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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 741351, 8 pages
The Study of Fractional Order Controller with SLAM in the Humanoid Robot
1Key Lab of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004, China
2Machanical Engineering, Yanshan University, Qinhuangdao 066004, China
3School of Engineering Sciences, Simon Fraser University, 250-13450, 102 Avenue, Surrey, BC, Canada V3T 0A3
Received 26 September 2013; Revised 15 November 2013; Accepted 17 November 2013; Published 28 January 2014
Academic Editor: Ming Li
Copyright © 2014 Shuhuan Wen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- K. J. Astrom and T. Hagglund, Advanced PID Control, ISA, USA, 2006.
- Z. Jiao and Y. Q. Chen, “Stability of fractional-order linear time-invariant systems with multiple noncommensurate orders,” Computers & Mathematics with Applications, vol. 64, no. 10, pp. 3053–3058, 2012.
- R. L. Magin, Fractional Calculus in Bioengineering, Begell House, 2006.
- R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
- I. Petráš, Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer, New York, NY, USA, 2011.
- F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, Imperial College Press, London, UK, 2010.
- J. Sabatier, O. P. Agrawal, and J. A. TenreiroMachado, Eds., Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, 2007.
- B. M. Vinagre, C. A. Monje, A. J. Caldern, and J. I. Surez, “Fractional PID controllers for industry application: a brief introduction,” Journal of Vibration and Control, vol. 13, no. 9-10, pp. 1419–1429, 2007.
- A. J. Calderón, B. M. Vinagre, and V. Feliu, “Fractional order control strategies for power electronic buck converters,” Signal Processing, vol. 86, no. 10, pp. 2803–2819, 2006.
- M. Schlegel and M. Cech, “Fractal system identification for robust control-the moment approach,” in Proceedings of the 5th International Carpathian Control Conference, pp. 1–6, AGH-UST, Krakَw, Poland, May 2004.
- V. Feliu-Batlle, R. R. Pérez, and L. S. Rodríguez, “Fractional robust control of main irrigation canals with variable dynamic parameters,” Control Engineering Practice, vol. 15, no. 6, pp. 673–686, 2007.
- F. Hongmei, S. Yu, and Z. Xiaobin, “Research on fractional order controller in servo press control system,” in Proceedings of the IEEE International Conference on Mechatronics and Automation (ICMA '07), pp. 2934–2938, August 2007.
- I. S. Jesus and J. A. Tenreiro Machado, “Fractional control of heat diffusion systems,” Nonlinear Dynamics, vol. 54, no. 3, pp. 263–282, 2008.
- M. Li, S. C. Lim, C. Cattani, and M. Scalia, “Characteristic roots of a class of fractional oscillators,” Advances in High Energy Physics, vol. 2013, Article ID 853925, 7 pages, 2013.
- M. Li, “Approximating ideal filters by systems of fractional order,” Computational and Mathematical Methods in Medicine, vol. 2012, Article ID 365054, 6 pages, 2012.
- M. Li, S. C. Lim, and S. Chen, “Exact solution of impulse response to a class of fractional oscillators and its stability,” Mathematical Problems in Engineering, vol. 2011, Article ID 657839, 9 pages, 2011.
- H. Hejazi, T. Moroney, and F. Liu, “Stability and convergence of a finite volume method for the space fractional advection-dispersion equation,” Journal of Computational and Applied Mathematics, vol. 255, pp. 684–697, 2014.
- J. Sabatier and C. Farges, “On stability of commensurate fractional order systems,” International Journal of Bifurcation and Chaos, vol. 22, no. 4, Article ID 1250084, 8 pages, 2012.
- J.-G. Lu, Y. Chen, and W. Chen, “Robust asymptotical stability of fractional-order linear systems with structured perturbations,” Computers & Mathematics with Applications, vol. 66, no. 5, pp. 873–882, 2013.
- I. Podlubny, “Fractional-order systems and -controllers,” IEEE Transactions on Automatic Control, vol. 44, no. 1, pp. 208–214, 1999.
- I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, Calif, USA, 1999.
- Ch. Lubich, “Discretized fractional calculus,” SIAM Journal on Mathematical Analysis, vol. 17, no. 3, pp. 704–719, 1986.
- I. Petras, “An adaptive fractional-order controller,” in Proceedings of the 14th IEEE International Carpathian Control Conference (ICCC '13), pp. 297–2301, Rytro, Poland, May 2013.
- I. Podlubny, “Fractional-order systems and fractional order controllers,” Technical Report UEF-03-94, Slovak Academy of Sciences. Institute of Experimental Physics, Department of Control Engineering. Faculty of Mining, University of Technology, Kosice, Slovak Republic, 1994.
- H. Durrant-Whyte and T. Bailey, “Simultaneous localization and mapping. Part I: the essential algorithms,” IEEE Robotics and Automation Magazine, vol. 13, no. 2, pp. 99–108, 2006.
- T. Bailey and H. Durrant-Whyte, “Simultaneous localization and mapping (SLAM). Part II: state of the art,” IEEE Robotics and Automation Magazine, vol. 13, no. 3, pp. 108–117, 2006.
- S. Shamsuddin, L. I. Ismail, H. Yussof, et al., “Humanoid robot NAO: review of control and motion exploration,” in Proceedings of the IEEE International Conference on Control System, Computing and Engineering (ICCSCE '11), pp. 511–5516, Penang, Malaysia, November 2011.