A sliding mode controller for a two-joint robot with an elastic link

In this paper the problem of the motion control of a two-joint planar robot with a flexible link is considered. The model of the robot is developed by using a simplified finite element technique referring to the elastic link. The sliding mode technique is considered. Two sliding surfaces are defined, as many as the control inputs. The required measurements are the position and velocity of the two motors and some positions of the elastic link. The equivalent motion is described by a linear system and its stability can be proved considering its eigenvalues. From this inspection some necessary conditions on the choice of the sliding surfaces are derived. Simulation tests have been carried out for some reference trajectories; the tracking error is always very small; in any case the elastic link behaves as it were almost rigid notwithstanding its stiffness is very small.