator is constituted by using its CAD simulation mechanism. With the characteristics of the workspace of the mechanism and the relation between scale parameters, a integrated processability index is proposed which can balance the conflict between the scale average value and range. Then the dimensional synthesis of the parallel subsystem is considered as a two-parameters optimizing problem, which avoids the complexity of nonlinear programming including constraints, and the feasibility and simplicity of the method is verified experimentally.
3. Inverse dynamic analysis and servomotor parameters estimation: Combining the branch-fixed secondary frame with the moving platform-fixed secondary frame, the decoupling mapping relation between the angular velocity and angular acceleration of branches and the velocity of the moving platform have been proposed, cleverly leading out the spin angular velocity and angular acceleration of three branches. Finally based on the inverse dynamic model, the speed rating, the power rating and torque of servomotor are estimated by the singular value of Jacobian matrix. The effectiveness of the approach has been verified using classic trajectory planning.
4. Trajectory planning: The movement of the robot end-effector can be grouped into the spatial point-vector movement. A trajectory planning algorithms of time synchronization is proposed for any more-mobility hybrid mechanism, as well as the planning method for any space curvilinear motion. Using cubic splines function, the real-time trajectory programming in joint space mapped from the workspace is obtained further, which can guarantee the running stability of joints. At last, the effectiveness of the above-mentioned approaches has been verified by the simulation of joints machining.
1.位置逆解和雅可比矩阵求解:根据EXE-M混联机械手的结构组成,将其分解为3-SPR并联模块与2自由串联模块,提出一种利用Sylvester法求解以位置坐标为独立变量并具有显式解的逆解分析法。借助循环搜索法和纯轨迹理论得到串联模块的逆解模型。利用螺旋理论建立了并联模块的完整雅可比矩阵,就此构建了一般雅可比矩阵;
2.尺度综合:为了克服机构正解的复杂性,提出一种利用CAD仿真模型求取3-SPR机构可达空间的简单方法。利用机构任务空间的特点及各尺度参数之间的关系,构造了一种可均衡条件数全域均值及其极差间矛盾的综合操作性能指标,进而将尺度综合归结为一类双参数的寻优问题,该方法避免了多参数非线性规划的复杂性,并通过算例验证了该方法的有效性和简单性;
3.逆动力学和伺服电机参数预估:提出了一种借助支链动坐标系和动平台动坐标系联合求解各部件角速度、角加速度与动平台速度的解耦映射关系的方法,巧妙地得到了各驱动杆自旋角速度和角加速度。进而利用虚功率原理列出了精确的逆动力学模型。借助雅可比奇异值法预估了驱动伺服电机的参数,并通过典型轨迹验证理论模型的正确性和预估方法的有效性;
4.轨迹规划:将机器人末端执行器的运动归为空间点矢的运动,提出适合任何混联机器人的时间同步运动轨迹规划算法及空间任意曲线运动的规划方法。应用三次样条函数进一步规划了从操作空间映射到关节空间的离散控制点,可防止驱动关节的运动波动,并通过节点的加工仿真验证了各方法的有效性。
With the aid of the 863 Exemplary Project, to meet the demand for the manufacture of a novel Bars-Converging Joint used in the steel structure, the dissertation investigates into the design theory and method of the EXE-M robot—a novel 5-DOF hybrid reconfigurable robot possessing proprietary intellectual property rights. Research includes inverse position analysis, Jacobian matrix solution, dimensional synthesis, inverse dynamic analysis, servomotor parameters estimation and trajectory planning. The following work has been accomplished:
1. Inverse position analysis and Jacobian matrix solution: According to the characteristics of the EXE-M robot, it is decomposed into 3-SPR parallel module and 2-DOF serial module. With three displacement variables, the former reveal inverse kinematic model has been developed by the Sylvester method, while the latter is proposed by the method of cyclic search and pure trajectory theory. The integrated Jacobian matrix of its parallel subsystem is simply formulated by the screw theory, and then the general Jacobian is constructed.
