一种用于柔性定位器的三自由度并联机构研究
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摘要
并联机器人的高刚度、高精度、强承载能力等许多优点使它成为一种与串联机器人品质截然不同的机器人类型。目前,并联机器人在数控加工、运动模拟、传感器、精细操作等这些领域得到了广泛的应用。可以说并联机器人尤其是少自由度并联机器人有着良好的发展应用前景。基于此,本文提出了用作定位器的Tripod并联机器人。它使用了三组电动推杆,每组电动推杆的两杆之间通过同步带与锥齿轮连接,构成了类似于Delta机构中的平行四边形结构。
本文分析了Tripod机构的自由度、位置正逆解的解析解、工作空间与奇异性,进行了轨迹规划。在此基础上设计完成了机构控制系统的硬件部分。该控制系统以交流伺服电机为驱动装置,采用PMAC多轴运动控制卡来协调各杆的运动。由于存在间隙等非线性因素,难以建立Tripod并联机器人的精确模型,因此机构的控制系统选用了模糊PID控制方法。设计了一个二维模糊控制器,并在MATLAB的SIMULINK环境下进行控制系统的仿真,仿真结果显示模糊PID控制算法具有很好的控制效果,可实现对Tripod定位器按照规划速度曲线上的运动控制。
最后,利用ADAMS软件对Tripod定位器进行了简单的动力学仿真,得到了驱动力随时间变化的曲线图。并对Tripod定位器在飞机装配对接中的应用做了简单的分析。
The virtues of parallel robot (P.R) such as high rigidity, excellent precision and strong carrying capacity make it a style with different characters to serial robot (S.R). At present, P.R is widely used in the fields of numerical control process, movement simulation, sensor and precise process and so on. Parallel robot, especial Low-DOF P.R has favorite perspective in development and application. Tripod, a P.R used as positioner is extracted in this paper based on the ground. The Tripod uses three groups legs. The two legs of each group joined by umbrella gear and synchronous strip are similar to the parallelogram of Delta P.R.
In this paper, a structure of Tripod control system is designed based on the analysis degree of freedom, displacement, workspace, singularities and path planning of the positioner. AC servo motors are the driving equipment, PMAC is the multi-shaft motion controller in the system. It is difficult to establish the exact model due to nonlinerity factors such as gap, so a Fuzzy-PID control is designed for the Tripod control system. Simulation of The control system is performed in MATLAB/SIMULINK. Result of simulation is descriped: Fuzzy-PID control algorithm has more effective performance.It can make the positioner to move under the planning path.
A graph of driving force is gained based on the dynamics simulation of Tripod by using ADAMS. The possibility that apply the Tripod positioner to aircraft assembles is presented at the end of this paper.
本文分析了Tripod机构的自由度、位置正逆解的解析解、工作空间与奇异性,进行了轨迹规划。在此基础上设计完成了机构控制系统的硬件部分。该控制系统以交流伺服电机为驱动装置,采用PMAC多轴运动控制卡来协调各杆的运动。由于存在间隙等非线性因素,难以建立Tripod并联机器人的精确模型,因此机构的控制系统选用了模糊PID控制方法。设计了一个二维模糊控制器,并在MATLAB的SIMULINK环境下进行控制系统的仿真,仿真结果显示模糊PID控制算法具有很好的控制效果,可实现对Tripod定位器按照规划速度曲线上的运动控制。
最后,利用ADAMS软件对Tripod定位器进行了简单的动力学仿真,得到了驱动力随时间变化的曲线图。并对Tripod定位器在飞机装配对接中的应用做了简单的分析。
The virtues of parallel robot (P.R) such as high rigidity, excellent precision and strong carrying capacity make it a style with different characters to serial robot (S.R). At present, P.R is widely used in the fields of numerical control process, movement simulation, sensor and precise process and so on. Parallel robot, especial Low-DOF P.R has favorite perspective in development and application. Tripod, a P.R used as positioner is extracted in this paper based on the ground. The Tripod uses three groups legs. The two legs of each group joined by umbrella gear and synchronous strip are similar to the parallelogram of Delta P.R.
In this paper, a structure of Tripod control system is designed based on the analysis degree of freedom, displacement, workspace, singularities and path planning of the positioner. AC servo motors are the driving equipment, PMAC is the multi-shaft motion controller in the system. It is difficult to establish the exact model due to nonlinerity factors such as gap, so a Fuzzy-PID control is designed for the Tripod control system. Simulation of The control system is performed in MATLAB/SIMULINK. Result of simulation is descriped: Fuzzy-PID control algorithm has more effective performance.It can make the positioner to move under the planning path.
