Abstract
This paper considers recursive solving methods in the control of modular and reconfigurable robot systems. The focus lies on the end-point accuracy and recursive methods for its improvement. The modeling of the robot systems under consideration is done by the Projection Equation in Subsystem representation. Due to gear elasticities and the lack of position sensors at the gearbox output shaft, deflections of the end-point cannot be compensated by standard PD motor control. Therefore, a novel approach is presented in this contribution to correct the resulting position errors of the end-points of the robot systems. This proposed method enables to do a flat parameterization of such elastically modeled systems in a recursive manner, which is contrasted to the generally used non-recursive exact feed-forward linearization method in minimal form for such under-actuated systems.
The ability to do the computation in such a recursive way offers the possibility to do the calculations systems for systems with many degrees-of-freedom (DOF) as well, where standard analytical methods reach their limits. And for modular systems, it is applicable as well. For validation, the proposed method is implemented for a robot arm with seven joints and simulation results are presented.
Similar content being viewed by others
Notes
Schunk GmbH & Co. KG: www.schunk.com.
Maple: www.maplesoft.com.
Bernecker & Rainer Industrie Elektronik Ges.m.b.H.: www.br-automation.com.
References
Blajer, W., Kolodziejczyk, K.: Modeling of underactuated mechanical systems in partly specified motion. J. Theor. Appl. Mech. 46(2), 383–394 (2008)
Bremer, H.: On the use of nonholonomic variables in robotics. In: Guran, A., Belayev, A. (eds.) Selected Topics in Structronics and Mechatronic Systems, pp. 1–48. World Scientific, Singapore (2003)
Bremer, H.: Elastic Multibody Dynamics—A Direct Ritz Approach. Springer, Berlin (2008)
Bremer, H., Pfeiffer, F.: Elastische Mehrkörpersysteme. Teubner Studienbücher, Stuttgart (1992)
Featherstone, R.: The calculation of robot dynamics using articulated-body inertias. Int. J. Robot. Res. 2(1), 13–30 (1983)
De Luca, A., Book, W.: Robots with flexible elements. In: Siciliano, B., Khatib, O. (eds.) Handbook of Robotics, pp. 287–320. Springer, Berlin (2008)
De Luca, A.: Decoupling and feedback linearization of robots with mixed rigid/elastic joints. Int. J. Robust Nonlinear Control Res. 8, 965–977 (1998)
Featherstone, R.: Rigid Body Dynamics Algorithms. Springer, New York (2008)
Fliess, M., Lévine, J., Martin, Ph., Rouchon, P.: On differentially flat nonlinear systems. In: Proc. IFAC-Symposium (NOLCOS’92), Bordeaux, pp. 408–412 (1992)
Fliess, M., Lévine, J., Martin, P., Rouchon, P.: Flatness and defect of non-linear systems: introductory theory and examples. Int. J. Control 61(6), 1327–1361 (1995)
Gattringer, H.: Starr-elastische Robotersysteme: Theorie und Anwendungen. Springer, Berlin (2011)
Gattringer, H., Bremer, H., Kastner, M.: Efficient dynamic modeling for rigid multi-body systems with contact and impact. Acta Mech. 219, 111–128 (2011)
Höbarth, W.: Modellierung, Steuerung und Regelung eines strukturelastischen Leichtbauroboters. Ph.D. thesis, Johannes Kepler University Linz (2010)
Rothfuss, R., Rudolph, J., Zeitz, M.: Flachheit: Ein neuer Zugang zur Steuerung und Regelung nichtlinearer Systeme. Automatisierungstechnik 45, 517–525 (1997)
Staufer, P., Gattringer, H.: State estimation on flexible robots using accelerometers and angular rate sensors. Mechatronics 22(8), 1043–1049 (2012)
Acknowledgements
Support of the present work in the framework of the peer-reviewed Austrian Center of Competence in Mechatronics (ACCM) is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gattringer, H., Oberhuber, B., Mayr, J. et al. Recursive methods in control of flexible joint manipulators. Multibody Syst Dyn 32, 117–131 (2014). https://doi.org/10.1007/s11044-013-9391-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11044-013-9391-6