2. Dimensional synthesis: To avoid the complexity of the forward solution, a simple solution to workspace of the 3-SPR parallel manipulator is constituted by using its CAD simulation mechanism. With the characteristics of the workspace of the mechanism and the relation between scale parameters, a integrated processability index is proposed which can balance the conflict between the scale average value and range. Then the dimensional synthesis of the parallel subsystem is considered as a two-parameters optimizing problem, which avoids the complexity of nonlinear programming including constraints, and the feasibility and simplicity of the method is verified experimentally.
3. Inverse dynamic analysis and servomotor parameters estimation: Combining the branch-fixed secondary frame with the moving platform-fixed secondary frame, the decoupling mapping relation between the angular velocity and angular acceleration of branches and the velocity of the moving platform have been proposed, cleverly leading out the spin angular velocity and angular acceleration of three branches. Finally based on the inverse dynamic model, the speed rating, the power rating and torque of servomotor are estimated by the singular value of Jacobian matrix. The effectiveness of the approach has been verified using classic trajectory planning.
4. Trajectory planning: The movement of the robot end-effector can be grouped into the spatial point-vector movement. A trajectory planning algorithms of time synchronization is proposed for any more-mobility hybrid mechanism, as well as the planning method for any space curvilinear motion. Using cubic splines function, the real-time trajectory programming in joint space mapped from the workspace is obtained further, which can guarantee the running stability of joints. At last, the effectiveness of the above-mentioned approaches has been verified by the simulation of joints machining.
引文
[1]车伟娴,李丽娟,空间网壳结构的理论研究,山西建筑,2005(12),31(24),54~56
[2] http://baike.baidu.com/view/1767791.htm
[3]张永贵,焦卫东,蔡善乐,网架节点球数控加工夹紧信息的识别与提取,甘肃工业大学学报,2001,27(3):23~26
[4]汪劲松,黄田,并联机床一机床行业ICI临的机遇与挑战,中国机械土程,1999,10(42): 1103~1107
[5] http://www.exechon.com
[6]黄田,刘海涛等,五自由度混联机器人,中国发明专利,CNl0l049692,2007
[7]Neumann K E. Tricept application, In The 3rd Chemnitz Parallel Kinematics Seminar, Zwickau, Germany, 2002. 547~551
[8]Neumann K E, Parallel-kinematical machine, WO/2006/05493, PCI/SE2005/001651, 2006
[9]路懿,毛秉毅,3-SPR并联解耦结构六维测力平台,中国发明专利,CN101246062,2008-10-05
[10]K H Hunt. Structural kinematics of in-parallel-actuated robot arms. ASME Trans. J. Mech.Trans. Autom. Des.105(1983): 705~712
[11]Lee K M, Shah D K, Kinematic analysis of a 3-degrees of freedom in-parallel actuated manipulator [J],IEEE Journal of Robotics and Automation, 1988, 4(3): 354~360
[12]Yi Lu, Bo Hu, Unification and simplification of velocity/acceleration of limited-dof parallel manipulators with linear active legs, Mechanism and Machine Theory, 2008, 43, 1112~1128
[13]石志新,罗玉峰,机器人机构的全域性能指标研究,机器人,27(5): 420-422
