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Modeling and control of a spherical rolling robot: a decoupled dynamics approach

Published online by Cambridge University Press:  08 August 2011

Erkan Kayacan ,
Zeki Y. Bayraktaroglu  and
Wouter Saeys
Erkan Kayacan*
Affiliation:
BIOSYST—MeBioS, Faculty of Bioscience Engineering, KU Leuven, Kasteelpark Arenberg 30, B-3001 Leuven, Belgium. E-mail: wouter.saeys@biw.kuleuven.be
Zeki Y. Bayraktaroglu
Affiliation:
Department of Mechanical Engineering, Istanbul Technical University, 34437 Istanbul, Turkey. E-mail: zeki.bayraktaroglu@itu.edu.tr
Wouter Saeys
Affiliation:
BIOSYST—MeBioS, Faculty of Bioscience Engineering, KU Leuven, Kasteelpark Arenberg 30, B-3001 Leuven, Belgium. E-mail: wouter.saeys@biw.kuleuven.be
*
*Corresponding author. E-mail: erkan.kayacan.@biw.kuleuven.be
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Summary

This paper presents the results of a study on the dynamical modeling, analysis, and control of a spherical rolling robot. The rolling mechanism consists of a 2-DOF pendulum located inside a spherical shell with freedom to rotate about the transverse and longitudinal axis. The kinematics of the model has been investigated through the classical methods with rotation matrices. Dynamic modeling of the system is based on the Euler–Lagrange formalism. Nonholonomic and highly nonlinear equations of motion have then been decomposed into two simpler subsystems through the decoupled dynamics approach. A feedback linearization loop with fuzzy controllers has been designed for the control of the decoupled dynamics. Rolling of the controlled mechanism over linear and curvilinear trajectories has been simulated by using the proposed decoupled dynamical model and feedback controllers. Analysis of radius of curvature over curvilinear trajectories has also been investigated.

Keywords

Spherical rolling robotDecoupled dynamicsFeedback linearization
Type
Articles
Information
Robotica , Volume 30 , Issue 4 , July 2012 , pp. 671 - 680
Copyright
Copyright © Cambridge University Press 2011

