Impedance Control of a Flexible Link Robot for Constrained and Unconstrained Maneuvers Using Sliding Mode Control (SMC) Method

In this paper, the modeling and impedance-control of a one link
exible robot is presented. The
concept of impedance control of
exible link robots is rather new and is being addressed for the
rst time. The control algorithm is valid for both constrained and unconstrained maneuvers.
First, equations of motion and the associated boundary conditions are derived using Hamilton's
principle. A linear nite dimensional model is, then, generated in the Cartesian coordinates, using
the assumed mode method and by introduction of a proper coordinate transformation. The target
impedance is, then, introduced in the Cartesian coordinate system and a control law is designed
to realize the proposed target impedance for a given frequency range, using the Sliding Mode
Control Theory. A set of computer simulations are carried out to demonstrate the eectiveness
of the proposed control law. Simulations are carried out with various contact stiness. As the
results show, when the environmental surface stiness is smaller than, or comparable to, that of
the link, the control system is able to achieve stable behavior and the link vibration diminishes
rather rapidly. However, when the environmental stiness is much greater than that of the
stiness of the link, although the robot achieves stable behavior during contact, the vibrations
tend to increase.