空间柔性机械臂的动力学特性与主动控制研究
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摘要
人类对太空探索的不断深入使得空间任务越来越多,而太空环境的特殊性和危险性使得很多任务不能完全依靠宇航员完成。空间柔性机械臂具有适应太空恶劣作业环境的能力,采用机械臂协助或代替宇航员完成一些太空作业在经济性和安全性两方面都具有现实意义,已成为当前空间技术领域的重要研究方向。本论文在教育部科学技术研究重大项目“空间柔性机器人动力学／控制耦合系统的研究”(课题编号：307005)的资助下,以空间柔性机械臂为研究对象,对其动力学特性和相关的主动控制策略展开了深入的分析和研究,本文的主要工作如下：
首先,提出空间机械臂的刚／柔／控耦合模态分析概念,借助反馈约束原理求得柔性臂在动约束状态下的复杂边界条件,并将关节控制器参数引入臂杆在离散平衡位置附近的振动动力方程,分别建立了频域空间和状态空间内模态求解的解析方法；针对机械臂的大范围运动影响臂杆自身的弹性振动模态问题,重点研究柔性臂动力学方程中切向惯性力项的影响,得到刚／柔耦合运动条件下臂杆的振动模态参数；特别地,研究了多活动部件柔体系统的有限元分析方法,并求解某型多自由度空间柔性机械臂的模态特性。
其次,从虚功的角度出发,采用哈密顿变分原理对含约束阻尼非保守力的柔性机械臂系统进行刚／柔／控耦合动力学建模；基于系统的状态空间模型设计一种适用于开、闭环条件的稳定数值PIM法,同时进行大量的数值实验以验证积分算法的有效性；对控制器反馈约束作用下系统的动力学响应进行数值求解并与KED法进行对比分析,得到不用于经典振动理论的结论。
再次,对机械臂柔性关节的动态不确定模型进行了建模分析,并提出一种同时补偿柔性、非连续摩擦、系统不确定性和外部干扰抑制的小波神经-鲁棒复合控制策略。全局采用Lyapunov函数的Backstepping方法设计具有柔性补偿和L2干扰抑制性能的控制器,同时,针对常规神经网络无法辨识非连续性函数的问题,提出在局部采用小波神经网络对摩擦和不确定项进行补偿。设计的控制策略不仅避免了单一反演鲁棒设计中复杂的求导运算,而且无须检测关节角加速度、辨识摩擦和估计不确定上界。
再其次,基于微分几何输入-输出线性化方法将双连杆柔性机械臂在新坐标系下分解为输入-输出子系统和内部子系统,导出零动力学规范化方程,并讨论系统观测输出位置的选择和零动力学稳定性之间的关系；建立柔性机械臂的全局快速收敛终端滑模控制策略,解决非最小相位系统的鲁棒控制问题,实现仅依靠关节处的驱动电机完成关节定位和臂杆残余振动的抑制。
最后,对空间柔性机械臂的相关动力学特性和控制策略进行实验研究,搭建空间柔性机械臂地面气浮式微重力模拟综合实验平台,设计并完成柔性关节的位置跟踪与测试、柔性机械臂的试验模态分析、柔性臂残余振动的主动控制等典型实验。
With the deepening of space exploration, the future space missions continue to be more and more, but it is hard to be completed entirely all by the astronauts as a results of the particularity and the risk of the space environment. The space flexible manipulator has the capability of adapting the vile space environment, so it is practically significant in both the economy and security aspects to assist or replace astronauts to complete some space operations utilizing the space manipulators, and it has become an important research direction in the space technology field. This paper is supported by the Key Project of Ministry of Education of China (307005) "space flexible robot dynamics/control coupling system research", and deeply focused on the dynamics and active control strategies for the space manipulator. The main work of this paper is as follows:
Firstly, the concept of rigid/flexible/control coupling mode analysis for the space flexible manipulator is proposed. The complex boundary conditions of flexible arm under the dynamic constraint state is obtained using feedback constraint theory, and the gain parameters of the joint controller are introduced into the vibration dynamic equation near the discrete equilibrium position. The analytic method of solving mode differential equations in frequency domain and state space are established separately. Taking into account the problem that the elastic modes are influenced by the large-scale movement, the mode parameters under the rigid/flexible coupling movement are solved in respect of the tangential inertia item. Especially, a multi degree of freedom mode characteristics of space manipulator are solved by the finite element method.
