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 Regul. Chaotic Dyn., 2017, Volume 22, Issue 3, Pages 226–238 (Mi rcd253)

Adaptive Estimation of Nonlinear Parameters of a Nonholonomic Spherical Robot Using a Modified Fuzzy-based Speed Gradient Algorithm

Mehdi Roozegara, Mohammad J. Mahjoobb, Moosa Ayatic

a Centre for Intelligent Machines (CIM), Department of Mechanical Engineering, McGill University, 817 Sherbrooke St. West, Montréal, QC H3A 0C3, Canada
b Centre for Mechatronics and Intelligent Machines, School of Mechanical Engineering, University of Tehran, Kargar St. North, Tehran, Iran
c School of Mechanical Engineering, University of Tehran, Kargar St. North, Tehran, Iran

Abstract: This paper deals with adaptive estimation of the unknown parameters and states of a pendulum-driven spherical robot (PDSR), which is a nonlinear in parameters (NLP) chaotic system with parametric uncertainties. Firstly, the mathematical model of the robot is deduced by applying the Newton–Euler methodology for a system of rigid bodies. Then, based on the speed gradient (SG) algorithm, the states and unknown parameters of the robot are estimated online for different step length gains and initial conditions. The estimated parameters are updated adaptively according to the error between estimated and true state values. Since the errors of the estimated states and parameters as well as the convergence rates depend significantly on the value of step length gain, this gain should be chosen optimally. Hence, a heuristic fuzzy logic controller is employed to adjust the gain adaptively. Simulation results indicate that the proposed approach is highly encouraging for identification of this NLP chaotic system even if the initial conditions change and the uncertainties increase; therefore, it is reliable to be implemented on a real robot.

Keywords: nonholonomic spherical robot, adaptive estimation, nonlinear in parameters, speed gradient method; fuzzy logic controller, Newton–Euler strategy

DOI: https://doi.org/10.1134/S1560354717030030

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Bibliographic databases:

Document Type: Article
MSC: 93E10, 37J60, 70E18, 70F25, 70E55, 93C42
Accepted:28.04.2017
Language: English

Citation: Mehdi Roozegar, Mohammad J. Mahjoob, Moosa Ayati, “Adaptive Estimation of Nonlinear Parameters of a Nonholonomic Spherical Robot Using a Modified Fuzzy-based Speed Gradient Algorithm”, Regul. Chaotic Dyn., 22:3 (2017), 226–238

Citation in format AMSBIB
\Bibitem{RooMahAya17} \by Mehdi Roozegar, Mohammad J. Mahjoob, Moosa Ayati \paper Adaptive Estimation of Nonlinear Parameters of a Nonholonomic Spherical Robot Using a Modified Fuzzy-based Speed Gradient Algorithm \jour Regul. Chaotic Dyn. \yr 2017 \vol 22 \issue 3 \pages 226--238 \mathnet{http://mi.mathnet.ru/rcd253} \crossref{https://doi.org/10.1134/S1560354717030030} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3658422} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000402746300003} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85020190662} 

• http://mi.mathnet.ru/eng/rcd253
• http://mi.mathnet.ru/eng/rcd/v22/i3/p226

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Roozegar M., Ayati M., Mahjoob M.J., “Mathematical Modelling and Control of a Nonholonomic Spherical Robot on a Variable-Slope Inclined Plane Using Terminal Sliding Mode Control”, Nonlinear Dyn., 90:2 (2017), 971–981
2. Ivanova T.B. Kilin A.A. Pivovarova E.N., “Controlled Motion of a Spherical Robot With Feedback. i”, J. Dyn. Control Syst., 24:3 (2018), 497–510
3. Jahanshahi H., Sari N.N., Viet-Thanh Pham, Alsaadi F.E., Hayat T., “Optimal Adaptive Higher Order Controllers Subject to Sliding Modes For a Carrier System”, Int. J. Adv. Robot. Syst., 15:3 (2018), 1729881418782097
4. Roozegar M., Mahjoob M.J., Ayati M., “Adaptive Tracking Control of a Nonholonomic Pendulum-Driven Spherical Robot By Using a Model-Reference Adaptive System”, J. Mech. Sci. Technol., 32:2 (2018), 845–853