两种并联机器人的机构性能分析与运动控制研究
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摘要
平面2自由度冗余驱动并联机器人和绳牵引并联机器人是并联机器人家族中重要的组成部分,具有广泛的应用领域和重要的开发价值。本文针对这两种并联机器人进行了工作空间分析、奇异性分析、刚度解析表达、冗余驱动力优化分配、动力学建模及运动控制的研究,旨在为这两种并联机器人的性能提升和实际工程应用提供理论依据和技术支持。完成的主要工作及取得的研究成果归纳如下：
1.建立了平面2自由度冗余驱动和非冗余驱动并联机器人结构参数与工作空间形状的函数关系,绘制了两者基于无量纲参数的工作空间图谱,比较了两类工作空间的特点与优缺点,为该并联机器人的机构设计提供了系统的参考依据。
研究了平面2自由度冗余驱动与非冗余驱动并联机器人的奇异性,推导了奇异轨迹的解析表达式,绘制了基于无量纲参数的奇异轨迹图谱,揭示了冗余驱动对消除机构奇异性的有效作用,为机构避免奇异性的路径规划提供了有益的参考。
2.对平面2自由度冗余驱动并联机器人的综合性能进行了优化设计。基于运动学模型,给出了该机器人的雅可比矩阵和最优拓扑构形,分析了结构参数对工作空间和奇异性的影响规律。提出了衡量机器人运动精度、力传递能力、结构刚度和工作空间利用率的综合评价指标,建立了以综合评价指标为目标函数,以任务空间和无奇异位形为约束条件的数学优化模型,采用自适应遗传算法完成了优化求解。
3.研究欠约束、完全约束及冗余约束绳牵引并联机器人的工作空间,给出了三类约束绳牵引并联机器人工作空间存在的普遍条件及证明,进而提出一种适用于三类约束绳牵引并联机器人工作空间的一致求解策略,并应用一致求解策略对三个典型机器人进行了工作空间的求解和对比分析。
4.建立了包含关节弹性变形以及绳拉力等因素的绳牵引并联机器人完整的刚度模型,推导了刚度矩阵的数学表达式。通过对理论模型进行数值仿真,探讨了绳牵引并联机器人的构型参数及驱动力对系统刚度的影响机理,为机器人的变刚度控制奠定理论基础。
5.针对飞行器风洞柔性支撑系统和大型射电望远镜舱索粗调子系统-两种不同应用背景的绳牵引并联机器人,进行动力学控制的研究。基于Newton-Euler法分别建立了两个绳牵引并联机器人的系统动力学模型。
以应用于低速风洞试验的6自由度绳牵引冗余并联机器人为研究对象,设计了基于刚度增强准则的关节空间PD修正前馈控制器,实现了以提高飞行器升力方向、顺风向和俯仰转动方向刚度为目标的绳系张力优化分配,解决飞行器模型在风荷作用下动态定位误差大的问题。
以应用于大型射电望远镜馈源位姿动态调整的绳牵引冗余并联机器人为研究对象,给出了以柔索强度和电机负荷为约束条件,以索力范数为目标的驱动力优化求解方法；利用基于绳长关节空间的PD修正前馈控制器引入非线性状态反馈补偿,通过干扰观测器观测外部扰动对电机跟踪性能的影响,有效进行了振动抑制。
The planar two degree-of-freedom parallel manipulators with redundant actuations and wire-driven parallel manipulators, which have abroad applications and valuable exploitations, play important roles in the family of parallel manipulators. Workspace, singularity, stiffness, optimal force distribution, dynamic modeling and motion control of the two types of parallel manipulators are studied in this paper, and the research results can found theoretical and technical basis for performance improvement and engineering application of the two manipulators. The main contents can be described as follows.
1. The functional relationship between the structural parameters of the planar two degree-of-freedom parallel manipulators with and without redundant actuations and the configurations of their workspaces is established. And the workspace spectrograms for the two parallel manipulators are drawn respectively. The strength and weakness of the two types of workspaces are compared, which provide a systematic basis of reference for the design of the two parallel manipulators.
The singularities of the planar two degree-of-freedom parallel manipulators with and without redundant actuations are discussed respectively. Further the analytic expressions of singular loci are derived and the spectrograms of singular loci are drawn in terms of some dimensionless parameters. By contrastive analysis of the spectrograms, the availability of actuation redundancy on eliminating singularities of the parallel manipulators is shown. The research provides a valuable reference for the singularity-free trajectory planning.
