With the goal of creating a flexible spatial parallel robot system in which the elastic deformation of the flexible link causes a rigid moving platform to produce small vibrations, we proposed an adaptive sliding mode control algorithm based on a neural network. To improve the calculation efficiency, the finite element method was used to discretize the flexible spatial link, and then the displacement field of the flexible spatial link was described based on floating frame of reference coordinates, and the dynamic differential equation of the flexible spatial link considering high-frequency vibrations was established through the Lagrange equation. This was combined with the dynamic equation of the rigid link and the dynamic equation considering small displacements of the rigid movable platform due to elastic deformation, and a highly nonlinear and accurate dynamic model with a rigid–flexible coupling effect was obtained. Based on the established accurate multi-body dynamics model, the driving torque with coupling effects was calculated in advance for feedforward compensation, and the adaptive sliding mode controller was used to improve the tracking performance of the system. The nonlinear error was examined to determine the performance of the neural network’s approximation of the nonlinear system. The trajectory errors of the moving platform in the X-, Y-, and Z-directions were reduced by 12.1%, 38.8%, and 50.34%, respectively. The results showed that the designed adaptive sliding mode neural network control met the control accuracy requirements, and suppressed the vibrations generated by the deformation of the flexible spatial link.

中文翻译：

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柔性空间并行机器人的自适应滑模神经网络控制和柔性振动抑制

为了创建一个柔性空间并行机器人系统，在该系统中，柔性链节的弹性变形导致刚性运动平台产生较小的振动，我们提出了一种基于神经网络的自适应滑模控制算法。为了提高计算效率，采用了有限元方法离散化柔性空间链，然后基于参考坐标的浮动框架描述了柔性空间链的位移场，并考虑了柔性空间链的动力微分方程。通过拉格朗日方程建立了高频振动。结合了刚性连杆的动力学方程和考虑到刚性可移动平台由于弹性变形而产生的小位移的动力学方程，得到了具有刚柔耦合效应的高度非线性和精确的动力学模型。在建立的精确多体动力学模型的基础上，预先计算了具有耦合效应的驱动转矩，以进行前馈补偿，并使用自适应滑模控制器来改善系统的跟踪性能。检查了非线性误差，以确定神经网络对非线性系统的逼近性能。平台中移动平台的轨迹误差 自适应滑模控制器用于提高系统的跟踪性能。检查了非线性误差，以确定神经网络对非线性系统的逼近性能。平台中移动平台的轨迹误差 自适应滑模控制器用于提高系统的跟踪性能。检查了非线性误差，以确定神经网络对非线性系统的逼近性能。平台中移动平台的轨迹误差X，Y和Z方向分别降低了12.1％，38.8％和50.34％。结果表明，所设计的自适应滑模神经网络控制方法满足控制精度要求，并抑制了柔性空间连杆变形产生的振动。