Quaternion Modeling of a Delta Planar Robot and Training of an Enhanced Multilayer Neural Network to Solve the Inverse Kinematic Problem

Abstract

This paper presents the modeling of the inverse kinematic problem related to the motions of a delta planar robot using the algebra of unitary Quaternions. The mathematical model resulting from the inverse kinematic analysis has an associated system of 8 nonlinear algebraic equations with 8 polynomial unknowns. The Newton-Raphson method was used to solve the mathematical model of the robot. Subsequently, using the inverse model of the robot, a database was constructed that relates the Cartesian coordinates of the end effector to the angles and axes of the rotations of the links. This database was used to train a multilayer neural network in order to have an equivalent model of the inverse problem. A series of experiments were performed to obtain an improved network configuration by varying four training parameters. The results obtained show that the improved trained network can be used to solve the inverse problem of the studied robot.