Abstract
This paper proposes a new method for the trajectory planning of a two-link rigid-flexible manipulator in a point-to-point motion. In order to obtain a mathematical model properly, the flexible link is modeled by considering the axial displacement and the nonlinear curvature due to large bending deformation. The Lagrangian approach in conjunction with the assumed modes method is applied to derive the equations of motion of the manipulator. In the trajectory planning, we express the desired joint angle of the flexible link by a cubic spline function, and then use a particle swarm optimization to minimize the joint driving torque. We show that the residual vibrations of the flexible link can be suppressed as a result of the minimum driving torque requirement. In the numerical calculation, we verify the effectiveness of the proposed trajectory planning.
