Artificial neural networks for the computation of the inverse kinematics of redundant manipulators

Date
2020-06-26
Authors
Habibkhah, Shahnaz
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Faculty of Graduate Studies and Research, University of Regina
Abstract

Robotic manipulators play a key role in the industry these days. These devices are used to manipulate many and diverse objects without human physical interference. Hence they are very useful in different industries and applications such as welding, space, surgery, and nuclear activities. If the number of degrees of freedom (DOF) of a manipulator is higher than what is required to perform a task, the manipulator is called ʺKinematically redundantʺ. In other words, for these kinds of manipulators, the number of joint angles are more than what is needed according to the task constraints. To move the robot manipulator’s end-effector to the desired coordinates, its links should be moved properly, which is made possible by imposing the control torque and changing the joint angles. The relationship between the joint angles and the end-effector’s position coordinates is described by Kinematics. Therefore, the robot manipulator Kinematics help to obtain the robot’s end-effector’s position coordinates with respect to the values of the joint angles variables. On the other hand, in many applications, the end-effector’s desired coordinates are available and engineers are needed to obtain the values of the joint angles related to each coordinate of the end-effector position. This helps to impose the suitable torque to the joints and move them properly to get the desired end coordinates. Representing the joint angles based on the end-effector’s position coordinates is called Inverse Kinematics (IK). iii Solving the robot manipulator Inverse Kinematic problem is complicated for the robots with more than two degrees of freedom, and different solutions to this problem have been suggested during the last years. In in this Thesis, in order to solve the IK problem for 3 and 4 DOF redundant robot manipulators, the Artificial Neural Networks (ANNs) toolbox from MATLAB is used. Aiming to obtain manipulators’ joint angles coordinates and solve the IK problem with acceptable accuracy; different scenarios with different training inputs and different training functions are considered to train ANNs. The training inputs are the position coordinates of the manipulators’ end-effector, as well as some introduced Virtual Dummy Functions (VDFs). In this Thesis, various VDFs (constraints) are defined as inputs of different ANNs with different number of hidden neurons; and performance of the ANNs are compared. The ANNs’ performance, error, training state are simulated to analyze the designed ANNs. Finally, aiming to investigate the ANNs’ performance, some target trajectories are designed inside the manipulator workspace and the ANNs’ abilities to track them are investigated. In order to design feasible target trajectories, some constraints are defined and considered according to the robot’s links limitations and it is shown that the designed ANNs are smart and it is impossible for them to follow infeasible trajectories.

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