三自由度并联机构分析与控制策略研究
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摘要
随着我国国防和军事工业的发展,迫切需要打破国外的技术垄断、提高自行武器火控系统测试水准,研制自己的自行武器火控系统实车道路模拟设备提到日程上来。本文以哈尔滨工业大学电液伺服仿真及试验系统研究所承接的科研项目“自行武器动态试验模拟设备”为背景,对三自由度并联机构的运动学、动力学、精度及控制策略进行理论分析和实验研究。
三自由度并联机构是典型Stewart并联机构的变体,它用三条作动器和三条支撑杆代替Stewart并联机构中的六条作动器来实现三个自由度的旋转运动。先建立三条支撑杆的约束方程,推导出运动学反解的解析解,然后在参考Stewart机构正解算法的基础上给出三自由度并联机构的运动学正解算法。针对该并联机构的支撑杆约束方程和结构特点,提出该机构特有的一种收敛快、精度高的运动学正解算法。利用运动学反解和正解算法,对三自由度并联机构的工作空间和附加平动等进行研究,全面揭示该并联机构的运动学特性。
在动力学研究中,先将三自由度并联机构简化成单刚体,采用牛顿-欧拉方程对系统进行动力学建模,利用所建的动力学模型对该机构在典型运动下支撑杆和作动器的受力进行分析。将并联机构的作动器和支撑杆等效成弹簧,推导系统的广义刚度矩阵,根据凯恩方程原理对支撑杆和作动器的惯性进行建模,进而推导出三自由度并联机构的的广义质量矩阵和固有频率方程,并对该机构的固有频率特性进行研究,为分析该三自由度并联机构的动态特性特供了依据。
在精度研究中,将三自由度并联机构的制造、装配以及作动器的控制误差归纳成42个误差源,根据运动学反解方程建立系统的误差模型,并对系统的误差分布规律进行仿真分析。为提高三自由度并联机构的静态精度,提出了一种精度综合的方法。该方法先用灵敏度来描述各项误差对系统精度的影响,根据灵敏度的大小将误差源的允许公差分为两个等级,通过逐步提高各误差源的精度等级的方法使系统的精度满足要求。以上研究提高系统的精度提供了重要的参考依据。
在控制策略研究中先给出作动器的数学模型,并据此对三自由度并联机构铰点空间PID控制、动压反馈及前馈等控制策略进行研究。为提高三自由度并联机构的姿态复现精度,提出了一种基于运动学正解的迭代补偿控制方法。该方法先辨识出三自由度并联机构的传递函数矩阵并求出传递函数矩阵的逆,试验中利用运动学正解计算出系统的姿态信号,然后根据系统的姿态偏差信号和传递函数矩阵的逆来修正系统的姿态驱动指令,通过多次迭代使系统的姿态复现精度满足要求。试验表明采用迭代补偿控制,三自由度并联机构的姿态复现精度提高到了5%,从而验证了该控制策略的有效性。
With the development of national defense and military industry,there is urgent need to develop real vehicle road simulator equipment on weapons fire controlling system in order to break the monopoly of foreign technology and enhance the testing standards. This thesis study the kinematics analysis, dynamics model, accuracy analysis and control strategy of a 3-dof parallel mechanism, and the background is the dynamical testing and simulation equipment on military vehicles which designed by HIT institute of electro-hydraulic servo simulation & testing system.
3-dof parallel mechanism is a variant of the typical Stewart platform, which used three drivers and threes struts instead the six drives of the Stewart platform. In this paper, the length constraint equations of three struts is established and the analytical solution of the inverse kinematics is derived, and the forward kinematics solution of the rotational parallel mechanism is presented based the typical method of the Stewart platform. Also, a new forward kinematics solution is derived according to the structural characteristics of the machine. The workspace and translation movement are studied in order to obtain the property of the parallel robot.
In the dynamic study, the 3-dof parallel mechanism is simplified into a single rigid body then the dynamical model is build by using Newton-Euler equations. The driving force of the drives and the struts in typical movement is analyzed with the help of the dynamical model. The general stiffness matrix is derived by acting the actuators and struts as spring. The multi-body dynamical model is presented through Kane equation and the influence of the legs’mass and inertia are considered. General mass matrix and natural frequency equation is proposed based on the multi-body dynamical model, then the frequency property of the robot is analyzed at the end.