2. The optimization of comprehensive performance of a planar two degree-of-freedom parallel manipulator with redundant actuation is investigated. Based on the kinematics model of the manipulator, its Jacobian matrix and optimal topologies are given. The influences of structural parameters of the manipulator on its workspace and singularity are discussed. A comprehensive performance criterion is proposed to evaluate kinematics accuracy, force transmissibility, structural stiffness and workspace utilization rate. An optimization model with the proposed criterion as the objective function and taskspace and nonsingular configuration as the constrains is constructed, and an adaptive genetic algorithm is utilized to obtain the optimal solution.
3. The workspaces of incompletely restrained, completely restrained and redundant restrained wire-driven parallel manipulators are investigated. Existence conditions of workspaces of the three types of wire-driven parallel manipulators are given and proved by a theorem and three corollaries. According to the theorem and corollaries, a uniform solution strategy is proposed to determine the workspaces of the three types of wire-driven parallel manipulators. The workspaces of three typical wire-driven parallel manipulators are obtained and compared using the proposed strategy.
4. A stiffness model of wire-driven parallel manipulators is established, which depends on the elastic deformation of joints and wire tension. And a mathematical formulation of stiffness matix is followed. Numerical simulations demonstrate the effect of configuration parameters and wire tension on stiffness of wire-driven parallel manipulators. The results lay theoretical foundations for stiffness control to wire-driven parallel manipulators.
5. The dynamic control of two wire-driven parallel manipulators which are employed as a flexible support system for the aircraft wind tunnel and a cable-cabin coarse tuning system of the large radio telescope, is presented. Firstly, the dynamic models of the two wire-driven parallel manipulators are developed respectively using Newton-Euler's method.
For a six degree-of-freedom wire-driven parallel manipulator with redundant actuations for low speed wind tunnels, a modified Proportional-Differential control strategy with feedforward compensation in the wire length coordinates is developed based on stiffness enhancement. And an optimal tension distribution is implemented for the enhancement of stiffness at lift, along-wind and pitching directions, in order that the problem of a high dynamic positioning errors of the aircraft model can be resolved.
A wire-driven parallel manipulator which has been found application in the large radio telescope is utilized to alter the pose of the cabin. Considering the constraints on the cable strength and the loads of the motors, the optimum tensions are obtained according to minimizing the norm of cable tensions. The nonlinear state feedback compensation is introduced to a modified PD forward controller in the cable length coordinates. And a disturbance observer is used to estimate the disturbance exerting on the motors to suppress the disturbance effect.
1.建立了平面2自由度冗余驱动和非冗余驱动并联机器人结构参数与工作空间形状的函数关系,绘制了两者基于无量纲参数的工作空间图谱,比较了两类工作空间的特点与优缺点,为该并联机器人的机构设计提供了系统的参考依据。
研究了平面2自由度冗余驱动与非冗余驱动并联机器人的奇异性,推导了奇异轨迹的解析表达式,绘制了基于无量纲参数的奇异轨迹图谱,揭示了冗余驱动对消除机构奇异性的有效作用,为机构避免奇异性的路径规划提供了有益的参考。
2.对平面2自由度冗余驱动并联机器人的综合性能进行了优化设计。基于运动学模型,给出了该机器人的雅可比矩阵和最优拓扑构形,分析了结构参数对工作空间和奇异性的影响规律。提出了衡量机器人运动精度、力传递能力、结构刚度和工作空间利用率的综合评价指标,建立了以综合评价指标为目标函数,以任务空间和无奇异位形为约束条件的数学优化模型,采用自适应遗传算法完成了优化求解。
3.研究欠约束、完全约束及冗余约束绳牵引并联机器人的工作空间,给出了三类约束绳牵引并联机器人工作空间存在的普遍条件及证明,进而提出一种适用于三类约束绳牵引并联机器人工作空间的一致求解策略,并应用一致求解策略对三个典型机器人进行了工作空间的求解和对比分析。
4.建立了包含关节弹性变形以及绳拉力等因素的绳牵引并联机器人完整的刚度模型,推导了刚度矩阵的数学表达式。通过对理论模型进行数值仿真,探讨了绳牵引并联机器人的构型参数及驱动力对系统刚度的影响机理,为机器人的变刚度控制奠定理论基础。
5.针对飞行器风洞柔性支撑系统和大型射电望远镜舱索粗调子系统-两种不同应用背景的绳牵引并联机器人,进行动力学控制的研究。基于Newton-Euler法分别建立了两个绳牵引并联机器人的系统动力学模型。
以应用于低速风洞试验的6自由度绳牵引冗余并联机器人为研究对象,设计了基于刚度增强准则的关节空间PD修正前馈控制器,实现了以提高飞行器升力方向、顺风向和俯仰转动方向刚度为目标的绳系张力优化分配,解决飞行器模型在风荷作用下动态定位误差大的问题。
以应用于大型射电望远镜馈源位姿动态调整的绳牵引冗余并联机器人为研究对象,给出了以柔索强度和电机负荷为约束条件,以索力范数为目标的驱动力优化求解方法；利用基于绳长关节空间的PD修正前馈控制器引入非线性状态反馈补偿,通过干扰观测器观测外部扰动对电机跟踪性能的影响,有效进行了振动抑制。
The planar two degree-of-freedom parallel manipulators with redundant actuations and wire-driven parallel manipulators, which have abroad applications and valuable exploitations, play important roles in the family of parallel manipulators. Workspace, singularity, stiffness, optimal force distribution, dynamic modeling and motion control of the two types of parallel manipulators are studied in this paper, and the research results can found theoretical and technical basis for performance improvement and engineering application of the two manipulators. The main contents can be described as follows.