[14]Kim J O, Khosla P K, Dexterity measure for design and control of manipulators, IEEE/RSJ International Workshop on Intelligent Robots and Systems(IROS'91), Osaka, Japan, 1991: 758~763
[15]Gosselin C, Angeles J, The optimum kinematics design of a spherical 3-degree-of-freedom parallel manipulator, Journal of Mechanisms, Transmissions, and Automation in Design, 1989, 111(2) : 202~207
[16]Huang T, Whitehouse D J, Wang J S, Local dexterity, optimum architecture and design criteria of parallel machine tools, Annals of the CIRP, 1998, 47(1) : 347~351
[17]Huang T, Gosselin C M, Whitehouse D J, et al, Analytic approach for optimal, design of a type of spherical parallel manipulators using dexterous performance indices, IMechE Journal of Mechanical Engineering Science, 2003, Part C, 217(4) : 447~455
[18]Huang T, Li M, Li Z X, et al, Optimal kinematics design of 2-DOF parallel manipulators with well-shaped workspace bounded by a specified conditioning index, TEEE Transactions on Robotics and Automation, 2004, 20(3) : 538~542
[19]Huang T, Li M, Zhao X M, et al, Conceptual design and dimensional synthesis for a 3-DOF module of the TriVariant一a novel 5-DOF recontigurable hybrid robot, IEEE Transactions of Robotics and Automation, 2005, 21(3) : 449~456
[20]Asada R, Dynamic analysis and design of robot manipulators using inertia ellipsoids, In Proceedings of the IEEE International Conference on Robotics and Automation, Atlanta, Georgia, 1984, 1: 94~102
[21]Yoshikawa T, Dynamic manipulability of robotic manipulators, In: Proceedings of the IEEE International Conference on Robotics and Automation, St. Louis, LA, 1985: 1033~1038
[22]Tadokoro S, Kimura I, Takamori T, A measure for evaluation of dynamic dexterity based on a stochastic interpretation of manipulator motion, In: Proceedings of the IEEE International Conference on Robotics and Automation, 1991: 509~514
[23]李永刚,宋轶民,冯志友等,基于牛顿欧拉法的3-RPS并联机构逆动力学分析,航空学报,2007,28(5),1210~1215
[24]张利敏,一种三平动高速并联机械手设计方法研究:[硕士学位论文],天津;天津大学,2008
[25]黄田,赵兴玉,梅江平等,并联机床伺服进给电机参数选择的一种方法,自然科学进展,2001,11(5),522~529
[26]Huang T, Li M, Zhao X Y, et al, Kinematics design of a reconfigurable miniature parallel kinematics machine, Chinese Journal of Mechanical, Engineering, 2003, 16(1): 79-82
[27]王攀峰,相贯线切割机器人作业单元关键技术研究,[博士学位论文],天津;天津大学,2008
[28]Bobrow J E, Dubowskys, Gibson J S, Time-Optimal Control of Robotic Manipulators Along Specified Paths, International Journal of Robotic Research, 1985, 4(3): 554~561
[29]Connolly C.I., Burns J.B., Weiss R., Path planning using Laplace’s equation. Proceedings of the 1990 IEEE International Conference on Yobotics and Automation, 1990.2102~2106
[30]Wong E.K., Fu K. S., A hierarchical orthogonal space approach to three dimensional path planning, IEEE J. Rob. Aut., 1986, 30: 42~53
[31]Lozano-Pere T., A simple motion-planning algorithm for general robot manipulators. IEEE J. Rob. Aut. 1987, 3: 224~238
[32]Hynn M., Kim J., Preliminary investigations into a two-stage method of evolutionary optimization on constrained problems, Proc. Of the Fourth Annual Conference on Evolution, 1995.449~463
[33]李占贤,高速轻型并联机械手关键技术及样机建造,[博士学位论文],天津大学,2004
