Control of an Underactuated Three Link Passive–Active–Active Manipulator Based on Three Stages and Stability Analysis

Abstract

This paper presents a novel threestage control strategy for the motion control of an underactuated threelink passive–active–active (PAA) manipulator. First, a nonlinear control law is designed to make the angle and angular velocity of the third link convergent to zero. Then, a swingup control law is designed to increase the system energy and control the posture of the second link. Finally, an integrated method with linear control and nonlinear control is introduced to stabilize the manipulator at the straightup position. The stability of the control system is guaranteed by Lyapunov theory and LaSalle’s invariance principle. Compared to other approaches, the proposed strategy innovatively introduces a preparatory stage to drive the third link to stretchout toward the second link in a natural way, which makes the swingup control easy and quick. Besides, the intergraded method ensures the manipulator moving into the balancing stage smoothly and easily. The effectiveness and efficiency of the control strategy are demonstrated by numerical simulations.