Direct kinematics solution of 3-RRR robot by using two different artificial neural networks

Abstract

In recent years neural networks have been considered as an apposite method for solving problems which come to system of nonlinear equations. On the other hand, in opposite to inverse kinematics problem of parallel manipulators, their direct kinematics problem has very complicated analytical solution which are dependent to solving system of nonlinear equations with numerical methods. Therefore this problem can be a good case for using artificial neural networks. In this paper, direct kinematics problem of a 3-RRR planar parallel robotic manipulator, is solved by using two different models of artificial neural networks, one a back propagation neural network and the other one a radial basis neural network. The proposed networks use training data set which is made by solving the inverse kinematics of the robot. After making the database for training the networks, different parameters of the neural networks are changed in a wide range and finally the best ones for each of BPNN and RBFNN models are selected. Then the number of the data used for training is minimized. So that computation time is optimized. Mean squared error of the proposed BP and RBF neural networks are 7.5×10−6 and 5 × 10−17. Much more precise results in solving FKP of the 3-RRR manipulator and also less computational time of RBFNN is obtained in this study. The designing approach of the proposed solution is presented in detail, and effectiveness of the solution is demonstrated by comparing a simulated spiral path with its real path. Finally the total error during the simulated path is calculated and the average of 4. 5 × 10−4 for BPNN and 1. 59 × 10−6 for RBFNN confirms the reliability of these methods.