Skip to main content
SpringerLink
Log in

Adaptive estimation of nonlinear parameters of a nonholonomic spherical robot using a modified fuzzy-based speed gradient algorithm

  • Published:
Regular and Chaotic Dynamics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Armour, Rh. H. and Vincent, J. F. V, Rolling in Nature and Robotics: A Review, J. Bionic Eng., 2006, vol. 3, no. 4, pp. 195–208.

    Article  Google Scholar 

  2. Mahboubi, S, Seyyed Fakhrabadi, M.M., and Ghanbari, A., Design and Implementation of a Novel Spherical Mobile Robot, J. Intell. Robot. Syst., 2013, vol. 71, no. 1, pp. 43–64.

    Article  Google Scholar 

  3. Zhan, Q., Zhou, T., Chen, M., and Cai, S, Dynamic Trajectory Planning of a Spherical Mobile Robot, in Proc. of the 2nd IEEE Internat. Conf. on Robotics, Automation and Mechatronics (Bangkok, Thailand, 2006), pp. 1–6.

    Google Scholar 

  4. Cai, Y., Zhan, Q., and Xi, X, Path Tracking Control of a Spherical Mobile Robot, Mech. Mach. Theory, 2012, vol. 51, pp. 58–73.

    Article  Google Scholar 

  5. Zhan, Q., Cai, Y., and Liu, Z., Near-Optimal Trajectory Planning of a Spherical Mobile Robot for Environment Exploration, in Proc. of the 3rd IEEE Internat. Conf. on Robotics, Automation and Mechatronics (Chengdu, China, 2008), pp. 84–89.

    Google Scholar 

  6. Li, Z. and Canny, J, Motion of Two Rigid Bodies with Rolling Constraint, IEEE Trans. Robot. Autom., 1990, vol. 6, no. 1, pp. 62–72.

    Article  Google Scholar 

  7. Javadi, A.H.A. and Mojabi, P, Introducing August: A Novel Strategy for an Omnidirectional Spherical Rolling Robot, IEEE Trans. Robot. Autom., 2002, vol. 4, pp. 3527–2533.

    Google Scholar 

  8. Bhattacharya, S. and Agrawal, S.K, Design, Experiments and Motion Planning of a Spherical Rolling Robot, in Proc. of the IEEE Internat. Conf. on Robotics and Automation (San Francisco,Calif., USA, 2000): Vol. 2, pp. 1207–1212.

    Google Scholar 

  9. Bhattacharya, S. and Agrawal, S.K, Spherical Rolling Robot: A Design and Motion Planning Studies, IEEE Trans. Robot. Autom., 2000, vol. 16, no. 6, pp. 835–839.

    Article  Google Scholar 

  10. Halme, A., Schonberg, T., and Wang, Y, Motion Control of a Spherical Mobile Robot, in Proc. of the 4th Internat. Workshop on Advanced Motion Control (Mie, Japan, 1996): Vol. 1, pp. 259–264.

    Chapter  Google Scholar 

  11. Halme, A., Suromela, J., Schonberg, T., and Wang, Y., A Spherical Mobile Micro-Robot for Scientific Applications, in Advanced Space Technologies for Robot Applications: Proc. of the 4th ESA Workshop (ASTRA’96, ESTEC, Noordwijk, The Netherlands, 1996): Part 3. Space A&R Technologies: Session 3.2a. Robot Mobility.

  12. Marigo, A. and Bicchi, A., A Local-Local Planning Algorithm for Rolling Objects, in Proc. of the IEEE Internat. Conf. on Robotics and Automation (Washington,D.C., USA, 2002): Vol. 2, pp. 1759–1764.

    Google Scholar 

  13. Bicchi, A., Balluchi, A., Prattichizzo, D., and Gorelli, A, Introducing the “SPHERICLE”: An Experimental Testbed for Research and Teaching in Nonholonomy, in Proc. of the IEEE Internat. Conf. on Robotics and Automation (Albuquerque,N.M., USA, 1997): Vol. 3, pp. 2620–2625.

    Chapter  Google Scholar 

  14. Joshi, V. A. and Banavar, R.N, Motion Analysis of a Spherical Mobile Robot, Robotica, 2009, vol. 27, no. 3, pp. 343–353.

    Article  Google Scholar 

  15. Joshi, V.A., Banavar, R.N., and Hippalgaonkar, R, Design and Analysis of a Spherical Mobile Robot, Mech. Mach. Theory, 2010, vol. 45, no. 2, pp. 130–136.

    Article  MATH  Google Scholar 

  16. Liu, D., Sun, H., and Jia, Q., A Family of Spherical Mobile Robot: Driving Ahead Motion Control by Feedback Linearization, in ISSCAA’2008: 2nd Internat. Symp. on Systems and Control in Aerospace and Astronautics (Shenzhen, China, 2008), pp. 1–6.

