飞行模拟器液压Stewart平台奇异位形分析及其解决方法研究
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摘要
液压Stewart平台属于典型的并联机构,由于其能够实现空间的六自由度运动并且具有刚度大、承载能力强、结构比较简单、精度高、控制比较容易等优点,被成功应用于大型飞机飞行模拟器的运动系统,成为其重要组成部分。但是其主要缺点是,在特殊情况下存在奇异位形,并且与串联机构相比工作空间非常有限。本论文在分析Stewart平台奇异位形的基础上,针对Stewart平台存在奇异位形的问题,对于不同的任务工作空间要求,从Stewart平台的无奇异结构设计、有奇异结构的液压Stewart平台的安全保护以及利用冗余机构消除奇异位形等方面进行了详细的、系统的研究,从而最终达到在满足工作空间要求的同时解决Stewart平台的奇异位形的目的。
液压Stewart平台是一种多变量和本质非线性的复杂系统,其运动学和动力学的研究是液压Stewart平台其他相关特性以及控制策略研究的基础。本文分析了液压Stewart平台的运动学和动力学,利用Kane方法建立了Stewart平台的多刚体动力学模型;推导了非对称伺服阀控制非对称液压缸的数学模型,在此基础上建立了完整的液压Stewart平台的动力学模型;利用所建立的完整动力学模型对液压Stewart平台自由度间的耦合特性进行了分析,并通过实验验证了分析结果的正确性。
空间的六路分支结构使得Stewart平台奇异位形的判断非常复杂。为了分析在一个Stewart平台的任务工作空间和可达工作空间中是否存在奇异位形,本文在前人关于并联机构奇异位形研究的基础上,对Stewart平台处于Hunt奇异位形处的相关特性进行了分析和实验研究;之后利用机构的雅可比矩阵,通过编程求解,得到了Stewart平台的含有任意三个位姿变量的奇异轨迹方程的解析表达式,将Stewart平台的奇异轨迹表示在三维空间中;利用所提出的奇异轨迹分析方法分析了一个电动Stewart平台在任务工作空间和可达工作空间中的奇异位形,并通过实验对所得出的结论进行了验证。
对于一定的任务工作空间需求来说,存在无奇异的Stewart平台来满足对工作空间的要求,因此需要研究一种Stewart平台的无奇异结构设计方法。本文构建了一种求解Stewart平台位置正解的同伦算法,在此基础上,通过对Stewart平台的结构参数进行分析,结合Stewart平台的极限位姿分析方法,综合考虑了Stewart平台的结构参数、支腿所受静态力、机构的最大条件数以及机构的构型分岔行为,设计了具有无奇异结构的Stewart平台。通过仿真和实验对所设计的Stewart平台进行分析和验证,表明所设计的Stewart平台在由支腿行程范围所确定的可达工作空间中不存在奇异位形。
针对因任务工作空间需求而在可达工作空间中存在奇异位形的液压Stewart平台,本文提出了奇异区和无奇异区的概念;利用支腿长度,结合极限位姿分析方法,建立了一种判断Stewart平台是否进入奇异区域的判据;设计了液压Stewart平台的液压保护装置,利用所提出的判据以及硬件设备,实现了对液压Stewart平台在发生因系统失控而进入奇异区的情况的安全保护。
针对冗余并联机构具有消除奇异位形的功能,在原来非冗余液压Stewart平台的基础上增加三条冗余支腿,设计了“6+3”结构形式的冗余液压Stewart平台,对其运动学、动力学进行分析,建立了冗余液压Stewart平台的多刚体动力学模型,并对冗余驱动力进行了优化;之后将非冗余液压Stewart平台和冗余液压Stewart平台的相关特性进行了对比,发现冗余Stewart平台能够进一步提高系统的性能;对冗余液压Stewart平台消除奇异位形的原理、作用进行了分析,并通过所建立的虚拟样机进行仿真,验证了其在解决Hunt奇异位形时的有效性;最终利用所设计的冗余液压Stewart平台消除了原来非冗余液压Stewart平台在可达工作空间中存在的奇异位形。
Hydraulic Stewart platform is the typical parallel manipulator, which has been successfully applied to the motion system of large aircraft flight simulator and has become its important components due to the capacity of realizing 6-DOF movement and the merits of high rigidity, large load capacity, relatively simple structure, high precision and relatively easy to control, etc. However, the major drawbacks of hydraulic Stewart platform are that there are singular configurations in special condition and the workspace is very limited in comparison with serial manipulator. Based on the singular configuration analysis of Stewart platform and aiming at the problem of existing singular configuration, for the different requirements of task workspace, the dissertation take specific and systematic study on the respects of nonsingular structure design, the safety protection of hydraulic Stewart platform with singular structure and eliminating singular configuration using redundant mechanism. Finally, it achieved the purpose of solving the problem of singular configuration and satisfying the requirement of workspace at the same time.