[34]石宏,3-TPS混联机床相关控制算法研究,[博士学位论文],东北大学,2005
[35]黄真,孔令富,方跃法等,并联机器人机构学理论及控制,北京,机械工业出版社,1997
[36]黄真,赵永生,赵铁石等,高等空间机构学,北京,高等教育出版社,2006
[37]莫贤,基于螺旋理论的3-PRS并联机构的运动学建模及仿真,[博士学位论文],扬州大学,2009
[38]李仕华,并联机器人机构分析与综合的理论研究,[博士学位论文],燕山大学,2004
[39]王凤岐,张连洪,邵宏宇,现代设计方法,天津,天津大学出版社,2005
[40]黄真,赵铁石,王晶,欠秩三自由度并联平台机构工作空间中的单纯性运动路径,机器人,1995,21(3),229~232
[41]刘海涛,五自由度混联机械手TriVariant_B的设计方法研究,[硕士学位论文],天津大学,2007
[42]孙涛,新型五坐标可重构混联机械手的尺度综合与静刚度分析,[硕士学位论文],天津大学,2007
[43]孙涛,新型五坐标可重构混联机械手的尺度综合与静刚度分析,[硕士学位论文],天津大学,2008
[44]Huang T, Whitehouse D J, Wang J S, Local dexterity, optimum architecture and design criteria of parallel machine tools, Annals of the CIRP, 1998, 47(1): 347~51
[45]Huang T, Mei J P, Li Z X, et al, A method for estimating servomotor parameters of a arallel robot for rapid pick-and-place operations, ASME Journal of Mechanical Design, 005, 127(4): 596~01
[46]张一巍,张永民,黄元庆,用高阶多项式插值解决机器人运动轨迹规划中的约束问题,机器人技术与应用,2002, 2: 19~21
[47]Ozaki H, Lin C J, Optimal B-spline joint trajectory generation for collision-free movements of a manipulator under dynamic constraints,International Journal of Robotics and Automation, 1996, 4: 22~28
[48]贾启芬,刘习军王春敏,理论力学,天津,天津大学出版社,2003
[49]江洪,陆立峰,魏峥等,Solidworks动画演示与运动分析实例解析,北京:机械工业出版社,2006
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[2] http://baike.baidu.com/view/1767791.htm
[3]张永贵,焦卫东,蔡善乐,网架节点球数控加工夹紧信息的识别与提取,甘肃工业大学学报,2001,27(3):23~26
[4]汪劲松,黄田,并联机床一机床行业ICI临的机遇与挑战,中国机械土程,1999,10(42): 1103~1107
[5] http://www.exechon.com
[6]黄田,刘海涛等,五自由度混联机器人,中国发明专利,CNl0l049692,2007
[7]Neumann K E. Tricept application, In The 3rd Chemnitz Parallel Kinematics Seminar, Zwickau, Germany, 2002. 547~551
[8]Neumann K E, Parallel-kinematical machine, WO/2006/05493, PCI/SE2005/001651, 2006
[9]路懿,毛秉毅,3-SPR并联解耦结构六维测力平台,中国发明专利,CN101246062,2008-10-05
[10]K H Hunt. Structural kinematics of in-parallel-actuated robot arms. ASME Trans. J. Mech.Trans. Autom. Des.105(1983): 705~712
[11]Lee K M, Shah D K, Kinematic analysis of a 3-degrees of freedom in-parallel actuated manipulator [J],IEEE Journal of Robotics and Automation, 1988, 4(3): 354~360
[12]Yi Lu, Bo Hu, Unification and simplification of velocity/acceleration of limited-dof parallel manipulators with linear active legs, Mechanism and Machine Theory, 2008, 43, 1112~1128
[13]石志新,罗玉峰,机器人机构的全域性能指标研究,机器人,27(5): 420-422
[14]Kim J O, Khosla P K, Dexterity measure for design and control of manipulators, IEEE/RSJ International Workshop on Intelligent Robots and Systems(IROS'91), Osaka, Japan, 1991: 758~763
[15]Gosselin C, Angeles J, The optimum kinematics design of a spherical 3-degree-of-freedom parallel manipulator, Journal of Mechanisms, Transmissions, and Automation in Design, 1989, 111(2) : 202~207
[16]Huang T, Whitehouse D J, Wang J S, Local dexterity, optimum architecture and design criteria of parallel machine tools, Annals of the CIRP, 1998, 47(1) : 347~351
[17]Huang T, Gosselin C M, Whitehouse D J, et al, Analytic approach for optimal, design of a type of spherical parallel manipulators using dexterous performance indices, IMechE Journal of Mechanical Engineering Science, 2003, Part C, 217(4) : 447~455
