Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T23:57:55.375Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-state trajectory tracking control of a spherical robot using neurodynamics

Published online by Cambridge University Press:  06 June 2011

Yao Cai ,
Qiang Zhan  and
Caixia Yan
Yao Cai*
Affiliation:
Robotics Institute, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China
Qiang Zhan
Affiliation:
Robotics Institute, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China
Caixia Yan
Affiliation:
Robotics Institute, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

Spherical robot is a special kind of nonholonomic system that cannot be converted to chained form, which means most of the well-known control methodologies are not suitable for this system. For the trajectory tracking of BHQ-1, a spherical robot designed by our lab, a two-state trajectory tracking controller is proposed in this paper. First, the kinematic model of the robot is built using screw theory and exponential method and the controllability is proved based on the differential geometric control theory. Then to solve the two-state trajectory tracking problem of BHQ-1, a shunting model of neurodynamics and Lyapunov's direct method are combined to design a two-state trajectory tracking controller, of which the Lyapunov stability is validated. Finally, typical simulation examples, such as tracking linear, circular, and sinusoidal trajectories, are introduced to verify the effectiveness of the proposed controller. In this paper the proposed method can also be applied to the control of other spherical robots.

Keywords

Spherical RobotTrajectory TrackingNeurodynamicsKinematics ModelingNonholonomic Systems
Type
Articles
Information
Robotica , Volume 30 , Issue 2 , March 2012 , pp. 195 - 203
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Murray, R. M., Li, Z. and Sastry, S. S., A Mathematical Introduction to Robotic Manipulation (CRC Press, Boca Raton, Florida, 1994).Google Scholar
2.Li, Z. and Canny, J., “Motion of two rigid bodies with rolling constraint,” IEEE Trans. Rob. Automat. 6 (1), 62–72 (1990).CrossRefGoogle Scholar
3.Das, T. and Mukherjee, R., “Exponential stabilization of the rolling sphere,” Automatica 40(Jun), 1877–1889 (2004).CrossRefGoogle Scholar
4.Das, T. and Mukherjee, R., “Reconfiguration of a rolling sphere: A problem in evolute-involute geometry,” ASME J.Appl. Mech. 73(Jul), 590–597 (2006).CrossRefGoogle Scholar
5.Javadi, A. H. A. 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, (May 2002), pp. 3527–3533.Google Scholar
6.Bhattacharya, S. and Agrawal, S. K., “Spherical rolling robot: A design and motion planning studies,” IEEE Trans. Rob. Automat. 16(Dec), 835–839 (2000).CrossRefGoogle Scholar
7.Halme, A., Schonberg, T. and Wang, Y., “Motion Control of a Spherical Mobile Robot,” Proceedings of Advanced Motion Control, Tsu-City, Japan (1996), Vol. 1, pp. 259–264.Google Scholar
8.Halme, A., Suromela, J., Schonberg, T. and Wang, Y., “A Spherical Mobile Microrobot for Scientific Applications,” Proceedings of ASTRA96, ESTEC, Noordwijk, The Netherlands (Nov. 6–7, 1996).Google Scholar
9.Bicchi, A., Balluchi, A., Prattichizzo, D. and Andrea, G., “Introducting the ‘Sphericle’: An Experimental Testbed for Research and Teaching in Nonholonomy,” International Conference on Robotics and Automation, Albuquerque, NM, USA (Apr. 1997) Vol. 3, pp. 2620–2625.CrossRefGoogle Scholar
10.Bicchi, A. and Marigo, A., “A Local–Local Planning Algorithm for Rolling Objects,” Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Washington, USA (May 2002) Vol. 2, pp. 1759–1764.Google Scholar
11.Joshi, V. A., Banavar, R. N. and Hippalgaonkar, R., “Motion analysis of a spherical mobile robot,” Robotica 27, 243–353 (2009).CrossRefGoogle Scholar
12.Joshi, V. A., Banavar, R. N. and Hippalgaonkar, R., “Design and analysis of a spherical mobile robot,” Mechanism and Machine Theory 45 (2), 130–136 (2010).CrossRefGoogle Scholar
13.Liu, D., Sun, H. and Jia, Q., “A Family of Spherical Mobile Robot: Driving Ahead Motion Control by Feedback Linearization,” 2nd International Symposium on Systems and Control in Aerospace and Astronautics, Shenzhen, China, (Dec. 12, 2008) pp. 1–6, 10–12.Google Scholar
14.Zhan, Q., Jia, C., Ma, X., Zhai, Y., “Mechanism design and motion analysis of a spherical mobile robot,” Chinese J. Mech. Eng. 18 (4), 542–545 (2005).CrossRefGoogle Scholar
15.Yang, H., “Tracking Control of a Nonholonomic Mobile Robot by Hybrid Feedback and Neural Dynamics Techniques,” Master's thesis, University of Guelph for Engineering (2004).Google Scholar
16.Hodgkin, A. L. and Huxley, A. F., “A quantitative description of membrane current and its application to conduction and excitation in nerve,” J. Phys. 117, 500–544 (1952).Google ScholarPubMed
17.Grossberg, S., “Nonlinear neural networks: Principles, mechanism and architectures,” Neural Netw. 1, 17–61 (1988).CrossRefGoogle Scholar
18.Isidori, A., Nonlinear Control Systems, 3rd ed (Springer, Berlin, 1955).Google Scholar