Task-space Feedback Control of Robot Manipulator with Uncertain Jacobian Matrix, Via Robust Adaptive Fuzzy Sliding Mode Control

In most of the researches that have been done in the position control of robot manipulator, the assumption is that robot manipulator kinematic or robot Jacobian matrix turns out from the joint-space to the task-space. Despite the fact that none of the existing physical parameters in the equations of the robot manipulator cannot be calculated with high precision. In addition, when the robot manipulator picks up an object, uncertainties occur in length, direction and contact point of the end-effector with it. So, it follows that the robot manipulator kinematic is also has the uncertainty and for the various operations that the robot manipulator is responsible, its kinematics be changed too, certainly. To overcome these uncertainties, in this paper, a simple adaptive fuzzy sliding mode control has been presented for tracking the position of the robot manipulator end-effector, in the presence of uncertainties in dynamics, kinematics and Jacobian matrix of robot manipulator. In the proposed control, bound of existing uncertainties is set online using an adaptive fuzzy approximator and in the end, controller performance happens in a way that the tracking error of the robot manipulator will converge to zero. In the proposed approximator design, unlike conventional methods, single input-single output fuzzy rules have been used. Thus, in the practical implementation of the proposed control, the need for additional sensors is eliminated and calculations volume of control input decreases too. Mathematical proofs show that the proposed control, is global asymptotic stability. To evaluate the performance of the proposed control, in a few steps, simulations are implemented on a two-link elbow robot manipulator. The simulation results show the favorable performance of the proposed control.