Model-Free Discrete Time Control for Scara Robot Manipulators Using Descending Gradient Algorithm

Discrete control of the robot manipulators with uncertain model is the purpose of this paper. The proposed control design is model-free by employing an adaptive fuzzy estimator in the controller for the estimation of uncertainty as unknown function. An adaptive mechanism is proposed in order to overcome uncertainties. Parameters of the fuzzy estimator are adapted to minimize the estimation error using a novel gradient descent algorithm. The proposed model-free discrete control is robust against all uncertainties associated with the robot manipulator and actuators including model’s uncertainty and external disturbances. The most gradient descent algorithms have used a known cost function based on the tracking error for adaptation whereas the proposed algorithm has proposed a cost function based on the uncertainty estimation error. Then, the uncertainty estimation error is calculated from the joint position error and its derivative using the closed-loop system. Most control algorithms require all state variable feedback to ensuring stability for the robot manipulators. Practical implementation of this control method is easy because it has a decentralized structure and measures only from the joint position. The simulation results confirm the correct operation of this method and we will prove the stability of the control system.