Iterative Contraction Stability Control Strategy for Planar Prismatic-Rotational Underactuated Robot

An iterative contraction stability control strategy is proposed to solve the end point position control problem of the planar prismatic-rotational (PR) underactuated robot. We establish the dynamic model of the planar PR underactuated robot, and use the algebra method to derive the nilpotent approximation model (NAM) with similar characteristics to the original system. According to the robot structure and control objectives, we propose a two-stage control idea: (1) Design a sliding mode variable structure controller to ensure that the active link can back to the target position after subsequent iterative operations; (2) Design an open-loop iterative control strategy based on the previous NAM to control the active link for iterative operation. The underactuated link is indirectly controlled and stabilized at any different accessible position under the action of the coupling relationship between links by controlling the active link. Finally, the simulation results prove that the end point of the robot can be effectively controlled to any positions.