[18]Huang T, Li M, Li Z X, et al, Optimal kinematics design of 2-DOF parallel manipulators with well-shaped workspace bounded by a specified conditioning index, TEEE Transactions on Robotics and Automation, 2004, 20(3) : 538~542
[19]Huang T, Li M, Zhao X M, et al, Conceptual design and dimensional synthesis for a 3-DOF module of the TriVariant一a novel 5-DOF recontigurable hybrid robot, IEEE Transactions of Robotics and Automation, 2005, 21(3) : 449~456
[20]Asada R, Dynamic analysis and design of robot manipulators using inertia ellipsoids, In Proceedings of the IEEE International Conference on Robotics and Automation, Atlanta, Georgia, 1984, 1: 94~102
[21]Yoshikawa T, Dynamic manipulability of robotic manipulators, In: Proceedings of the IEEE International Conference on Robotics and Automation, St. Louis, LA, 1985: 1033~1038
[22]Tadokoro S, Kimura I, Takamori T, A measure for evaluation of dynamic dexterity based on a stochastic interpretation of manipulator motion, In: Proceedings of the IEEE International Conference on Robotics and Automation, 1991: 509~514
[23]李永刚,宋轶民,冯志友等,基于牛顿欧拉法的3-RPS并联机构逆动力学分析,航空学报,2007,28(5),1210~1215
[24]张利敏,一种三平动高速并联机械手设计方法研究:[硕士学位论文],天津;天津大学,2008
[25]黄田,赵兴玉,梅江平等,并联机床伺服进给电机参数选择的一种方法,自然科学进展,2001,11(5),522~529
[26]Huang T, Li M, Zhao X Y, et al, Kinematics design of a reconfigurable miniature parallel kinematics machine, Chinese Journal of Mechanical, Engineering, 2003, 16(1): 79-82
[27]王攀峰,相贯线切割机器人作业单元关键技术研究,[博士学位论文],天津;天津大学,2008
[28]Bobrow J E, Dubowskys, Gibson J S, Time-Optimal Control of Robotic Manipulators Along Specified Paths, International Journal of Robotic Research, 1985, 4(3): 554~561
[29]Connolly C.I., Burns J.B., Weiss R., Path planning using Laplace’s equation. Proceedings of the 1990 IEEE International Conference on Yobotics and Automation, 1990.2102~2106
[30]Wong E.K., Fu K. S., A hierarchical orthogonal space approach to three dimensional path planning, IEEE J. Rob. Aut., 1986, 30: 42~53
[31]Lozano-Pere T., A simple motion-planning algorithm for general robot manipulators. IEEE J. Rob. Aut. 1987, 3: 224~238
[32]Hynn M., Kim J., Preliminary investigations into a two-stage method of evolutionary optimization on constrained problems, Proc. Of the Fourth Annual Conference on Evolution, 1995.449~463
[33]李占贤,高速轻型并联机械手关键技术及样机建造,[博士学位论文],天津大学,2004
[34]石宏,3-TPS混联机床相关控制算法研究,[博士学位论文],东北大学,2005
[35]黄真,孔令富,方跃法等,并联机器人机构学理论及控制,北京,机械工业出版社,1997
[36]黄真,赵永生,赵铁石等,高等空间机构学,北京,高等教育出版社,2006
[37]莫贤,基于螺旋理论的3-PRS并联机构的运动学建模及仿真,[博士学位论文],扬州大学,2009
[38]李仕华,并联机器人机构分析与综合的理论研究,[博士学位论文],燕山大学,2004
[39]王凤岐,张连洪,邵宏宇,现代设计方法,天津,天津大学出版社,2005
[40]黄真,赵铁石,王晶,欠秩三自由度并联平台机构工作空间中的单纯性运动路径,机器人,1995,21(3),229~232
[41]刘海涛,五自由度混联机械手TriVariant_B的设计方法研究,[硕士学位论文],天津大学,2007
[42]孙涛,新型五坐标可重构混联机械手的尺度综合与静刚度分析,[硕士学位论文],天津大学,2007
[43]孙涛,新型五坐标可重构混联机械手的尺度综合与静刚度分析,[硕士学位论文],天津大学,2008
[44]Huang T, Whitehouse D J, Wang J S, Local dexterity, optimum architecture and design criteria of parallel machine tools, Annals of the CIRP, 1998, 47(1): 347~51
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