Secondly, the rigid/flexible/control coupling dynamics equations for the space manipulator involving the constrained damping non-conservative forces are established with Hamilton variational principle from the perspective of virtual work. Based on state space model, a stable numerical PIM that is suitable for both open and closed-loop conditions system is designed, and a large number of numerical experiments are implemented to verify the integration algorithma. The dynamic response under the feedback constraint is resolved by the PIM in oeder to compare with the traditional KED method, and some conclusions different from the classical vibration theory are obtained.
Thirdly, the uncertain second-order cascade dynamics equations including non-consecutive friction and external interference were modelled. In view of the complex dynamics character that flexibility coexists with friction, uncertain parameter perturbations and disturbances, a wavelet neural networks-robust hybrid control strategy was proposed. The global controller was designed using backstepping technique to compensate the flexibility and suppress disturbance based on L2 property. Considering it is difficult for the conventional neural networks to identify the non-consecutive items, the wavelet neural networks approach was locally utilized to estimate the nonlinear terms including friction and uncertainties. This strategy can avoid the complicated derivation, acceleration measurement, friction identification and uncertain upper bound forecast.
Fourthly, the two-link manipulator system was decomposed into input-output subsystem and internal subsystem by differential geometry input-output linearization method, and then the normalized equation of zero-dynamics is educed. The relationship between the choice of system observation output position and the zero-dynamic stability is discussed. A robust control approach using global terminal sliding mode was developed and the nonminimum phase control problem of two-link flexible space manipulator was solved. The target completing joint positioning and residual vibration suppression is achieved only rely on the joint driven motor.
Finally, some experiments about dynamics and control strategy of flexible space manipulator are researched. A ground gravity flotation simulation integrated experimental platform for space flexible manipulator is designed, and some typical experiments, such as flexible joint position tracking and testing, experimental modal analysis for the flexible beam, and residual vibration suppression are performed.
首先,提出空间机械臂的刚／柔／控耦合模态分析概念,借助反馈约束原理求得柔性臂在动约束状态下的复杂边界条件,并将关节控制器参数引入臂杆在离散平衡位置附近的振动动力方程,分别建立了频域空间和状态空间内模态求解的解析方法；针对机械臂的大范围运动影响臂杆自身的弹性振动模态问题,重点研究柔性臂动力学方程中切向惯性力项的影响,得到刚／柔耦合运动条件下臂杆的振动模态参数；特别地,研究了多活动部件柔体系统的有限元分析方法,并求解某型多自由度空间柔性机械臂的模态特性。
其次,从虚功的角度出发,采用哈密顿变分原理对含约束阻尼非保守力的柔性机械臂系统进行刚／柔／控耦合动力学建模；基于系统的状态空间模型设计一种适用于开、闭环条件的稳定数值PIM法,同时进行大量的数值实验以验证积分算法的有效性；对控制器反馈约束作用下系统的动力学响应进行数值求解并与KED法进行对比分析,得到不用于经典振动理论的结论。
再次,对机械臂柔性关节的动态不确定模型进行了建模分析,并提出一种同时补偿柔性、非连续摩擦、系统不确定性和外部干扰抑制的小波神经-鲁棒复合控制策略。全局采用Lyapunov函数的Backstepping方法设计具有柔性补偿和L2干扰抑制性能的控制器,同时,针对常规神经网络无法辨识非连续性函数的问题,提出在局部采用小波神经网络对摩擦和不确定项进行补偿。设计的控制策略不仅避免了单一反演鲁棒设计中复杂的求导运算,而且无须检测关节角加速度、辨识摩擦和估计不确定上界。
再其次,基于微分几何输入-输出线性化方法将双连杆柔性机械臂在新坐标系下分解为输入-输出子系统和内部子系统,导出零动力学规范化方程,并讨论系统观测输出位置的选择和零动力学稳定性之间的关系；建立柔性机械臂的全局快速收敛终端滑模控制策略,解决非最小相位系统的鲁棒控制问题,实现仅依靠关节处的驱动电机完成关节定位和臂杆残余振动的抑制。
最后,对空间柔性机械臂的相关动力学特性和控制策略进行实验研究,搭建空间柔性机械臂地面气浮式微重力模拟综合实验平台,设计并完成柔性关节的位置跟踪与测试、柔性机械臂的试验模态分析、柔性臂残余振动的主动控制等典型实验。
With the deepening of space exploration, the future space missions continue to be more and more, but it is hard to be completed entirely all by the astronauts as a results of the particularity and the risk of the space environment. The space flexible manipulator has the capability of adapting the vile space environment, so it is practically significant in both the economy and security aspects to assist or replace astronauts to complete some space operations utilizing the space manipulators, and it has become an important research direction in the space technology field. This paper is supported by the Key Project of Ministry of Education of China (307005) "space flexible robot dynamics/control coupling system research", and deeply focused on the dynamics and active control strategies for the space manipulator. The main work of this paper is as follows:
