Trajectory planning for residual vibration suppression of a two-link rigid-flexible manipulator considering large deformation

In this paper an optimal trajectory planning technique for suppressing residual vibrations in two-link rigid-flexible manipulators is proposed. In order to obtain an accurate mathematical model, the flexible link is modeled by taking the axial displacement and nonlinear curvature arising from large bending deformation into consideration. The equations of motion of the manipulator are derived using the Lagrangian approach and the assumed modes method. For the trajectory planning, the joint angle of the flexible link is expressed as a cubic spline function, and then the particle swarm optimization algorithm is used to determine the optimal trajectory. The optimal trajectory thus obtained satisfies the minimum vibration condition. By performing numerical simulations, the effectiveness of the proposed trajectory planning technique is verified.