A Stewart Platform Inverse Kinematics Algorithm Linear Model

Abstract

The aim of the study is to improve the quality of reproducing real aircraft movements in laboratory conditions using the Stewart platform. To achieve this, a key source of accuracy limitation is identified. This is an imperfection in the movement control systems of such platforms. There are two main reasons for such situation. The first one is the random nature of the platform multidimensional motions during  reproducing flight conditions. The second one is connected with the presence of significant nonlinearities acting on the inputs and outputs of the platform due to the need to solve inverse and forward kinematics problems.

The article analyzes the methods for solving the Stewart platform kinematics inverse problem and shows that they all involve performing a number of nonlinear transformations. As a result of comparing the linearization methods and the experience of replacing a nonlinear element with a family of linear ones, active identification was chosen as the method for determining the specified family. A linearized model’s structural diagram of the inverse kinematics problem solving process was developed. An algorithm for searching for transfer function matrices of this structural diagram was justified. The implementation of a new identification algorithm using the functions of the Matlab environment was presented. The influence of the intensity of a multidimensional broadband stationary random process on the parameters and structure of the linearized model was studied. The quality of linearization was assessed based on the determination of the mean square deviation of the signals at the outputs of the inverse kinematics unit and its linear model.

The results of the study show that linearization is expedient and possible to carry out by applying the technology of multidimensional object the dynamics model identification  in the state space; the initial data for identification should be obtained from a computational or full-scale experiment; the dynamics of the platform desired position vector r should correspond to the problem that needs to be solved using the Stewart platform; the virtual or physical model of the process of solving the inverse kinematics problem should correspond to the design of the Stewart platform and the characteristics of the microcontroller controlling the position of the platform; further research should be directed to the linearization of the process of inverse kinematics of the Stewart platform with a narrow-band random vector of its desired position.