Global stabilization of underactuated spring-coupled three-link horizontal manipulator using position measurements only

Abstract This paper concerns the global stabilization of an underactuated spring-coupled three-link horizontal manipulator (STHM), which is an underactuated mechanical system (UMS) with two actuators and three degrees of freedom (DOF). A new control method is developed that asymptotically stabilizes the STHM at the origin using the position measurements of the manipulator only. First, we introduce a homeomorphic coordinate transformation for the STHM system. This changes the stabilization of the STHM into that of the transformed system. Next, we analyze the characteristics of the transformed system. After that, we construct an equivalent-input-disturbance- (EID-) based control system to globally stabilize the transformed system at the origin. Finally, a numerical example demonstrates the validity of the presented method. Our method only uses the position measurements of the STHM to design stabilizing controller. It reduces the cost of the whole control system and avoids the influence on the system’s control performance imposed by velocity noises. In addition, the analysis and control method of this paper is easy to extend to the global stabilization of other n -DOF ( n ⩾ 3 ) UMSs.

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