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Polynomial neural network for robot forward and inverse kinematics learning computations

Knowing the end-effector location (position and orientation) and the joint angles of the robot manipulator in real-time will assist the manipulator in negotiating around the obstacles when the manipulator is moving in a crowded environment. Thus, Forward and Inverse Kinematics Computations (FKC and IKC) play very important roles in robotic manipulators. The main objective of this paper is to demonstrate the capability of learning different trajectories of the robot reachable space by using the proposed PNN model. A software package has been developed for solving both FKC and IKC. The software can discover both the structure and the coefficients of a model to describe the dependent output variables in terms of the independent input variables identified by the users. The simulation is performed in a two degree-of-freedom manipulator. The solutions of the built FKC and IKC networks are compared with the analytic equations. The PNN learns successfully the indicated path. The simulation result shows that the PNN can interpolate the indicated path better than 99.87% of accuracy by only training the built PNN network 361 data pairs (out of 2D space point). The approach presented here can be expanded to six degree-of-freedom type of manipulators. Detailed algorithms of the GMDH to construct the PNN kinematics models will be discussed.