Firstly, the concept of rigid/flexible/control coupling mode analysis for the space flexible manipulator is proposed. The complex boundary conditions of flexible arm under the dynamic constraint state is obtained using feedback constraint theory, and the gain parameters of the joint controller are introduced into the vibration dynamic equation near the discrete equilibrium position. The analytic method of solving mode differential equations in frequency domain and state space are established separately. Taking into account the problem that the elastic modes are influenced by the large-scale movement, the mode parameters under the rigid/flexible coupling movement are solved in respect of the tangential inertia item. Especially, a multi degree of freedom mode characteristics of space manipulator are solved by the finite element method.
Secondly, the rigid/flexible/control coupling dynamics equations for the space manipulator involving the constrained damping non-conservative forces are established with Hamilton variational principle from the perspective of virtual work. Based on state space model, a stable numerical PIM that is suitable for both open and closed-loop conditions system is designed, and a large number of numerical experiments are implemented to verify the integration algorithma. The dynamic response under the feedback constraint is resolved by the PIM in oeder to compare with the traditional KED method, and some conclusions different from the classical vibration theory are obtained.
Thirdly, the uncertain second-order cascade dynamics equations including non-consecutive friction and external interference were modelled. In view of the complex dynamics character that flexibility coexists with friction, uncertain parameter perturbations and disturbances, a wavelet neural networks-robust hybrid control strategy was proposed. The global controller was designed using backstepping technique to compensate the flexibility and suppress disturbance based on L2 property. Considering it is difficult for the conventional neural networks to identify the non-consecutive items, the wavelet neural networks approach was locally utilized to estimate the nonlinear terms including friction and uncertainties. This strategy can avoid the complicated derivation, acceleration measurement, friction identification and uncertain upper bound forecast.
Fourthly, the two-link manipulator system was decomposed into input-output subsystem and internal subsystem by differential geometry input-output linearization method, and then the normalized equation of zero-dynamics is educed. The relationship between the choice of system observation output position and the zero-dynamic stability is discussed. A robust control approach using global terminal sliding mode was developed and the nonminimum phase control problem of two-link flexible space manipulator was solved. The target completing joint positioning and residual vibration suppression is achieved only rely on the joint driven motor.
Finally, some experiments about dynamics and control strategy of flexible space manipulator are researched. A ground gravity flotation simulation integrated experimental platform for space flexible manipulator is designed, and some typical experiments, such as flexible joint position tracking and testing, experimental modal analysis for the flexible beam, and residual vibration suppression are performed.
引文
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