Adaptive Non-linear Control for a Virtual 3D Manipulator

Abstract

This work focuses on two main problems in the field of robotic manipulators: modeling and non-linear robust control for trajectory tracking. The kinematic and dynamic model of a three degree of freedom (DoF) commercial manipulator is summarized. Through 3D simulation, the robot is implemented in a virtual environment using Autodesk Inventor and Matlab-Simulink in order to have a robotic computational platform for didactic and research purposes. Using the virtual robot, a non-linear controller is implemented for each joint and the tracking response of the tip to a sinusoidal input is verified. This controller presents a good performance when the manipulator parameters are known with accuracy, so the non-linearities are canceled. However, it is more challenging to consider a real case in which the manipulator holds an object that changes its dynamics. Therefore, an adaptive algorithm is designed and implemented for this case when the cancellation of non-linearities is not exact. This algorithm is based on Lyapunov stability to generate a control law that allows the estimation of the link masses and allowing a better cancellation of non-linearities. This control scheme provides a better performance compared with the case of a non-linear controller but not adaptive.