Closed Loop Optimal Control of a Stewart Platform Using an Optimal Feedback Linearization Method

Abstract

Optimal control of a Stewart robot is performed in this paper using a sequential optimal feedback linearization method considering the jack dynamics. One of the most important applications of a Stewart platform is tracking a machine along a specific path or from a defined point to another point. However, the control procedure of these robots is more challenging than that of serial robots since their dynamics are extremely complicated and non-linear. In addition, saving energy, together with achieving the desired accuracy, is one of the most desirable objectives. In this paper, a proper non-linear optimal control is employed to gain the maximum accuracy by applying the minimum force distribution to the jacks. Dynamics of the jacks are included in this paper to achieve more accurate results. Optimal control is performed for a six-DOF hexapod robot and its accuracy is increased using a sequential feedback linearization method, while its energy optimization is realized using the LQR method for the linearized system. The efficiency of the proposed optimal control is verified by simulating a six-DOF hexapod robot in MATLAB, and its related results are gained and analysed. The actual position of the endeffector, its velocity, the initial and final forces of the jacks and the length and velocity of the jacks are obtained and then compared with open loop and non-optimized systems; analytical comparisons show the efficiency of the proposed methods.

Introduction of Feedback Linearization to Robust LQR and LQI Control – Analysis of Results from an Unmanned Bicycle Robot with Reaction Wheel

“…Some of the newest applications of the method show that it successfully helps to design control systems in the wide range of nonlinear problems. Several examples of those applications are the following: [38] where the authors use feedback linearization with linear-quadratic regulator to control Stewart robot; [22,24] where feedback linearization in combination with sliding mode control is used to control induction motor drives; or [34] where, for spring loaded inverted pendulum as a model for legged locomotion, the authors use partial feedback linearization. Additionally, feedback linearization is applied also when the problem of uncertainties occurs, as in [43] where the authors consider control of nonlinear hydraulic generator with external disturbances and system uncertainty; in [25] where feedback linearization and extended state observer based control is proposed that deals with uncertainties of rotor-active magnetic bearings system; or in [46] where a neural network-based supple-mentary control system for a nonlinear plant is build on the basis of feedback linearization.…”

Adaptive 6 DOF Self-Balancing Platform for Autonomous Vehicles

“…Reference [17] suggested the use of dynamic neural network. Other work suggests optimal control of a Stewart robot using a sequential optimal feedback linearization method considering the jack dynamics to secure optimal and accurate control of a Stewart robot that is supposed to carry a machine along a specified path [18] Other recent work proposed H-infinity theory to control 6 DOF motion [19]. However, to avoid complexity and high computation requirements, linear regression is used in this paper [20].…”

Discrete Time Delay Feedback Control of Stewart Platform with Intelligent Optimizer Weight Tuner

“…The key aim of the parallel robot control system architecture is to ensure an exact continuation for the target position and orientation of dynamic and static variables in the moving endeffector of the robot [11]. Due to their extreme complexity, the robot's dynamics have lower control methods for the rotary Stewart robot while a wide range of control mechanisms are available, for example, optimum feedback robotic control [12]; backstage adaptive control [13]- [15]; and backstage adaptive control [16], [17]. In order to directly exploit the movement of the end-effector, reverse dynamic controls are extremely necessary.…”