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A Comparative Study of Three Inverse Kinematic Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework

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A Comparative Study of Three Inverse Kinematic Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework University of Wollongong Research Online Faculty of Engineering and Information Faculty of Engineering and Information Sciences - Papers: Part B Sciences 2011 A Comparative Study of Three Inverse Kinematic Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework Emre Sariyildiz University of Wollongong, [email protected] Eray Cakiray Istanbul Technical University Hakan Temeltas Istanbul Technical University Follow this and additional works at: https://ro.uow.edu.au/eispapers1 Part of the Engineering Commons, and the Science and Technology Studies Commons Recommended Citation Sariyildiz, Emre; Cakiray, Eray; and Temeltas, Hakan, "A Comparative Study of Three Inverse Kinematic Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework" (2011). Faculty of Engineering and Information Sciences - Papers: Part B. 242. https://ro.uow.edu.au/eispapers1/242 Research Online is the open access institutional repository for the University of Wollongong. For further information contact the UOW Library: [email protected] A Comparative Study of Three Inverse Kinematic Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework Abstract In this paper, we compare three inverse kinematic formulation methods for the serial industrial robot manipulators. All formulation methods are based on screw theory. Screw theory is an effective way to establish a global description of rigid body and avoids singularities due to the use of the local coordinates. In these three formulation methods, the first one is based on quaternion algebra, the second one is based on dual-quaternions, and the last one that is called exponential mapping method is based on matrix algebra. Compared with the matrix algebra, quaternion algebra based solutions are more computationally efficient and they need less storage area. The method which is based on dual-quaternion gives the most compact and computationally efficient solution.aden-Kahan P sub-problems are used to derive inverse kinematic solutions. 6-DOF industrial robot manipulator's forward and inverse kinematic equations are derived using these formulation methods. Simulation and experimental results are given. Keywords screw, manipulators, robot, industrial, serial, methods, kinematic, inverse, three, study, framework, comparative, theory Disciplines Engineering | Science and Technology Studies Publication Details Sariyildiz, E., Cakiray, E. & Temeltas, H. (2011). A Comparative Study of Three Inverse Kinematic Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework. International Journal of Advanced Robotic Systems, 8 (5), 9-24. This journal article is available at Research Online: https://ro.uow.edu.au/eispapers1/242 ARTICLE International Journal of Advanced Robotic Systems A Comparative Study of Three Inverse Kinematic Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework Regular Paper Emre Sariyildiz, Eray Cakiray and Hakan Temeltas Department of Control Engineering, Istanbul Technical University, Turkey * Corresponding author E-mail: [email protected] Received 26 Apr 2011; Accepted 24 Aug 2011 © 2011 Sariyildiz et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we compare three inverse Keywords Dual‐Quaternion, Industrial Robot Manipulator, kinematic formulation methods for the serial industrial Paden‐Kahan sub‐problems, Quaternion, Screw Theory, robot manipulators. All formulation methods are based Singularity Free Inverse Kinematic. on screw theory. Screw theory is an effective way to establish a global description of rigid body and avoids 1. Introduction singularities due to the use of the local coordinates. In these three formulation methods, the first one is based on In industrial applications of robotic and automation quaternion algebra, the second one is based on dual‐ systems, it is demanded that the robot manipulators track quaternions, and the last one that is called exponential a desired trajectory precisely. This goal can be achieved mapping method is based on matrix algebra. Compared by finding a map which transforms the desired trajectory with the matrix algebra, quaternion algebra based into the motion of joints of the robot manipulators. It can solutions are more computationally efficient and they also be described as a mapping from Cartesian coordinate need less storage area. The method which is based on space to the joint space. Kinematic gives us this mapping dual‐quaternion gives the most compact and without considering the forces or torques which cause the computationally efficient solution. Paden‐Kahan sub‐ motion. Since the kinematic based solutions are easy to problems are used to derive inverse kinematic solutions. obtain and requires less number of computations 6‐DOF industrial robot manipulator’s forward and compared with dynamical equations, they are frequently inverse kinematic equations are derived using these used in the industrial robot applications. formulation methods. Simulation and experimental results are given. Several methods are used in robot kinematics and screw theory is one of the most important methods among them. www.intechweb.org Emre Sariyildiz, Eray Cakiray and Hakan Temeltas: A IntComparative J Adv Robotic Study Sy, of 2011, Three Vol. Inverse 8, No. Kinematic 5, 9-24 9 Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework Danialidis et al. compared screw theory with the most J. Funda analyzed transformation operators of screw motion common method in robot kinematics called homogenous and he found that dual operators are the best way to transformation method and they found that screw theory describe screw motion and also the dual‐quaternion is the based solution offers more compact and consistent way for most compact and efficient dual operator to express screw the robot kinematics than homogeneous transformation one displacement [14‐15]. A. Perez and J.M. McCarthy analyzed [1]. Although screw theory based solution methods have dual‐quaternion for 4‐DOF constrained robotic systems [16]. been widely used in many robotic applications for the last R. Campa et al. proposed kinematic model and control of few decades, the elements of screw theory can be traced to robot manipulators by using unit‐quaternions [17]. Finally the work of Chasles and Poinsot in the early 1800s. Using the E. Sariyildiz and H. Temeltas investigated the kinematics of theorems of Chasles and Poinsot as a starting point, Robert 6‐DOF serial industrial robot manipulators by using S. Ball developed a complete theory of screws which he quaternions in the screw theory framework and they published in 1900 [2]. In screw theory every transformation showed its superior performance over D‐H method [18]. of a rigid body or a coordinate system with respect to a Moreover authors also developed the methodology by reference coordinate system can be expressed by a screw employing dual‐quaternion operators in order to increase displacement, which is a translation by along a λ axis with a computational performance [19]. rotation by a θ angle about the same axis [3]. This description of transformation is the basis of the screw theory. In this paper, we present a comparison study for the three There are two main advantages of using screw theory for inverse kinematic formulation methods which are all based describing the rigid body kinematics. The first one is that it on screw theory. In these methods, the first one uses allows a global description of the rigid body motion that quaternions as a screw motion operator which combines a does not suffer from singularities due to the use of local unit quaternion plus a pure quaternion, the second one coordinates. The second one is that the screw theory uses the dual‐quaternion, which is the most compact and provides a geometric description of the rigid motion which efficient dual operator to express the screw displacement, greatly simplifies the analysis of mechanisms [4]. and the last one uses matrix algebra to express the screw motion. The first two methods given in [18] and [19] are Several applications of screw theory have been introduced in extensively developed in mathematical formulations and the kinematic problem. Yang and Freudenstein were the first all of these methods are analyzed in details. Additionally, to apply line transformations to spatial mechanism by using the methods are implemented into the 6‐DOF industrial quaternion algebra [5]. Yang also investigated the kinematic robot manipulator namely Stäubli RX 160L in order to of special five bar linkages using dual 3 3 orthogonal show real time performance results. Comparison results of matrices [6]. Pennock and Yang extended this method to these formulation methods are given in section VI. This robot kinematics [7]. J.M. McCarthy presented a detailed paper is also included the mathematical preliminary in research on dual 3 3 orthogonal matrices and its section II, screw theory by using matrix and quaternion application to velocity analysis using screw theory [8]. algebras in section III, the kinematic scheme of n‐DOF Defining screw motion using dual 3 3 orthogonal matrices serial robot manipulator in section IV, forward and inverse is not a compact and computationally efficient solution kinematic solutions
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