Multiple Manifold Types of Synergetic Control Applied on a 4-DOF Robot Manipulator

This work presents a comparative study of different types of synergetic control applied to a Four Degrees of Freedom Robot (4-DOF) manipulator to track the desired trajectories in the workspace and joint space. Synergetic control theory arises in control science with the principle of performing self-organization in the system. It provides asymptotic stability in complicated control problems of nonlinear systems. The control methodology is based on three main steps. First, the desired trajectories are converted from the workspace to the joint space through the inverse kinematics. Second, a synergetic controller is developed to closely track the desired joint space trajectories. Finally, in the third step, the forward kinematics is used to convert the real joint space trajectories to the workspace trajectories. The main purpose of this work is to evaluate experimentally the synergetic control performance on a robotic arm. Three different manifolds; conventional, terminal and nonsingular terminal manifolds are used for this comparative study to develop the control law. Lyapunov approach is then used to analyse the closed loop stability. The obtained experimental results are statistically compared among them in order to find the best manifold for such robotic systems.