1. The functional relationship between the structural parameters of the planar two degree-of-freedom parallel manipulators with and without redundant actuations and the configurations of their workspaces is established. And the workspace spectrograms for the two parallel manipulators are drawn respectively. The strength and weakness of the two types of workspaces are compared, which provide a systematic basis of reference for the design of the two parallel manipulators.
The singularities of the planar two degree-of-freedom parallel manipulators with and without redundant actuations are discussed respectively. Further the analytic expressions of singular loci are derived and the spectrograms of singular loci are drawn in terms of some dimensionless parameters. By contrastive analysis of the spectrograms, the availability of actuation redundancy on eliminating singularities of the parallel manipulators is shown. The research provides a valuable reference for the singularity-free trajectory planning.
2. The optimization of comprehensive performance of a planar two degree-of-freedom parallel manipulator with redundant actuation is investigated. Based on the kinematics model of the manipulator, its Jacobian matrix and optimal topologies are given. The influences of structural parameters of the manipulator on its workspace and singularity are discussed. A comprehensive performance criterion is proposed to evaluate kinematics accuracy, force transmissibility, structural stiffness and workspace utilization rate. An optimization model with the proposed criterion as the objective function and taskspace and nonsingular configuration as the constrains is constructed, and an adaptive genetic algorithm is utilized to obtain the optimal solution.
3. The workspaces of incompletely restrained, completely restrained and redundant restrained wire-driven parallel manipulators are investigated. Existence conditions of workspaces of the three types of wire-driven parallel manipulators are given and proved by a theorem and three corollaries. According to the theorem and corollaries, a uniform solution strategy is proposed to determine the workspaces of the three types of wire-driven parallel manipulators. The workspaces of three typical wire-driven parallel manipulators are obtained and compared using the proposed strategy.
4. A stiffness model of wire-driven parallel manipulators is established, which depends on the elastic deformation of joints and wire tension. And a mathematical formulation of stiffness matix is followed. Numerical simulations demonstrate the effect of configuration parameters and wire tension on stiffness of wire-driven parallel manipulators. The results lay theoretical foundations for stiffness control to wire-driven parallel manipulators.
5. The dynamic control of two wire-driven parallel manipulators which are employed as a flexible support system for the aircraft wind tunnel and a cable-cabin coarse tuning system of the large radio telescope, is presented. Firstly, the dynamic models of the two wire-driven parallel manipulators are developed respectively using Newton-Euler's method.
For a six degree-of-freedom wire-driven parallel manipulator with redundant actuations for low speed wind tunnels, a modified Proportional-Differential control strategy with feedforward compensation in the wire length coordinates is developed based on stiffness enhancement. And an optimal tension distribution is implemented for the enhancement of stiffness at lift, along-wind and pitching directions, in order that the problem of a high dynamic positioning errors of the aircraft model can be resolved.
A wire-driven parallel manipulator which has been found application in the large radio telescope is utilized to alter the pose of the cabin. Considering the constraints on the cable strength and the loads of the motors, the optimum tensions are obtained according to minimizing the norm of cable tensions. The nonlinear state feedback compensation is introduced to a modified PD forward controller in the cable length coordinates. And a disturbance observer is used to estimate the disturbance exerting on the motors to suppress the disturbance effect.
引文
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