Hydraulic Stewart Platform is a multi-variable and non-linear complex system in nature. The kinematics and dynamics study of hydraulic Stewart platform is the research basis of other related characteristics and control strategies. The dissertation analyzed the kinematics and dynamics of hydraulic Stewart platform. It established multi-body dynamics model of Stewart platform using Kane method, derived mathematical model of asymmetric servo valve control of asymmetric hydraulic cylinder. On the base of that, it established entire dynamics model of the whole hydraulic Stewart platform. After that, it analyzed the coupling characteristic between DOF using the established entire dynamics model and verified the correctness of analytic results through experiments.
Due to the spatial structure of six branches, it makes the singular configuration judgment of Stewart platform very complex. To analyze if there exist singular configuration in the task workspace and reachable workspace of a Stewart platform, based on the singularity study of parallel manipulator by predecessors, the dissertation analyzed the relevant characteristics of Stewart platform at the Hunt singular configuration and the relevant experiments was taken. Then, using Jacobian matrix of the mechanism and solved the matrix through programming, it achieved the analytical expression of singular locus equation of the Stewart platform which contains arbitrary three posture variables and represented the singular locus of Stewart platform in three-dimensional space. After that, it analyzed the singular configuration of an electric Stewart platform in task workspace and reachable workspace with the proposed singular locus analysis method and verified the conclusion through experiments.
For a certain demand of the task workspace, there exists nonsingular Stewart platform to meet the requirements, so it needs to study a method to design Stewart platform with nonsingular structure. The dissertation established a homotopy algorithm to solve forward position kinematics of Stewart platform. On this base, After analyzing the structural parameters, combined with the extreme pose analysis method of Stewart platform, considering the structural parameters of the Stewart platform, the static force applied on legs, the maximum condition number and configuration bifurcation behavior of the mechanism, it designed Stewart platform with nonsingular structure. Then, it analyzed and verified the designed Stewart platform through simulations and experiments and found out that there does not exist singular configuration in the reachable workspace of the designed Stewart platform which is determined by the legs.
For the hydraulic Stewart platform which has singular configuration in the reachable workspace due to the workspace requirement of task, the dissertation proposed concept of singular zone and nonsingular zone. Using the legs length and combined with the extreme poses analysis method, it established a criterion to judge if the Stewart platform entered into the singular zone. Then, it designed hydraulic protection device of hydraulic Stewart platform. Using the proposed criterion and hardware devices, it realized the protection of hydraulic Stewart platform when entered into the singular zone because of the system being out of control.
