Self-tuning control of planar two-link manipulator with non-rigid arm

The control of the motion of a two-link manipulator with a flexible arm is studied. The first link is rigid, and the second link has a flexible part as an extension of a rigid part. The motion of the manipulator takes place on a horizontal plane. The dynamics of the manipulator are determined in Lagrange's formulation. The positions (output) of specified points on the flexible link are obtained in the Cartesian base coordinate system using strain-gage and joint-variable measurements. The inputs are applied to the actuators of the revolute and prismatic joints. For the controller design, a time-series multivariate model of the autoregressive exogeneous (ARX) type is used to describe the input-output relation. The discounted least-square method is used to estimate parameters of the time-series model. A self-tuning controller (STC) is designed so that the positions of specified points on the flexible link track the given trajectory points. The controller operates on the Cartesian coordinates, specifying the positions of the chosen discrete points on the flexible link. Simulation results as well as laboratory experiments on a Stanford/JPL arm controlled by an STC are presented to illustrate the approach.<
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