A graph of driving force is gained based on the dynamics simulation of Tripod by using ADAMS. The possibility that apply the Tripod positioner to aircraft assembles is presented at the end of this paper.
引文
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[2]王巍,贺平,万良辉.飞机柔性装配技术研究.机械设计与制造[J].2006,(11):88-90
[3]邹方,薛汉杰,周万勇等.飞机数字化柔性装配关键技术及其发展[J].航空制造技术,2006,(9):30-35
[4]邹冀华,刘志存,范玉青.大型飞机部件数字化对接装配技术研究[J].计算机集成制造系统,2007-07,13(7):1367-1373
[5]邹冀华,刘志存,范玉青.大型飞行器舱段数字化装配方法[J].制造业自动化,2007-01,29(1):1-4,24
[6]郭恩明.国外飞机柔性装配技术[J].航空制造技术,2005,(9):28-32
[7].景奉水,谭民,侯增广等.船体分段位姿找正对接系统-一个多机器人协调操作系统的实现[J].自动化学报,2002,28(5):709-714
[8] D.Stewart.A platform with six degrees of freedom[J]. Proceedings of the ImechE, 1965,Vol.180,No.15:371-385.
[9]黄真.并联机器人机构学理论及控制[M] .北京:机械工业出版社.1997.
[10]Richard M.Murray, Zexiang Li, S.Shankar Sastry.机器人操作的数学导论[M].北京:机械工业出版社.1997
[11]高秀兰,鲁开讲,王娟平.Delta并联机构工作空间解析及尺度综合[J] .农业机械学报,2008,39(5):145~149.
[12]朱思俊.少自由度并联机构运动学及五自由度并联机构的相关理论,[博士学位论文].秦皇岛:燕山大学,2007.4
[13]S.Modic.Virtual Axis Machining-the Shape of Things to Come.Tooling& Production, 1994,7:13-14
[14]H.J.Warnecke,R.Neggebauer and F.Wieland.Development of Hexapod Based Machine Tool. Annals of the CIRP,1998,47(1):337-340.
[15]Tsai L-W, Kinematics of a three-dof platform with three extensible limbs, ARK, Portoroz-Bernadin, 22-26 June 1996, pp. 401-410.
[16] J.R.Phillips.Freedom in Machinery.England:Cambridge University Press,1990.
[17]赵景山,冯之敬,褚福磊.机器人机构自由度分析理论[M].北京:科学出版社,2009,3
[18] R.S.Ball.The Theory of Screws.England:Cambridge University Press,1900.
[19]李仕华,黄真.一种特殊3-UPU并联平台机构瞬时运动特性[J] .中国机械工程,2005,16(18):1641~1646.
[20]W.X.Zhang, Z.C.Xu. Algebraic Construction of the Three-System of Screws. Mach. Theory. 1998,33(7):925~930.
[21]Chablat, D.Wenger.“Architecture Optimisation of a 3-dof Translational Parallel Mechanism for Machining Applications”, the Orthoglide. In: IEEE Trans. on Rob. and Autom, Vol. 19(3), 2003, pp. 403-410.
[22]丁学明.一种空间三自由度平动并联机床研究,[硕士学位论文].南京:南京航空航天大学,2003,3
[23]LUO You-gao, ZHENG Xiang-zhou, BIN Hong-zan. Workspace of Translation 3-UPU Parallel Manipulators[J]. Journal of Shanghai University(English Edition), 2005,9(1):62～67.
[24]Luli. Computer-aided geometric machining of a 3D free surface using a 3-UPU spatial parallel machine tool. Int J Adv Manuf Technol, vol.26, 2005: 1018~1025.
[25]于靖军,毕树生,宗光华.三自由度3-CS并联平台机构的运动学分析[J].航空学报, vol.22,No.3,2001:217~221.
[26] C.Gosselin.Determination of the Workspace of 6-DOF parallel Manipulators.ASME Journal Design,1990,Vol.112(3):331~336.
[27] I.A.Bonev,C.Gosselin.A Geometric Algorithm for the Computation of the Constant Orientation Workspace of 6-RUS Parallel Manipulators.Proceedings of the ASME DETC,Baltimore,Maryland,2000:832~845.
[28]J.P.Merlet.Workspace-oriented Methodology for Designing a Parallel Manipulators. Proceedings of the 1996 IEEE International Conference on Robotics and Automaton,1996:3726~3731.
[29] J.P.Merlet,Determination of 6-D Workspaces of Gough-Type Parallel Manipulator and Comparison Between Different Geometries.International Journal of Robotics Research,1996,Vol.18(9):902~916.