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References

1.Bicchi, A., Balluchi, A., Prattichizzo, D. and Gorelli, A., “Introducing the Sphericle: An Experimental Testbedfor Research and Teaching in Nonholonomy,” Proceedings of the IEEE International Conference on Robotics and Automation, Albuquerque, NM, USA (1997) vol. 3, pp. 2620–2625.CrossRefGoogle Scholar
2.Alves, J. and Dias, J., “Design and control of a spherical mobile robot,” Proc. Inst. Mech. Eng. Part I: J. Syst. Control Eng. 217, 457–467 (2003).Google Scholar
3.Camicia, C., Conticelli, F. and Bicchi, A., “Nonholonomic Kinematics and Dynamics of the Sphericle,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Takamatsu, Japan (2000) vol. 1, pp. 805–810.Google Scholar
4.Halme, A., Schonberg, T. and Wang, Y., “Motion Control of a Spherical Mobile Robot,” Proceedings of the Fourth International Workshop on Advanced Motion Control, Albuquerque, NM, USA (1996) vol. 1, pp. 259–264.CrossRefGoogle Scholar
5.Javadi, A. A. H. and Mojabi, P., “Introducing August: A Novel Strategy for an Omnidirectional Spherical Rolling Robot,” Proceedings of the IEEE International Conference on Robotics and Automation, Washington DC, USA (2002) vol. 4, pp. 3527–3533.Google Scholar
6.Javadi, A. A. H. and Mojabi, P., “Introducing glory: A novel strategy for an omnidirectional spherical rolling robot,” J. Dyn. Syst. Meas. Control 126, 678–683 (2004).CrossRefGoogle Scholar
7.Mukherjee, R., Minor, M. A. and Pukrushpan, J. T., “Simple Motion Planning Strategies for Spherobot: A Spherical Mobile Robot,” Proceedings of the 38th IEEE Conference on Decision and Control, Washington DC, USA (1999) vol. 3, pp. 2132–2137.Google Scholar
8.Ming, Y., Zongquan, D., Xinyi, Y. and Weizhen, Y., “Introducing Hit Spherical Robot: Dynamic Modeling and Analysis Based on Decoupled Subsystem,” Proceedings of the IEEE International Conference on Robotics and Biomimetics, Harbin, China (2006), pp. 181–186.Google Scholar
9.Joshi, V. A. and Banavar, R. N., “Motion analysis of a spherical mobile robot,” Robotica 27, 343–353 (2009).CrossRefGoogle Scholar
10.Joshi, V. A., Banavar, R. N. and Hippalgaonkar, R., “Design and analysis of a spherical mobile robot,” Mech. Mach. Theory 45, 130–136 (2010).CrossRefGoogle Scholar
11.Bhattacharya, S. and Agrawal, S. K., “Spherical rolling robot: A design and motion planning studies,” IEEE Trans. Robot. Autom. 16, 835–839 (2000).CrossRefGoogle Scholar
12.Bhattacharya, S. and Agrawal, S. K., “Design, Experiments and Motion Planning of a Spherical Rolling Robot,” Proceedings of the International Conference on Robotics and Automation, San Francisco, CA, USA (2000) vol. 2, pp. 1207–1212.Google Scholar
13.Rosen, A., “Modified lagrange method to analyze problems of sliding and rolling,” J. Appl. Mech. 67, 697–704 (2000).CrossRefGoogle Scholar
14.Bloch, A. M., Nonholonomic Mechanics and Control (Springer, New York, USA, 2004).Google Scholar
15.Qiang, Z., Zengbo, L. and Yao, C., “A back-stepping based trajectory tracking controller for a non-chained nonholonomic spherical robot,” Chin. J. Aeronaut. 21, 472–480 (2008).CrossRefGoogle Scholar
16.Zhuang, W., Liu, X., Fang, C. and Sun, H., “Dynamic Modeling of a Spherical Robot with Arms by Using Kane's Method,” Proceedings of the Fourth International Conference on Natural Computation, Beijing, China (2008) vol. 4, pp. 373–377.Google Scholar
17.Gonzalez, L. A., “Design, modelling and control of an autonomous underwater vehicle,” Ph.D. dissertation, The University of Western Australia (Oct. 2004).Google Scholar
18.Kennedy, J., “Decoupled Modelling and Controller Design for the Hybrid Autonomous Underwater Vehicle: Maco,” Ph.D. Dissertation (Victoria, Canada: University of Victoria, 2002).Google Scholar
19.Sienel, W., “Robust Decoupling for Active Car Steering Holds for Arbitrary Dynamic Tire Characteristics,” Proceedings of the Third European Control Conference, Rome, Italy (1995) pp. 744–748.Google Scholar
20.Ackermann, J. and Bunte, T., “Handling Improvement for Robustly Decoupled Car Steering Dynamics,” Proceedings of the Fourth IEEE Mediterranean Symposium on New Directions in Control and Automation, Materne, Krete, Greece (1996) pp. 83–88.Google Scholar
21.Nakajima, R., Tsubouchi, T., Yuta, S. and Koyanagi, E., “A Development of a New Mechanism of an Autonomous Unicycle,” Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robots and Systems, Grenoble, France (1997) vol. 2, pp. 906–912.Google Scholar
22.Schoonwinkel, A., “Design and Test of a Computer Stabilized Unicycle,” Ph.D. Dissertation (Stanford, CA, USA: University of Stanford, 1987).Google Scholar
23.Miklosovic, R. and Gao, Z., “A Dynamic Decoupling Method for Controlling High Performance Turbofan Engines,” Proceedings of the 16th IFAC World Congress, Prague, Czech Republic (2005).Google Scholar
24.Au, K. W. and Xu, Y., “Decoupled Dynamics and Stabilization of Single Wheel Robot,” Proceedings of 1999 IEEE/RSJ International Conference on Intelligent Robots and Systems, Kyongju, Korea (1999) vol. 1, pp. 197–203.Google Scholar
25.Lemos, N. A., “Nonholonomic constraints and voronec's equations,” arXiv:physics/0306078v1 [physics.ed-ph] (Jun. 2003).Google Scholar
26.Hand, L. N. and Finch, J. D., Analytical Mechanics (Cambridge University Press, Cambridge, 1998).CrossRefGoogle Scholar