As for the redundant parallel manipulator having function of eliminating singular configuration, the dissertation increased three redundant legs on the base of the original non-redundant hydraulic Stewart platform and designed redundant hydraulic Stewart platform with "6+3" style structure. Then, it analyzed kinematics, dynamics, and established multi-body dynamic model of redundant hydraulic Stewart platform and optimized redundant driving force. After that, it compared the relevant characteristics of non-redundant hydraulic Stewart platform with redundant hydraulic Stewart platform and found out that redundant hydraulic Stewart platform can further improve the performances of the system. It analyzed the principle and function of eliminating singular configuration of redundant hydraulic Stewart platform, and simulating with the established virtual prototype to verify the effect in solving Hunt singular configuration. Finally, with the designed redundant hydraulic Stewart platform, it eliminated the existed singular configuration in the reachable workspace of the original non-redundant one.
液压Stewart平台是一种多变量和本质非线性的复杂系统,其运动学和动力学的研究是液压Stewart平台其他相关特性以及控制策略研究的基础。本文分析了液压Stewart平台的运动学和动力学,利用Kane方法建立了Stewart平台的多刚体动力学模型;推导了非对称伺服阀控制非对称液压缸的数学模型,在此基础上建立了完整的液压Stewart平台的动力学模型;利用所建立的完整动力学模型对液压Stewart平台自由度间的耦合特性进行了分析,并通过实验验证了分析结果的正确性。
空间的六路分支结构使得Stewart平台奇异位形的判断非常复杂。为了分析在一个Stewart平台的任务工作空间和可达工作空间中是否存在奇异位形,本文在前人关于并联机构奇异位形研究的基础上,对Stewart平台处于Hunt奇异位形处的相关特性进行了分析和实验研究;之后利用机构的雅可比矩阵,通过编程求解,得到了Stewart平台的含有任意三个位姿变量的奇异轨迹方程的解析表达式,将Stewart平台的奇异轨迹表示在三维空间中;利用所提出的奇异轨迹分析方法分析了一个电动Stewart平台在任务工作空间和可达工作空间中的奇异位形,并通过实验对所得出的结论进行了验证。
对于一定的任务工作空间需求来说,存在无奇异的Stewart平台来满足对工作空间的要求,因此需要研究一种Stewart平台的无奇异结构设计方法。本文构建了一种求解Stewart平台位置正解的同伦算法,在此基础上,通过对Stewart平台的结构参数进行分析,结合Stewart平台的极限位姿分析方法,综合考虑了Stewart平台的结构参数、支腿所受静态力、机构的最大条件数以及机构的构型分岔行为,设计了具有无奇异结构的Stewart平台。通过仿真和实验对所设计的Stewart平台进行分析和验证,表明所设计的Stewart平台在由支腿行程范围所确定的可达工作空间中不存在奇异位形。
针对因任务工作空间需求而在可达工作空间中存在奇异位形的液压Stewart平台,本文提出了奇异区和无奇异区的概念;利用支腿长度,结合极限位姿分析方法,建立了一种判断Stewart平台是否进入奇异区域的判据;设计了液压Stewart平台的液压保护装置,利用所提出的判据以及硬件设备,实现了对液压Stewart平台在发生因系统失控而进入奇异区的情况的安全保护。
针对冗余并联机构具有消除奇异位形的功能,在原来非冗余液压Stewart平台的基础上增加三条冗余支腿,设计了“6+3”结构形式的冗余液压Stewart平台,对其运动学、动力学进行分析,建立了冗余液压Stewart平台的多刚体动力学模型,并对冗余驱动力进行了优化;之后将非冗余液压Stewart平台和冗余液压Stewart平台的相关特性进行了对比,发现冗余Stewart平台能够进一步提高系统的性能;对冗余液压Stewart平台消除奇异位形的原理、作用进行了分析,并通过所建立的虚拟样机进行仿真,验证了其在解决Hunt奇异位形时的有效性;最终利用所设计的冗余液压Stewart平台消除了原来非冗余液压Stewart平台在可达工作空间中存在的奇异位形。
Hydraulic Stewart platform is the typical parallel manipulator, which has been successfully applied to the motion system of large aircraft flight simulator and has become its important components due to the capacity of realizing 6-DOF movement and the merits of high rigidity, large load capacity, relatively simple structure, high precision and relatively easy to control, etc. However, the major drawbacks of hydraulic Stewart platform are that there are singular configurations in special condition and the workspace is very limited in comparison with serial manipulator. Based on the singular configuration analysis of Stewart platform and aiming at the problem of existing singular configuration, for the different requirements of task workspace, the dissertation take specific and systematic study on the respects of nonsingular structure design, the safety protection of hydraulic Stewart platform with singular structure and eliminating singular configuration using redundant mechanism. Finally, it achieved the purpose of solving the problem of singular configuration and satisfying the requirement of workspace at the same time.
