Neuro-Fuzzy based Approach for Inverse Kinematics Solution of Industrial Robot Manipulators

Obtaining the joint variables that result in a desired position of the robot end-effector called as inverse kinematics is one of the most important problems in robot kinematics and control. As the complexity of robot increases, obtaining the inverse kinematics solution requires the solution of non linear equations having tran- scendental functions are difficult and computationally expensive. In this paper, using the ability of ANFIS (Adaptive Neuro-Fuzzy Inference System) to learn from train- ing data, it is possible to create ANFIS, an implementation of a representative fuzzy inference system using a BP neural network-like structure, with limited mathematical representation of the system. Computer simulations conducted on 2 DOF and 3DOF robot manipulator shows the effectiveness of the approach. A robot manipulator is composed of a serial chain of rigid links connected to each other by revolute or prismatic joints. A revolute joint rotates about a motion axis and a prismatic joint slide along a motion axis. Each robot joint location is usually defined relative to neighboring joint. The relation between successive joints is described by 4£ 4 homogeneous transformation matrices that have orientation and position data of robots. The number of those transformation matrices determines the degrees of freedom of robots. The product of these transformation matrices produces final orientation and position data of a n degrees of freedom robot manipulator. Robot control actions are executed in the joint coordinates while robot motions are specified in the Cartesian coordinates. Conversion of the position and orientation of a robot manipulator end-effector from Cartesian space to joint space, called as inverse kinematics problem, which is of fundamental importance in calculating desired joint angles for robot manipulator design and control. For a manipulator with n degree of freedom, at any instant of time joint variables is denoted by q i = q(t), i = 1; 2; 3;:::; n and position variables x j = x(t), j = 1; 2; 3;:::; m. The relations between the end-effector position x(t) and joint angle q(t) can be represented by forward kinematic equation,