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Reduced order modelling based control of two wheeled mobile robot

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Abstract

This paper proposes a novel technique to design a pre-specified structure controller for balancing control of two wheeled mobile robot via reduced order modelling using cuckoo search algorithm. As the two wheeled mobile robot is an unstable system with various uncertainties and the controllers, available in the literature, comes up with higher order, the overall system becomes complex from analysis and manufacturing point of view. Therefore, in this paper, a lower order pre-specified structure controller is designed which is efficient enough to handle uncertain dynamics. The results of proposed controllers are compared with the results of controller designed by genetic algorithm, particle swarm optimization, Schur analysis, balanced truncation, modal truncation and conventional PD controllers. It is revealed that the proposed controller exhibit better performance comparatively. The performance of the higher and lower order controllers is also analysed with perturbed two wheeled mobile robot in terms of time response specifications and performance indices such as integral square error, integral absolute error and integral time absolute error.

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References

  • Akesson, J., Blomdell, A., & Braun, R. (2006). Design and control of yaip—An inverted pendulum on two wheels robot. In Proceedings of the IEEE international conference on control applications (pp. 2178–2183).

  • Alarfaj, M., & Kantor, G. (2010). Centrifugal force compensation of a two-wheeled balancing robot. In 11th international conference on control, automation, robotics and vision, ICARCV 2010 (pp. 2333–2338).

  • Bernstein, D. S., & Haddad, W. M. (1989). LQG control with an H performance bound: A Riccati equation approach. IEEE Transactions on Automatic Control, 34(3), 293–305.

    Article  Google Scholar 

  • Beznos, A. V., Formal’sky, A. M., Gurfinkel, E. V., Jicharev, D. N., Lensky, A. V., Savitsky, K. V., & Tchesalin, L. S. (1998). Control of autonomous motion of two-wheel bicycle with gyroscopic stabilisation. In Proceedings of IEEE international conference on robotics and automation (Cat. No.98CH36146) (Vol. 3).

  • Brown, C. T., Liebovitch, L. S., & Glendon, R. (2007). Lévy flights in Dobe Ju/hoansi foraging patterns. Human Ecology, 35(1), 129–138.

    Article  Google Scholar 

  • Bui, T. T., & Parnichkun, M. (2008). Balancing control of Bicyrobo by particle swarm optimization based structure-specified mixed \({H_2}/{H_\infty }\) control. International Journal of Advanced Robotic Systems, 5(4), 395–402.

    Google Scholar 

  • Bui, T. T., Parnichkun, M., & Le, C. H. (2010). Structure-specified \({H_2}/{H_\infty }\) loop shaping control for balancing of bicycle robots: A particle swarm optimization approach. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 224(7), 857–867.

    Google Scholar 

  • Butler, L. J. & Bright, G. (2008). Feedback control of a self-balancing materials handling robot. In 2008 10th international conference on control, automation, robotics and vision, ICARCV 2008 (pp. 274–278).

  • Chang, Y. F. (2005). Mixed \({H_2}/{H_\infty }\) optimization approach to gap control on EDM. Control Engineering Practice, 13(1), 95–104.

    Article  Google Scholar 

  • Chen, B. S., Cheng, Y. M., & Lee, C. H. (1995). Genetic approach to mixed \({H_2}/{H_\infty }\) optimal PID control. IEEE Control Systems Magazine, 15(5), 51–60.

    Article  Google Scholar 

  • Coelho, V., Liew, S., Stol, K., & Liu, G. (2008). Development of a mobile two wheel balancing platform for autonomous applications. In 15th international conference on mechatronics and machine vision in practice (M2VIP08), Auckland.

  • Das, T., & Kar, I. N. (2006). Design and implementation of an adaptive fuzzy logic-based controller for wheeled mobile robots. IEEE Transactions on Control Systems Technology, 14(3), 501–510.

    Article  Google Scholar 

  • Gallaspy, J. M. (1999). Gyroscopic stabilization of an unmanned bicycle. M.S. Thesis, Auburn University.

  • Grasser, F., D’Arrigo, A., Colombi, S., & Rufer, A. C. (2002). JOE: A mobile, inverted pendulum. IEEE Transactions on Industrial Electronics, 49(1), 107–114.

    Article  Google Scholar 

  • Ha, Y., & Yuta, S. (1994). Trajectory tracking control for navigation of self-contained mobile inverse pendulum. In Proceedings of IEEE/RSJ international conference on intelligent robots and systems (IROS’94), Munich (Vol. 3, pp. 1875–1882).

