The mode shape function is difficult to determine in modeling manipulators with flexible links using the assumed mode method. In this paper, for a planar 3-RRR parallel manipulator with flexible actuation links, we provide a data-driven method to identify the mode shape of the flexible links and propose a model-based controller for the vibration suppression. By deriving the inverse kinematics of the studied mechanism in analytical form, the dynamic model is established by using the assumed mode method. To select the mode shape function, the software of multi-body system dynamics is used to simulate the dynamic behavior of the mechanism, and then the data-driven method which combines the DMD and SINDy algorithms is employed to identify the reasonable mode shape functions for the flexible links. To suppress the vibration of the flexible links, a state observer for the end-effector is constructed by a neural network, and the model-based control law is designed on this basis. In comparison with the model-free controller, the proposed controller with developed dynamic model has promising performance in terms of tracking accuracy and vibration suppression.

翻译：在采用假设模态法对含柔性连杆的机器人进行建模时，模态振型函数难以确定。针对平面3-RRR型柔性驱动连杆并联机器人，本文提出一种数据驱动方法以识别柔性连杆的模态振型，并设计基于模型的振动抑制控制器。通过解析形式推导研究机构逆运动学，采用假设模态法建立动力学模型。为选择模态振型函数，利用多体系统动力学软件模拟机构动态行为，进而采用结合DMD与SINDy算法的数据驱动方法，识别柔性连杆的合理模态振型函数。为抑制柔性连杆振动，通过神经网络构建末端执行器状态观测器，并据此设计基于模型的控制律。与无模型控制器相比，所提出的基于改进动力学模型的控制器在跟踪精度与振动抑制方面表现出优良性能。