Tuning Proportional-Integral-Derivative Gains of a Three-Dimensional RRRP Pick and Place Robot for Asymptotic Trajectory Tracking

Abstract

Abstract This paper uses the Floquet theory for tuning the feedback gains to stabilize the tracking errors of a revolute-revolute-revolute-prismatic (RRRP) robot moving in a three-dimensional (3D) workspace. This robot is driven by a proportional-integral-derivative (PID) control law, tracking a time-varying trajectory in joint space, without knowledge of any bounds of the inertia matrix and/or Jacobian of the gravity vector. The Floquet theory is used to obtain the values of feedback gains for which the asymptotic stability of the tracking errors is obtained. The numerical results obtained by Floquet theory are verified by the tracking error plots and phase portraits. The obtained results will be very useful for the control of any industrial robot, required to perform repetitive tasks like assembly of parts and inspection of products, amongst others.