  • Hatakeyama, N., & Shimada, A. (2008). Movement control using zero dynamics of two-wheeled inverted pendulum robot. In International workshop on advanced motion control, AMC (Vol. 1, pp. 38–43).

  • Hess, R. A., Moore, J. K., & Hubbard, M. (2012). Modeling the manually controlled bicycle. IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, 42(3), 545–557.

    Article  Google Scholar 

  • Ho, S. J., Ho, S. Y., Hung, M. H., Shu, L. S., & Huang, H. L. (2005). Designing structure-specified mixed \({H_2}/{H_\infty }\) optimal controllers using an intelligent genetic algorithm IGA. IEEE Transactions on Control Systems Technology, 13(6), 1119–1124.

    Article  Google Scholar 

  • Ho, S. J., Ho, S. Y., & Shu, L. S. (2004). OSA: Orthogonal simulated annealing algorithm and its application to designing mixed \({H_2}/{H_\infty }\) optimal controllers. IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans., 34(5), 588–600.

    Article  Google Scholar 

  • Hummer, G., & Szabo, A. (2015). Optimal dimensionality reduction of multistate kinetic and Markov–State models. The Journal of Physical Chemistry-B, 119(29), 9029–9037.

    Article  Google Scholar 

  • Humphries, N. E., Weimerskirch, H., Queiroz, N., Southall, E. J., & Sims, D. W. (2012). Foraging success of biological Lévy flights recorded in situ. Proceedings of the National Academy of Sciences, 109(19), 7169–7174.

    Article  Google Scholar 

  • Kausar, Z., Stol, K., & Patel, N. (2012a). Nonlinear control design using Lyapunov function for two-wheeled mobile robots. In 19th international conference on mechatronics and machine vision in practice (M2VIP) (pp. 123–128).

  • Kausar, Z., Stol, K., & Patel, N. (2012b). The effect of terrain inclination on performance and the stability region of two-wheeled mobile robots. International Journal of Advanced Robotic Systems, 9(218), 1–11.

    Google Scholar 

  • Kausar, Z., Stol, K., & Patel, N. (2013). Lyapunov function-based non-linear control for two-wheeled mobile robots. International Journal of Biomechatronics and Biomedical Robotics, 2(2/3/4), 172–183.

    Article  Google Scholar 

  • Keo, L., Yoshino, K., Kawaguchi, M., & Yamakita, M. (2011). Experimental results for stabilizing of a bicycle with a flywheelbalancer. In Proceedings of IEEE international conference onrobotics and automation, Shanghai, China (pp. 6150–6155).

  • Khargonekar, P. P., & Rotea, M. A. (1991). Mixed \({H_2}/{H_\infty }\) control: A convex optimization approach. IEEE Transactions on Automatic Control, 36(7), 824–837.

    Article  Google Scholar 

  • Kim, Y., Kim, S. H., & Kwak, Y. K. (2005). Dynamic analysis of a nonholonomic two-wheeled inverted pendulum robot. Journal of Intelligent and Robotic Systems: Theory and Applications, 44(1), 25–46.

    Article  Google Scholar 

  • Kim, Y., Kim, S. H., & Kwak, Y. K. (2006). Improving driving ability for a two-wheeled inverted-pendulum-type autonomous vehicle. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 220, 65–175.

    Google Scholar 

  • Kocaturk, B. (2015). Motion control of wheeled mobile robots. Interdisciplinary Description of Complex Systems, 13(1), 41–47.

    Article  Google Scholar 

  • Krohling, R. A. (1998). Genetic algorithms for synthesis of mixed \({H_2}/{H_\infty }\) fixed-structure controllers. In Proceedings of the 1998 IEEE international symposium on intelligent control (ISIC) held jointly with IEEE international symposium on computational intelligence in robotics and automation (CIRA) Intell.

  • Lee, S. L. S., & Ham, W. H. W. (2002). Self stabilizing strategy in tracking control of unmanned electric bicycle with mass balance. IEEE/RSJ international conference on intelligent robots and systems (Vol. 3).

  • Liao, Y., & Ming, L. (2010). The design of two-wheel mobile platform. In 2010 international conference on intelligent computation technology and automation, ICICTA 2010 (Vol. 3, pp. 784–787).

