Abstract
In this paper, the collocated virtual holonomic constraints for the underactuated mechanical system are represented in a special canonical form using its Hamiltonian description. This form is used to provide an alternative, backstepping based, algorithm how to impose these constraints. Its robustness is illustrated by simulated swinging up the mechanical four link chain with precisely unknown masses of its links.
Supported by the Czech Science Foundation Grant No. 17-04682S.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Anderle, M., Čelikovský, S.: Sustainable Acrobot walking based on the swing phase exponentially stable tracking. In: Proceedings of the ASME 2010 Dynamic Systems and Control Conference, pp. 1/8–8/8. ASME, Cambridge (2010)
Anderle, M., Čelikovský, S., Henrion, D., Zikmund, J.: Advanced LMI based analysis and design for Acrobot walking. Int. J. Control 83(8), 1641–1652 (2010)
Bortoff, S., Spong, M.: Pseudolinearization of the Acrobot using spline functions. In: Proceedings of the 31st IEEE Conference on Decision and Control, vol. 1, pp. 593–598 (1992)
Cambrini, L., Chevallereau, C., Moog, C., Stojic, R.: Stable trajectory tracking for biped robots. In: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, pp. 4815–4820 (2000)
Chevallereau, C., Bessonnet, G., Abba, G., Aoustin, Y.: Bipedal Robots: Modeling, Design and Walking Synthesis. Wiley-ISTE, Hoboken (2009)
Grizzle, J., Chevalereau, C., Sinnet, R., Ames, A.: Models, feedback control and open problems of 3D bipedal robotic walking. Automatica 50(8), 1955–1988 (2014)
Grizzle, J., Moog, C., Chevallereau, C.: Nonlinear control of mechanical systems with an unactuated cyclic variable. IEEE Trans. Autom. Control 50(5), 559–576 (2005)
Kozlov, V.V.: The dynamics of systems with servoconstraints. I. Regul. Chaotic Dyn. 20(3), 205–224 (2015)
Maggiori, M., Consolini, L.: Virtual holonomic constraints for Euler-Lagrange systems. IEEE Trans. Autom. Control 58(4), 181–185 (2013)
Mohammadi, A., Maggiore, M., Consolini, L.: When is a Lagrangian system with virtual holonomic constraints Lagrangian? In: Proceedings of the 9th IFAC Symposium NOLCOS, Toulouse, France, pp. 512–517 (2013)
Olfati-Saber, R.: Normal forms for underactuated mechanical systems with symmetry. IEEE Trans. Autom. Control 47(2), 305–308 (2002)
Čelikovský, S.: Flatness and realization of virtual holonomic constraints. In: Proceedings of the 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, Lyon, France, pp. 25–30 (2015)
Čelikovský, S., Anderle, M.: Collocated virtual holonomic constraints in Lagrangian systems and their application. In: American Control Conference 2016, Boston, MA, USA, pp. 6030–6035 (2016)
Čelikovský, S., Anderle, M.: Hybrid invariance of the collocated virtual holonomic constraints and its application in underactuated walking. In: IFAC-PapersOnLine, IFAC NOLCOS 2016, Monterey, CA, USA, vol. 49–18, pp. 802–807 (2016)
Čelikovský, S., Anderle, M., Moog, C.: Embedding the Acrobot into a general underactuated n-link with application to novel walking design. In: Proceedings of the Europen Control Conference 2013, Zurich, Switzerland, pp. 682–689 (2013)
Westervelt, E., Grizzle, J., Chevallereau, C., Choi, J., Morris, B.: Feedback Control of Dynamic Bipedal Robot Locomotion. CRC Press, Boca Raton (2007)
Zikmund, J., Čelikovský, S., Moog, C.: Nonlinear control design for the Acrobot. In: Preprints of the 3rd IFAC Symposium on Systems Structure Control, Foz do Iguassu, Brazil (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Čelikovský, S., Anderle, M. (2018). On the Hamiltonian Approach to the Collocated Virtual Holonomic Constraints in the Underactuated Mechanical Systems. In: Duy, V., Dao, T., Zelinka, I., Kim, S., Phuong, T. (eds) AETA 2017 - Recent Advances in Electrical Engineering and Related Sciences: Theory and Application. AETA 2017. Lecture Notes in Electrical Engineering, vol 465. Springer, Cham. https://doi.org/10.1007/978-3-319-69814-4_53
Download citation
DOI: https://doi.org/10.1007/978-3-319-69814-4_53
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-69813-7
Online ISBN: 978-3-319-69814-4
eBook Packages: EngineeringEngineering (R0)