To solve the problem of Acrobot that an underactuated robot relying on excitation combined with other control methods can not achieve complete the action of catching the target rod, we firstly propose concept of research of big damping nonholonomic constraint in underactuated robot and control strategy of stably grasping target rod, design the gripper dedicated to this kind of robot, which can grasp the rod constitutes a big damping nonholonomic constraint state, and propose the control strategy of using rapidly swing up combined with turn back feedback control for the underactuated robot stable grasping rod motion. The corresponding controller is designed, and the robot simulation model is established using ADAMS and MATLAB software. The simulation achieves reliable grasping rod motion control of the robot, and the experimental results verify the driving ability of each joint of the robot and the effectiveness of the proposed control strategy.