Robust Control of a Bimorph Piezoelectric Robotic Manipulator Considering Ellipsoidal-Type State Restrictions

The current study presents an adaptive control approach to solve the tracking trajectory problem for a robotic manipulator that uses a gripper based on bimorph piezoelectric actuators. The development of an adaptive gain state feedback form that considers the state restrictions is proposed using a novel class of barrier Lyapunov function that drives the effective control of joints and piezoelectric actuators. The proposed method allows for the inclusion of complex combinations of state restrictions in the Lyapunov function, yielding the construction of differential forms for the gains in the controller that can handle the evolution of trajectories of the robotic arm inside the restricted region. The proposed control design successfully tracks reference trajectories for both joints of the robotic arm as well as the motion of the piezoelectric device during several operative scenarios. A comprehensive experimental study evaluates the effect of introducing state-dependent gain considering state restrictions of the ellipsoidal type. The comparison of the mean square error confirms the contributions of the developed control action, showing better tracking quality for less control power with the same evaluation, which is a desirable characteristic in the controlled motion of micromanipulators. The proposed controller solves the tracking trajectory problem for the micromanipulation system, satisfies the motion restrictions, and allows better tracking performance to be enforced. Furthermore, comparison of the obtained trajectories seems to validate the proposed controller’s contribution concerning a feedback form with fixed gains.