  • Liu, Y., & Anderson, B. D. O. (1989). Singular perturbation approximation of balanced systems. International Journal of Control, 50(4), 1379–1405.

    Article  Google Scholar 

  • Martínez, R., Castillo, O., & Aguilar, L. T. (2009). Optimization of interval type-2 fuzzy logic controllers for a perturbed autonomous wheeled mobile robot using genetic algorithms. Information Sciences, 179(13), 2158–2174.

    Article  Google Scholar 

  • Moore, B. C. (1981). Principal component analysis in linear systems: Controllability, observability, and model reduction. IEEE Transactions on Automatic Control, 26(1), 17–32.

    Article  Google Scholar 

  • Nasir, K., Nor, A., Ahmad, M. A., Ghazali, R., & Pakheri, N. S. (2011). Performance comparison between fuzzy logic controller (FLC) and pid controller for a highly nonlinear two-wheels balancing robot. In Proceedings—1st international conference on informatics and computational intelligence, ICI 2011 (pp. 176–181).

  • Nguyen, C. H., Vu, K. N., & Dao, D. H. (2013). Applying order reduction model algorithm for balancing control problems of two-wheeled mobile robot. In 8th IEEE conference on industrial electronics and applications (ICIEA) (pp. 1302–1307).

  • Rotea, M. A., & Khargonekar, P. P. (1991). \(H_2\) optimal control with an H constraint: The state feedback case. Automatica, 27(2), 301–316.

    Article  Google Scholar 

  • Sambariya, D. K., & Gyanendra, A. (2016). High order diminution of LTI system using stability equation method. British Journal of Mathematics & Computer Science, 13(5), 1–15.

    Google Scholar 

  • Scherer, C. W. (1995). Multiobjective \({H_2}/{H_\infty }\) control. IEEE Transactions on Automatic Control, 40(6), 1054–1062.

    Article  Google Scholar 

  • Sikander, A., & Prasad, R. (2015a). A novel order reduction method using Cuckoo search algorithm. IETE Journal of Research, 61(2), 83–90.

    Article  Google Scholar 

  • Sikander, A., & Prasad, R. (2015b). Linear time-invariant system reduction using a mixed methods approach. Applied Mathematical Modelling, 39(16), 4848–4858.

    Article  Google Scholar 

  • Sikander, A., & Prasad, R. (2015c). Soft computing approach for model order reduction of linear time invariant systems. Circuits, Systems, and Signal Processing, 34(11), 3471–3487.

  • Suprapto, S. (2006). Development of a gyroscopic unmanned bicycle. Technical report, M.Eng. Thesis, Asian Institute of Technology, Thailand.

  • Takahashi, Y., Ishikawa, N., & Hagiwara, T. (2001). Inverse pendulum controlled two wheel drive system. SICE 2001. Proceedings of the 40th SICE annual conference. International session papers (IEEE Cat. No.01TH8603).

  • Takei, T., Imamura, R., & Yuta, S. (2009). Baggage transportation and navigation by a wheeled inverted pendulum mobile robot. IEEE Transactions on Industrial Electronics, 56(10), 3985–3994.

    Article  Google Scholar 

  • Tanaka, Y., & Murakami, T. (2004). Self sustaining bicycle robot with steering controller. In The 8th IEEE international workshop on advanced motion control, 2004. AMC ’04.

  • Vishwakarma, C. B., & Prasad, R. (2014). Time domain model order reduction using Hankel matrix approach. Journal of the Franklin Institute, 351, 3445–3456.

    Article  Google Scholar 

  • Viswanathan, G. M. (2010). Fish in Levy-flight Foraging. Nature, 465, 1018–1019.

    Article  Google Scholar 

  • Yamada, H. S., & Ikeda, K. S. (2014). A numerical test of Padé approximation for some functions with singularity. International Journal of Computational Mathematics, 2014, 1–17.

  • Yang, X. S., & Deb, S. (2008). Nature-inspired metaheuristic algorithms. Bristol: Luniver Press.

    Google Scholar 

  • Yang, X. S., & Deb, S. (2009). Engineering optimisation by cuckoo search. International Journal of Mathematical Modelling and Numerical Optimisation, 1, 330–343.

    Article  Google Scholar 

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Correspondence to Afzal Sikander.

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Sikander, A., Prasad, R. Reduced order modelling based control of two wheeled mobile robot. J Intell Manuf 30, 1057–1067 (2019). https://doi.org/10.1007/s10845-017-1309-3

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