[30]Huang Zhen, Li Qinchuan. Type synthesis principle of minor-mobility parallel manipulators. Science in China(series E), vol.45, No.3, 2002: 241~248
[31]Gegorio R D. Statics and singularity loci of the 3-UPU wrist. Proc. IEEE/ ASME Int . Conf . on Advanced Intelligent Mechatronics, 2001, 1 : 470～475
[32] Joshi S, Tsai L W. A comparison study of two 3-DOF parallel manipulators: One with three and the other with four supporting legs[J]. IEEE Transaction of Robotics and Automation, 2003, 19(2):200-209.
[33]胡波,路懿.求解3-RPS并联机构刚度的新方法[J].机械工程学报,2010,46(1):24-29
[34]李世敬,王解法.层叠CMAC补偿的并联机器人变结构控制研究[J].系统仿真学报2002(8)
[35]代颖,施颂椒.基于非线性滑动模的机器人鲁棒自适应分散控制策略[J].上海交通大学学报2000(12)
[36]卢旭.基于PMAC的伺服控制系统的开发[J].扬州:舰船电子对抗,2009,30(2):112~114.
[37]李铁民,汪劲松,杨向东等.基于Stewart平台数控机床的轨迹规划研究[J].北京:中国机械工程,1999,10(10):1118~1120.
[38]焦晓红,耿秋实等.并联机器人的鲁棒自适应控制[J].机器人技术与应用,2002(4)
[39]Spong M.W. On the Robust Control of Robot Manipulators[J].IEEE Trans on Automatic Control, 1992(11).
[40]张国良,曾静,柯熙政等.模糊控制及其MATLAB应用[M] .西安:西安交通大学,2002:69~70.
[41]张敏,余纯.基于MATLAB的PID参数模糊自整定控制器设计及仿真[J].自动化技术与应用,2005,24(7):23~24.
[42]殷云华,樊水康,陈闽鄂.自适应模糊PID控制器的设计和仿真[J].火力与指挥控制,2008,33(7):96~98.
[43]郭卫东.虚拟样机技术与ADAMS应用实例教程[M].北京:北京航空航天大学出版社,2007,11.
[44]邹方,张书生.飞机总装自动化校准对接系统[J].航空制造技术,2008,7:32-36.
[45]梅中义,范玉青.基于激光跟踪定位的部件对接柔性装配技术[J].北京航空航天大学学报,2009,35(1): 65-69
[2]王巍,贺平,万良辉.飞机柔性装配技术研究.机械设计与制造[J].2006,(11):88-90
[3]邹方,薛汉杰,周万勇等.飞机数字化柔性装配关键技术及其发展[J].航空制造技术,2006,(9):30-35
[4]邹冀华,刘志存,范玉青.大型飞机部件数字化对接装配技术研究[J].计算机集成制造系统,2007-07,13(7):1367-1373
[5]邹冀华,刘志存,范玉青.大型飞行器舱段数字化装配方法[J].制造业自动化,2007-01,29(1):1-4,24
[6]郭恩明.国外飞机柔性装配技术[J].航空制造技术,2005,(9):28-32
[7].景奉水,谭民,侯增广等.船体分段位姿找正对接系统-一个多机器人协调操作系统的实现[J].自动化学报,2002,28(5):709-714
[8] D.Stewart.A platform with six degrees of freedom[J]. Proceedings of the ImechE, 1965,Vol.180,No.15:371-385.
[9]黄真.并联机器人机构学理论及控制[M] .北京:机械工业出版社.1997.
[10]Richard M.Murray, Zexiang Li, S.Shankar Sastry.机器人操作的数学导论[M].北京:机械工业出版社.1997
[11]高秀兰,鲁开讲,王娟平.Delta并联机构工作空间解析及尺度综合[J] .农业机械学报,2008,39(5):145~149.
[12]朱思俊.少自由度并联机构运动学及五自由度并联机构的相关理论,[博士学位论文].秦皇岛:燕山大学,2007.4
[13]S.Modic.Virtual Axis Machining-the Shape of Things to Come.Tooling& Production, 1994,7:13-14
[14]H.J.Warnecke,R.Neggebauer and F.Wieland.Development of Hexapod Based Machine Tool. Annals of the CIRP,1998,47(1):337-340.
[15]Tsai L-W, Kinematics of a three-dof platform with three extensible limbs, ARK, Portoroz-Bernadin, 22-26 June 1996, pp. 401-410.
[16] J.R.Phillips.Freedom in Machinery.England:Cambridge University Press,1990.