In the accuracy study, the manufacturing error, assembly error and actuators’control error of the 3-dof parallel mechanism is grouped into 42 error source. The error model of the parallel mechanism is brought forward accordance to the inverse kinematics of the robot, and the error distribution of the system is studied through simulation. Accuracy synthesis is used to enhance the precision of the system, in this method, error sensitivity is proposed to describe the error sources’impact on the system accuracy. All the allowed tolerance of the error sources are divided into two categories based on the value of the sensitivity, then decrease the allowed tolerance step by step until the accuracy of the robot meet the requirement. This research provides every important references for the tolerance design of the 3-dof robot.
The PID controller in joint space and computed torque controller in workspace are introduced. Then the mathematical model and frequency domain characteristics of the hydraulic actuators is derived, and the control strategy in joint space is investigated. A iterative compensation control strategy based on forward kinematics is proposed in order to enhance the performance of the robot. In this method, the transfer function matrix of the robot is obtained through identification, then the command signals of the robot is adjusted based on the posture error and the inverse transfer function matrix of the 3-dof parallel mechanism. The tracking accuracy of the robot can be enhanced to meet the requirement through many iterations. Experiment shows the precision of replication is 5% , which verified the validity of the iterative control strategy.
三自由度并联机构是典型Stewart并联机构的变体,它用三条作动器和三条支撑杆代替Stewart并联机构中的六条作动器来实现三个自由度的旋转运动。先建立三条支撑杆的约束方程,推导出运动学反解的解析解,然后在参考Stewart机构正解算法的基础上给出三自由度并联机构的运动学正解算法。针对该并联机构的支撑杆约束方程和结构特点,提出该机构特有的一种收敛快、精度高的运动学正解算法。利用运动学反解和正解算法,对三自由度并联机构的工作空间和附加平动等进行研究,全面揭示该并联机构的运动学特性。
在动力学研究中,先将三自由度并联机构简化成单刚体,采用牛顿-欧拉方程对系统进行动力学建模,利用所建的动力学模型对该机构在典型运动下支撑杆和作动器的受力进行分析。将并联机构的作动器和支撑杆等效成弹簧,推导系统的广义刚度矩阵,根据凯恩方程原理对支撑杆和作动器的惯性进行建模,进而推导出三自由度并联机构的的广义质量矩阵和固有频率方程,并对该机构的固有频率特性进行研究,为分析该三自由度并联机构的动态特性特供了依据。
在精度研究中,将三自由度并联机构的制造、装配以及作动器的控制误差归纳成42个误差源,根据运动学反解方程建立系统的误差模型,并对系统的误差分布规律进行仿真分析。为提高三自由度并联机构的静态精度,提出了一种精度综合的方法。该方法先用灵敏度来描述各项误差对系统精度的影响,根据灵敏度的大小将误差源的允许公差分为两个等级,通过逐步提高各误差源的精度等级的方法使系统的精度满足要求。以上研究提高系统的精度提供了重要的参考依据。
在控制策略研究中先给出作动器的数学模型,并据此对三自由度并联机构铰点空间PID控制、动压反馈及前馈等控制策略进行研究。为提高三自由度并联机构的姿态复现精度,提出了一种基于运动学正解的迭代补偿控制方法。该方法先辨识出三自由度并联机构的传递函数矩阵并求出传递函数矩阵的逆,试验中利用运动学正解计算出系统的姿态信号,然后根据系统的姿态偏差信号和传递函数矩阵的逆来修正系统的姿态驱动指令,通过多次迭代使系统的姿态复现精度满足要求。试验表明采用迭代补偿控制,三自由度并联机构的姿态复现精度提高到了5%,从而验证了该控制策略的有效性。
With the development of national defense and military industry,there is urgent need to develop real vehicle road simulator equipment on weapons fire controlling system in order to break the monopoly of foreign technology and enhance the testing standards. This thesis study the kinematics analysis, dynamics model, accuracy analysis and control strategy of a 3-dof parallel mechanism, and the background is the dynamical testing and simulation equipment on military vehicles which designed by HIT institute of electro-hydraulic servo simulation & testing system.
3-dof parallel mechanism is a variant of the typical Stewart platform, which used three drivers and threes struts instead the six drives of the Stewart platform. In this paper, the length constraint equations of three struts is established and the analytical solution of the inverse kinematics is derived, and the forward kinematics solution of the rotational parallel mechanism is presented based the typical method of the Stewart platform. Also, a new forward kinematics solution is derived according to the structural characteristics of the machine. The workspace and translation movement are studied in order to obtain the property of the parallel robot.
