Lyapunov stability of PD visual control on a planar parallel robot
Abstract
This work studies the stability of proportional-derivative regulators using visual information for position control of planar parallel robots. Hence, it is mentioned literature research according control of this kind of robots, as well as references where techniques are used in open kinematic chain mechanisms to ensure stability. It presents stability analysis employing strict Lyapunov functions and the second Lyapunov method to ensure closed-loop asymptotically stability at the equilibrium point. Differing this procedure from the usual analysis which require special Lyapunov candidate functions together with global stability theorems as Barbashin-Krasovsky theorem or the LaSalle`s invariance principle. The proposed visual control algorithms, using velocity estimation from position measurement, calculate the joint torques on the parallel robot´s active joints needed to move the end-effector to the desired position. Finally, these proposed control laws are evaluated on a laboratory prototype and the corresponding experimental results are illustrated.
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