  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.
