Mathematical Models and Adaptive Control System of Rigid and Flexible 4-DOF Joint Robotic Manipulator with Executive Electric Drives

Abstract

Mathematical model of a rigid and flexible 4 degrees of freedom (DOF) joint robotic manipulator with executive electric drives has been developed. The mathematical model of the robotic manipulator is designed based on the Lagrange - Euler formula, and the result of calculating the nonlinear inertia matrix, the matrix of Centrifugal and Coriolis forces, and the Gravitational force vector are presented. The mathematical model of the electromechanical drive is developed based on the two-mass model “executive electric drive - mechanism”. Adaptive systems for rigid and flexible robotic manipulators are designed by syntheses on using computed torque (Li-Stoline) method and backstepping (step-by-step synthesis). The calculation and synthesis algorithm was implemented using the Mathcad and Matlab-Simulink software packages.