ANALYTICAL DESIGN OF RESONANT CONTROLLER APPLIED FOR SOLVING ROBOT ARM TRACKING PROBLEM

Abstract

This paper deals with a topic of robot following a trajectory in three-dimensional space with a prescribed velocity law. Considering the nonlinear nature of robot manipulators, and high demands regarding tracking performances, this task is very challenging, but also very popular in control community because of its importance in industrial applications. To tackle successfully this problem, we proposed a resonant controller, which outperforms classical control schemes usually employed in this situation. In this particular case, robot manipulator needs to follow an ellipse trajectory with constant speed along the curve. First, mathematical model of three degrees of freedom robot arm is derived with included actuator dynamics. Then, numerical solution of inverse kinematics problem needs to be calculated in order to obtain desired trajectory in joint space. Third, analytical procedure for designing resonant controller is given, with parameters of the controller chosen in order to achieve a good performance/robustness trade-off, which is a key element in modern control design. Finally, proposed control scheme is tested and results of robot simulation are given in the end. Final remarks conclude the paper.