Trajectory tracking for robot manipulators using differential flatness
Seguimiento de trayectorias en manipuladores robóticos usando Differential Flatness
DOI:
https://doi.org/10.15446/ing.investig.v31n2.23468Keywords:
condition-based maintenance, fault detection, neuronal networks, permanent magnet synchronous motor. (en)Seguimiento de trayectorias, Manipuladores robóticos, Brazo Humano, Differential Flatness, Control PD. (es)
This paper proposes applying differential flatness to robot manipulator trajectory tracking. The trajectories for each generalised coordinate are proposed as a function and the corresponding input must be found to guarantee tracking. It is shown that the position in the generalised coordinates and their derivatives are flat inputs which, together with a PD controller, could determine (with some restrictions) manipulator movement having minimal deviation throughout its trajectory in both plane movements and in space.
Este documento propone una aplicación con Differential Flatness para el problema de seguimiento de trayectorias en manipuladores robóticos. Para cada coordenada generalizada, se proponen sus trayectorias como una función en el tiempo donde deben encontrar las entradas correspondientes para garantizar el seguimiento. Se demuestra que la posición de cada coordenada generalizada del manipulador robótico y sus correspondientes derivadas son salidas planas que, en conjunto con un controlador PD pueden determinar, con algunas restricciones, los valores de fuerza para conseguir un movimiento en el manipulador con una mínima desviación a lo largo del trayecto, tanto en movimientos planos como en el espacio.
References
Achir, A. Sueur, C., Dauphin-Tanguy, G., Bond graph and flatness- based control of a salient permanent magnetic synchronous motor., Proceedings IMenchE, Vol. 219, Part I: J. Systems and Control Engineering, 2005, pp. 461- 476.
Aguilar-Ibañez, C., Suárez-Castañón, M., Sira-Ramírez H., Control of the Chua´s System based on a Differential Flatness Approach., International Journal of Bifurcation and Chaos, Vol. 14, No. 3, 2004, pp. 1059-1069.
Barczyk, M., Lynch, A. F., Flatness-based estimated state feedback control for a rotating flexible beam: experimental results., IET Control Theory and Applications, Vol. 2, No.4, 2008, pp. 288-302
Carvajal, J. H., Modelamiento y diseño de Robots Industriales., Ediciones Unisalle, Bogotá-Colombia, 2007.
Defoort, M., Floquet, T., Kokosy, A., Perruqueth, W., Integral sliding mode control for trajectory tracking of an unicycle type mobile robot., Inregrated Computer-Aided Engineering, Vol. 13, 2006, pp.277-288.
Deligiannis V., Davrazos, G., Manesis, S., Arampatzis, T., Flatness Conservation in the N-Trailer System Equipped with a Sliding Kingpin Mechanism., Journal of Intelligent and Robotic System, Vol. 46 No. 2, 2006, pp. 151-162.
Fliess M., Lévine, J., Martin, P., Rouchon, P., Flatness and Defect of Non Liner Systems: Introductory Theory and Examples., CAS internal report A-284, January ,1994.
Franch, J., Agrawal, S.K., Design of differentially Flat Planar Space Robots: A Stepforward in their Planning and Control, Proceedings of the IEEE/RSJ Interntational Conference on Intelligente Robots and Systems, 2003, pp. 3053-3058.
Lévine, J., Analysis and Control of Non Linear Systems: A Flatness Based Approach., Springer-Verlag Berlin Heilderberg, 2009, pp.131-145.
Marguitu, D. B., Mechanics and Robot Analysis with MATLAB., Springer-Verlag London Limited, 2009, pp. 183-204.
Martin, P., Murray, R., Rouchon, P., Flat Systems., Mini-course European Control Conference, Brussels, July 1997.
Murray, R., Rathinam, M., Sluis, W., Differential Flatness of Mechanical Control Systems: A Catalog of Prototype Systems, ASME International Mechanical Engineering Congress and Expo., San Francisco, California, California, USA. November 12-17, 1995a, pp. 1-9.
Murray, R., Non Linear Control of Mechanical Systems a Lagrangian Perspective., In IFAC Symposium on Nonlinear Control Systems Design (NOLCOS), 1995b.
Rathinam, M., Differentially flat nonlinear Control Systems. Ph.D dissertation., University of California at Berkeley, Berkeley, California, USA, 1997.
Rotella F., Zambettakis, I., Comande des Systèmes par Platitude Available: http://www.techniquesingenieur.fr/book/s7450/commande-des-systemes-par-platitude.html, Site Access: August 2008, pp. 5-6.
Siciliano, B., Sciavicco, L., Villani, L., Oriolo, G., Robotics, Modeling, Planning and Control., Springer-Verlag London Limited,2009, pp. 161-189.
VanNieuwstadt, M.J.., Trajectory Generation for Nonlinear Control Systems., Technical Report CS 96-011 del Department of Mechanical Engineering, California Institute of Technology, Pasadena, California, 1997a, pp. 54-57.
Spong, M.W., On the Robust Control of Robot Manipulators., Transactions on Automatic Control of Robot Manipulators, Vol. 37 No. 11, 1992, pp. 1782-1786.
VanNieuwstadt, M.J., Trajectory Generation of Non Linear Control Systems., Ph. D. dissertation, University of California at Berkeley, Berkeley, California, USA, 1997b.
Veslin E., Slama, J., Dutra, M., Lengerke, O., Análisis cinemático de un Exoesqueleto de Partes Superiores de 7 GDL., Proceedings of II Congreso Internacional de Ingeniería Mecatrónica, Bucaramanga, Colombia, Sept. 30, Oct.1-2,2009.
Veslin E., Implementaçâo dos Sistemas diferencialmente planos para o contrôle de um manipulador robótico tipo braço humano., M.Sc. Dissertation, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil, 2010.
Wang H., Xie, Y., Adaptative Inverse Dynamics Control of Robot with Uncertain Kinematics and Dynamics., Automatica 45, 2009, pp. 2114-2119.
Dimensions
PlumX
Article abstract page views
Downloads
How to Cite
License
Copyright (c) 2011 Elkin Veslin Diaz, Jules Slama, Max Dutra, Omar Lengerke, Magda Morales Tavera

This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors or holders of the copyright for each article hereby confer exclusive, limited and free authorization on the Universidad Nacional de Colombia's journal Ingeniería e Investigación concerning the aforementioned article which, once it has been evaluated and approved, will be submitted for publication, in line with the following items:
1. The version which has been corrected according to the evaluators' suggestions will be remitted and it will be made clear whether the aforementioned article is an unedited document regarding which the rights to be authorized are held and total responsibility will be assumed by the authors for the content of the work being submitted to Ingeniería e Investigación, the Universidad Nacional de Colombia and third-parties;
2. The authorization conferred on the journal will come into force from the date on which it is included in the respective volume and issue of Ingeniería e Investigación in the Open Journal Systems and on the journal's main page (https://revistas.unal.edu.co/index.php/ingeinv), as well as in different databases and indices in which the publication is indexed;
3. The authors authorize the Universidad Nacional de Colombia's journal Ingeniería e Investigación to publish the document in whatever required format (printed, digital, electronic or whatsoever known or yet to be discovered form) and authorize Ingeniería e Investigación to include the work in any indices and/or search engines deemed necessary for promoting its diffusion;
4. The authors accept that such authorization is given free of charge and they, therefore, waive any right to receive remuneration from the publication, distribution, public communication and any use whatsoever referred to in the terms of this authorization.










