Point-to-point control of a 2R planar horizontal underactuated manipulator

This paper presents a control strategy for a two-link manipulator with revolute joints (2R) with an unactuated second joint, wherein the motion of the system is confined to a horizontal plane. The model takes into account the frictional forces present in the system. The control objective is to move the end-effector from a given position to a target point. The methodology involves two stages. In the first stage a finite-time controller is used to move the passive link to its desired position. In the second stage, the first link is moved to its desired position keeping the second link at rest, using friction as a “brake” and subject to the constraint that the cross-coupling torque acting on the second joint does not exceed the static friction.