In the dynamic study, the 3-dof parallel mechanism is simplified into a single rigid body then the dynamical model is build by using Newton-Euler equations. The driving force of the drives and the struts in typical movement is analyzed with the help of the dynamical model. The general stiffness matrix is derived by acting the actuators and struts as spring. The multi-body dynamical model is presented through Kane equation and the influence of the legs’mass and inertia are considered. General mass matrix and natural frequency equation is proposed based on the multi-body dynamical model, then the frequency property of the robot is analyzed at the end.
In the accuracy study, the manufacturing error, assembly error and actuators’control error of the 3-dof parallel mechanism is grouped into 42 error source. The error model of the parallel mechanism is brought forward accordance to the inverse kinematics of the robot, and the error distribution of the system is studied through simulation. Accuracy synthesis is used to enhance the precision of the system, in this method, error sensitivity is proposed to describe the error sources’impact on the system accuracy. All the allowed tolerance of the error sources are divided into two categories based on the value of the sensitivity, then decrease the allowed tolerance step by step until the accuracy of the robot meet the requirement. This research provides every important references for the tolerance design of the 3-dof robot.
The PID controller in joint space and computed torque controller in workspace are introduced. Then the mathematical model and frequency domain characteristics of the hydraulic actuators is derived, and the control strategy in joint space is investigated. A iterative compensation control strategy based on forward kinematics is proposed in order to enhance the performance of the robot. In this method, the transfer function matrix of the robot is obtained through identification, then the command signals of the robot is adjusted based on the posture error and the inverse transfer function matrix of the 3-dof parallel mechanism. The tracking accuracy of the robot can be enhanced to meet the requirement through many iterations. Experiment shows the precision of replication is 5% , which verified the validity of the iterative control strategy.
引文
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101 Kim D. H., Kang J. Y and Lee K. I. Robust Tracking Control Design for a 6 DOF Parallel Manipulator. Journal of Robotic Systems. 2000, 17(10): 527~547
102 Lee S. H., Song J. B., Choi W. C. and Hong D. Position Control of a Stewart Platform Using Inverse Dynamics Control with Approximate Dynamics. Mechatronics. 2003, 13(6): 605~619
103 C. Nguyen, S. Antrazi, Z. Zhou, and C. Campbell, Adaptive control of a Stewart platform-based manipulator, J Robotic Syst 1993,10:657~687
104 R. Colbaugh, K. Glass, and H. Seraji, Direct adaptive control of robotics systems, American Control Conf. 1993: 1138~1143
105 C.M. Gosselin, S.Lemieux, J.P. Merlet. A new architecture of planar three degrees of freedom parallel manipulator [J]. In: proceedings of the IEEE International Conference on Robotics and Automation, Minneapolies, MN, April 22-28, 1996, p3738~3743.
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107王国强.虚拟样机技术及其在ADAM S上的实践.西安:西北工业大学出版社. 2002
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110 C.K.Chua, S.H.Tehl, R.K.L.Gay. Rapid Prototyping Versus Virtual Prototyping in Product Design and Manufacturing. Advanced Manufacturing Technology, 1999(15):597~603
111 S.C. Fok, W. Xiang, F.F.Yap. Feature-Based Component Models for Virtual Prototyping of Hydraulic Systems. Advanced Manufacturing Technology, 2001(18):665~672
112 Q.M.Li, F.C.Lee, T.G. Wilson. Design verification and testing of power supply system by using virtual prototype, Power Electronics ,IEEE Transactions. 2003,18(3):733~739
113 Y.J.Lin, R.Farahati1. CAD-Based Virtual Assembly Prototyping-A Case Study. Advanced Manufacturing Technology, 2003(21):263~274
114 Q.Li. Developing modeling and simulation methodology for virtual prototype power supply system. Virginia Polytechnic Institute and State University.1999
115李薇,虚拟样机技术的研究和实现: [硕士学位论文].南京:南京理工大学, 2002
116李伯虎,柴旭东.复杂产品虚拟样机工程.计算机集成制造系统. 2002,8(9 ): 678~683
117冯晨华,徐捷. CSCW系统中共享对象的协作支持模型计算机研究与发展. 1999,36(3):304~308
118 S.R.S, C.E.J. Role-Based Access Control Models. IEEE Computer.1996, 29(2):38~47
119邸彦强,李伯虎等.多学科虚拟样机协同建模与仿真平台及关键技术研究.计算机集成制造系统-CIMS,2005,(11)7:901~908
120孔建寿,张友良.协同开发环境中项目管理与工作流管理的集成.中国机械工程,2003,14(13):1122~1125
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