Hydraulic Stewart Platform is a multi-variable and non-linear complex system in nature. The kinematics and dynamics study of hydraulic Stewart platform is the research basis of other related characteristics and control strategies. The dissertation analyzed the kinematics and dynamics of hydraulic Stewart platform. It established multi-body dynamics model of Stewart platform using Kane method, derived mathematical model of asymmetric servo valve control of asymmetric hydraulic cylinder. On the base of that, it established entire dynamics model of the whole hydraulic Stewart platform. After that, it analyzed the coupling characteristic between DOF using the established entire dynamics model and verified the correctness of analytic results through experiments.
Due to the spatial structure of six branches, it makes the singular configuration judgment of Stewart platform very complex. To analyze if there exist singular configuration in the task workspace and reachable workspace of a Stewart platform, based on the singularity study of parallel manipulator by predecessors, the dissertation analyzed the relevant characteristics of Stewart platform at the Hunt singular configuration and the relevant experiments was taken. Then, using Jacobian matrix of the mechanism and solved the matrix through programming, it achieved the analytical expression of singular locus equation of the Stewart platform which contains arbitrary three posture variables and represented the singular locus of Stewart platform in three-dimensional space. After that, it analyzed the singular configuration of an electric Stewart platform in task workspace and reachable workspace with the proposed singular locus analysis method and verified the conclusion through experiments.
For a certain demand of the task workspace, there exists nonsingular Stewart platform to meet the requirements, so it needs to study a method to design Stewart platform with nonsingular structure. The dissertation established a homotopy algorithm to solve forward position kinematics of Stewart platform. On this base, After analyzing the structural parameters, combined with the extreme pose analysis method of Stewart platform, considering the structural parameters of the Stewart platform, the static force applied on legs, the maximum condition number and configuration bifurcation behavior of the mechanism, it designed Stewart platform with nonsingular structure. Then, it analyzed and verified the designed Stewart platform through simulations and experiments and found out that there does not exist singular configuration in the reachable workspace of the designed Stewart platform which is determined by the legs.
For the hydraulic Stewart platform which has singular configuration in the reachable workspace due to the workspace requirement of task, the dissertation proposed concept of singular zone and nonsingular zone. Using the legs length and combined with the extreme poses analysis method, it established a criterion to judge if the Stewart platform entered into the singular zone. Then, it designed hydraulic protection device of hydraulic Stewart platform. Using the proposed criterion and hardware devices, it realized the protection of hydraulic Stewart platform when entered into the singular zone because of the system being out of control.
As for the redundant parallel manipulator having function of eliminating singular configuration, the dissertation increased three redundant legs on the base of the original non-redundant hydraulic Stewart platform and designed redundant hydraulic Stewart platform with "6+3" style structure. Then, it analyzed kinematics, dynamics, and established multi-body dynamic model of redundant hydraulic Stewart platform and optimized redundant driving force. After that, it compared the relevant characteristics of non-redundant hydraulic Stewart platform with redundant hydraulic Stewart platform and found out that redundant hydraulic Stewart platform can further improve the performances of the system. It analyzed the principle and function of eliminating singular configuration of redundant hydraulic Stewart platform, and simulating with the established virtual prototype to verify the effect in solving Hunt singular configuration. Finally, with the designed redundant hydraulic Stewart platform, it eliminated the existed singular configuration in the reachable workspace of the original non-redundant one.
引文
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