Approach to Positioning Links of the Manipulator Using Neural Networks

Abstract

This paper considers development of positioning systems for manipulator links to solve the forward kinematics problem (FKP) and inverse kinematics problem (IKP). Here we study a robotic manipulator with four degrees of freedom. It should be noted, that one of the relevant research problems of modern modular robotic devices consists in the lack of the universal algorithms, that would ensure kinematics problem recalculations in the cases of reconfigurations of the whole system. Challenges, the researchers are facing with when solving this problem, have to do with geometrical and non-linear equations (trigonometric equations), finding of inverse matrix of the Denavit—Hartenberg presentation, as well with other problems, such as multiple solutions when using the analytical approach. Common mathematical solutions of the inverse kinematics problem, such as geometric, iterative and algebraic ones, may not always lead to physically appropriate solutions. It’s also noteworthy, that, trying to introduce physical solutions for the manipulator, we need to take into account, that the number of calculation formulas increases, what, in turn, causes further computing power consumption increase. If the manipulator acquires additional degrees of freedom, analytical modeling becomes virtually impossible. One of relevant inverse kinematics solution methods consists in implementation of neural networks to that end. To solve this problem various sources were analyzed, considering alternative ways of target point discovery. Considering the analyzed papers, we propose to use a perceptron. Before training the network, we compose an algorithm, calculating the Denavit—Hartman presentation matrix and check for correctness of target point reach by the terminal manipulator link. We did calculations for a thousand positions of manipulator and object in the environment, fed to the neural network. When solving FKP we obtain object coordinates as network output, whereas in the case of IKP — manipulator link angles. We present kinematic scheme testing results, as well a control scheme for a manipulator with four degrees of freedom.