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Evgeniy Krastev



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Evgeniy Krastev


WSEAS Transactions on Systems


Print ISSN: 1109-2777
E-ISSN: 2224-2678

Volume 16, 2017

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 16, 2017



Mathematical Model for Motion Control of Redundant Robot Arms

AUTHORS: Evgeniy Krastev

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ABSTRACT: Motion planning is an essential activity in executing manipulation tasks with robot arms like weld-ing, painting or simple “pick-and-place” operations. A typical requirement for such tasks is to achieve flexibil-ity of the robot arm motion similar to that of a human hand. The objective of the here proposed mathematical model is to satisfy this requirement in path planning a robot arm motion with redundant degrees of freedom. This model provides an efficient procedure for the computation of the motion in the joints that makes the end- effector motion to trace a given geometrical curve with prescribed linear and angular velocity. The novelty of the mathematical model is the clear separation of concerns related to planning the geometrical path in task space on the one hand and on the other hand, the control of motion along this path. This guiding design princi-ple is implemented through vector space methods. It enables a new insight about identifying and processing Jacobian singularities by means of the Continuity principle. The application of the model is enabled through a detailed algorithm for computing the Jacobian, equations for kinematic path control and a heuristic procedure for handling the singularities of the Jacobian. The obtained results can be extended to non- redundant robot arms.

KEYWORDS: robot motion, kinematics, separation of concerns, redundant robot arm, continuity principle

REFERENCES:

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[3] D. Megherbi, 'Method and apparatus for controlling robot motion at and near singularities and for robot mechanical design'. USA Patent US5159249 A, 27 10 1992.

[4] S. Kucuk and Z. Bingul, 'Robot Kinematics: Forward and Inverse Kinematics,' in Industrial Robotics: Theory, Modelling and Control, S. Cubero, Ed., Pro Literatur Verlag, Germany / ARS, 2006, pp. 117- 148.

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[7] F. C. Park and K. M. Lynch, Introduction to Robotics. Mechanics, Planning and Control, Cambridge University Press, 2017.

[8] L. Lilov and G. Bojaddziev, Dynamics and Control of Manipulative Robots, Sofia: St. Kliment Ohridski University Press, 1997.

[9] G. Calafiore and L. E. Ghaoui, Optimization Models, Cambridge University Press , 2014.

[10] M. J. Mirza, M. W. Tahir and N. Anjum, 'On Singularities Computation and Classification of Redundant Robots,' in International Conference on Computing, Communication and Control Engineering (IC4E'2015), Dubai (UAE), 2015.

[11] B. Tondu, 'A Theorem on the Manipulability of Redundant Serial Kinematic Chains,' Engineering Letters, vol. 15, no. 2, p. 362, 2007.

[12] J. Solomon, Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics, CRC Press , 2015.

WSEAS Transactions on Systems, ISSN / E-ISSN: 1109-2777 / 2224-2678, Volume 16, 2017, Art. #5, pp. 36-42


Copyright © 2017 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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