[17]赵景山,冯之敬,褚福磊.机器人机构自由度分析理论[M].北京:科学出版社,2009,3
[18] R.S.Ball.The Theory of Screws.England:Cambridge University Press,1900.
[19]李仕华,黄真.一种特殊3-UPU并联平台机构瞬时运动特性[J] .中国机械工程,2005,16(18):1641~1646.
[20]W.X.Zhang, Z.C.Xu. Algebraic Construction of the Three-System of Screws. Mach. Theory. 1998,33(7):925~930.
[21]Chablat, D.Wenger.“Architecture Optimisation of a 3-dof Translational Parallel Mechanism for Machining Applications”, the Orthoglide. In: IEEE Trans. on Rob. and Autom, Vol. 19(3), 2003, pp. 403-410.
[22]丁学明.一种空间三自由度平动并联机床研究,[硕士学位论文].南京:南京航空航天大学,2003,3
[23]LUO You-gao, ZHENG Xiang-zhou, BIN Hong-zan. Workspace of Translation 3-UPU Parallel Manipulators[J]. Journal of Shanghai University(English Edition), 2005,9(1):62～67.
[24]Luli. Computer-aided geometric machining of a 3D free surface using a 3-UPU spatial parallel machine tool. Int J Adv Manuf Technol, vol.26, 2005: 1018~1025.
[25]于靖军,毕树生,宗光华.三自由度3-CS并联平台机构的运动学分析[J].航空学报, vol.22,No.3,2001:217~221.
[26] C.Gosselin.Determination of the Workspace of 6-DOF parallel Manipulators.ASME Journal Design,1990,Vol.112(3):331~336.
[27] I.A.Bonev,C.Gosselin.A Geometric Algorithm for the Computation of the Constant Orientation Workspace of 6-RUS Parallel Manipulators.Proceedings of the ASME DETC,Baltimore,Maryland,2000:832~845.
[28]J.P.Merlet.Workspace-oriented Methodology for Designing a Parallel Manipulators. Proceedings of the 1996 IEEE International Conference on Robotics and Automaton,1996:3726~3731.
[29] J.P.Merlet,Determination of 6-D Workspaces of Gough-Type Parallel Manipulator and Comparison Between Different Geometries.International Journal of Robotics Research,1996,Vol.18(9):902~916.
[30]Huang Zhen, Li Qinchuan. Type synthesis principle of minor-mobility parallel manipulators. Science in China(series E), vol.45, No.3, 2002: 241~248
[31]Gegorio R D. Statics and singularity loci of the 3-UPU wrist. Proc. IEEE/ ASME Int . Conf . on Advanced Intelligent Mechatronics, 2001, 1 : 470～475
[32] Joshi S, Tsai L W. A comparison study of two 3-DOF parallel manipulators: One with three and the other with four supporting legs[J]. IEEE Transaction of Robotics and Automation, 2003, 19(2):200-209.
[33]胡波,路懿.求解3-RPS并联机构刚度的新方法[J].机械工程学报,2010,46(1):24-29
[34]李世敬,王解法.层叠CMAC补偿的并联机器人变结构控制研究[J].系统仿真学报2002(8)
[35]代颖,施颂椒.基于非线性滑动模的机器人鲁棒自适应分散控制策略[J].上海交通大学学报2000(12)
[36]卢旭.基于PMAC的伺服控制系统的开发[J].扬州:舰船电子对抗,2009,30(2):112~114.
[37]李铁民,汪劲松,杨向东等.基于Stewart平台数控机床的轨迹规划研究[J].北京:中国机械工程,1999,10(10):1118~1120.
[38]焦晓红,耿秋实等.并联机器人的鲁棒自适应控制[J].机器人技术与应用,2002(4)
[39]Spong M.W. On the Robust Control of Robot Manipulators[J].IEEE Trans on Automatic Control, 1992(11).
[40]张国良,曾静,柯熙政等.模糊控制及其MATLAB应用[M] .西安:西安交通大学,2002:69~70.
[41]张敏,余纯.基于MATLAB的PID参数模糊自整定控制器设计及仿真[J].自动化技术与应用,2005,24(7):23~24.
[42]殷云华,樊水康,陈闽鄂.自适应模糊PID控制器的设计和仿真[J].火力与指挥控制,2008,33(7):96~98.
[43]郭卫东.虚拟样机技术与ADAMS应用实例教程[M].北京:北京航空航天大学出版社,2007,11.
[44]邹方,张书生.飞机总装自动化校准对接系统[J].航空制造技术,2008,7:32-36.
[45]梅中义,范玉青.基于激光跟踪定位的部件对接柔性装配技术[J].北京航空航天大学学报,2009,35(1): 65-69