Journal of Automation and Control
ISSN (Print): 2372-3033 ISSN (Online): 2372-3041 Website: http://www.sciepub.com/journal/automation Editor-in-chief: Santosh Nanda
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Journal of Automation and Control. 2016, 4(2), 10-14
DOI: 10.12691/automation-4-2-1
Open AccessSpecial Issue

Base Space of Nonholonomic System

Tomáš Lipták1, , Michal Kelemen1, Alexander Gmiterko1, Ivan Virgala1 and Ľubica Miková1

1Department of Mechatronics, Faculty of Mechanical Engineering, Technical University of Košice, Košice, Slovakia

Pub. Date: December 14, 2016

Cite this paper:
Tomáš Lipták, Michal Kelemen, Alexander Gmiterko, Ivan Virgala and Ľubica Miková. Base Space of Nonholonomic System. Journal of Automation and Control. 2016; 4(2):10-14. doi: 10.12691/automation-4-2-1

Abstract

The article deals with the issue of use of geometric mechanics tools at modelling nonholonomic systems. The introductory part of article contains theory of geometric mechanics that we use at creating mathematical model of nonholonomic locomotion system with undulatory movement. Further it contains the determination of reconstruction equation for three-link snake-like robot where we consider ideal source of velocity. The relation between changes of shape and position variables was expressed using the local connection. After determination of controllability of kinematic snake, in last part we created reduced base dynamic equations in case when base variables do not represent ideal source of velocity.

Keywords:
reconstruction equation connection reduced base dynamic equation reduced Lagrangian snake-like robot

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References:

[1]  HU D., NIRODY J., SCOTT T., SHELEY M.: The mechanics of slithering locomotion, Proceedings of the National Academy of Sciences, USA 106 (2009), pp. 10081-10085.
 
[2]  SHAPARE A., WILCZEK F.: Geometry of self-propulsion at low Reynolds number, Journal of Fluid Mechanics 198 (1989) 557-585.
 
[3]  MURRAY R., SASTRY S.: Nonholonomic motion planning: steering using sinusoids, IEEE Transactions on Automatic Control, Jan 1993.
 
[4]  KELLY S. D., MURRAY R. M.: Geometric phases and locomotion, Journal of Robotic Systems, vol. 12(6), June 1995, pp. 417-431.
 
[5]  OSTROWSKI J.: The Mechanics and Control of Undulatory Robotic Locomotion, The dissertation thesis, California Institute of Technology Pasadena, September 19, 1995.
 
[6]  OSTROWSKI J.: Computing reduced equations for robotic systems with constraints and symmetries. In: IEEE Transactions on Robotics and Automation, vol. 15, No. 1, Feb 1999.