Two-Link Flexible Manipulator Modelling and Tip Trajectory Tracking Based on the Absolute Nodal Coordinate Method

It has been demonstrated that the absolute nodal coordinate formulation (ANCF) proposed recently in literature can be used to exactly describe the flexible multibody system unlike traditional methods such as the floating coordinate method and assumed mode method. Therefore, in this paper a new dynamic modeling technique for a two-link flexible manipulator based on absolute nodal coordinate method is proposed. The link shear effect was taken into account by using the 2D ANCF shear beam element. The resulting state equation can be explicitly described by generalized coordinate since the system mass matrix is constant in the ANCF framework. The proposed method is validated through the two-link flexible manipulator tip circle and square trajectory tracking control simulations by using a simple PD controller. To improve computational efficiency, the invariant matrix method and the Broyden quasi-Newton method are introduced. To improve the tracking accuracy, different PD parameters in different simulation periods are used. The simulation results indicate that modeling and controlling the flexible manipulator based on the ANCF is effective.