Robust Finite-Time Tracking of Stewart Platform: A Super-Twisting Like Observer-Based Forward Kinematics Solution

Abstract

The paper presents the robust finite-time tracking of Stewart platform using super-twisting sliding mode observer based forward kinematics solution. The forward kinematics problem—finding the states from the leg length measurements—in Stewart platform gives nonunique solution for any given leg lengths, and due to this it poses difficulties in the control design. The super-twisting observer is designed from the available leg length measurements which is the output of the system to obtain the position and orientation of movable platform and their respective derivatives. The finite-time convergence of this observer and the stability of the closed loop system are presented in detail. It is shown that using this leg length measurements, the states of the observer converge to actual state in finite-time and hence, it provides a solution to the forward kinematics problem. Using these estimated states, a robust finite-time tracking control is designed for the Stewart platform by considering all the uncertainties and parameter variations. However, the proposed method for forward kinematics solution can also be incorporated with any other control strategies. Simulation results are given to demonstrate the performance of the proposed observer for the Stewart platform.