    Google Scholar 

  17. Zhan, Q., Jia, Ch., Ma, X., and Zhai, Yu., Mechanism Design and Motion Analysis of a Spherical Mobile Robot, Chin. J. Mech. Eng., 2005, vol. 18, no. 4, pp. 542–545.

    Article  Google Scholar 

  18. Zhan, Q., Liu, Z., and Cai, Y., A Back-Stepping Based Trajectory Tracking Controller for a Non-Chained Non-Holonomic Spherical Robot, Chin. J. Aeronaut., 2008, vol. 21, no. 5, pp. 472–480.

    Article  Google Scholar 

  19. Sun, H., Xiao, A.P., Jia, Q., and Wang, L, Omnidirectional Kinematics Analysis on Bi-Driver Spherical Robot, J. Beijing Univ. Aeronaut. Astronaut., 2005, vol. 31, no. 7, pp. 736–739 (Chinese).

    Google Scholar 

  20. Yu, T., Sun, H., and Zhang, Y., Dynamic Analysis of a Spherical Mobile Robot in Rough Terrains, in Sensors and Systems for Space Applications 4, Kh.D. Pham, H. Zmuda, J. L. Cox, G. J. Meyer (Eds.), Proc. of SPIE, vol. 8044, Bellingham,Wash.: SPIE, 2011.

    Google Scholar 

  21. Yu, T., Sun, H., Zhang, Y., and Zhao, W, Control and Stabilization of a Pendulum-Driven Spherical Mobile Robot on an Inclined Plane, in Proc. of the 11th Internat. Symp. on Artificial Intelligence, Robotics and Automation in Space (Turin, Italy, 2012), 7 pp.

    Google Scholar 

  22. Yu, T., Sun, H., Jia, Q., Zhang, Y., and Zhao, W, Stabilization and Control of a Spherical Robot on an Inclined Plane, Res. J. Appl. Sci. Eng. Tech., 2013, vol. 5, no. 6, pp. 2289–2296.

    Google Scholar 

  23. Azizi, M. R. and Naderi, D, Dynamic Modeling and Trajectory Planning for a Mobile Spherical Robot with a 3-DoF Inner Mechanism, Mech. Mach. Theory, 2013, vol. 64, pp. 251–261.

    Article  Google Scholar 

  24. Roozegar, M., Mahjoob, M. J., and Shafiekhani, A, Using Dynamic Programming for Path Planning of a Spherical Mobile Robot, in Proc. of the Internat. Conf. on Advances in Control Engineering (Istanbul, Turkey, 2013), pp. 139–143.

    Google Scholar 

  25. Roozegar, M., Mahjoob, M. J., and Jahromi, M., DP-Based Path Planning of a Spherical Mobile Robot in an Environment with Obstacles, J. Franklin Inst., 2014, vol. 351, no. 10, pp. 4923–4938.

    Article  Google Scholar 

  26. Roozegar, M., Mahjoob, M. J., and Jahromi, M, Optimal Motion Planning and Control of a Nonholonomic Spherical Robot Using Dynamic Programming Approach: Simulation and Experimental Results, Mechatronics, 2016, vol. 39, pp. 174–184.

    Article  Google Scholar 

  27. Kilin, A.A., Pivovarova, E.N., and Ivanova, T.B, Spherical Robot of Combined Type: Dynamics and Control, Regul. Chaotic Dyn., 2015, vol. 20, no. 6, pp. 716–728.

    Article  MathSciNet  MATH  Google Scholar 

  28. Karavaev, Yu. L. and Kilin, A.A, The Dynamics and Control of a Spherical Robot with an Internal Omniwheel Platform, Regul. Chaotic Dyn., 2015, vol. 20, no. 2, pp. 134–152.

    Article  MathSciNet  MATH  Google Scholar 

  29. Esfandyari, M. J., Roozegar, M., Panahi, M. S., and Mahjoob, M. J, Motion Planning of a Spherical Robot Using eXtended Classifier Systems, in Proc. of the 21st Iranian Conf. on Electrical Engineering (ICEE, Mashhad, Iran, 2013), pp. 1–6.

    Google Scholar 

  30. Roozegar, M., Mahjoob, M. J., Esfandyari, M. J., Shariat Panahi, M., XCS-Based Reinforcement Learning Algorithm for Motion Planning of a Spherical Mobile Robot, Appl. Intell., 2016, vol. 45, no. 3, pp. 736–746.

    Google Scholar 

  31. Chen, W.H., Chen, C.P., Tsai, J. S., Yang, J., and Lin, P.C, Design and Implementation of a Ball-Driven Omnidirectional Spherical Robot, Mech. Mach. Theory, 2013, vol. 68, pp. 35–48.

    Article  Google Scholar 

  32. Roozegar, M. and Mahjoob, M. J, Modelling and Control of a Non-Holonomic Pendulum-Driven Spherical Robot Moving on an Inclined Plane: Simulation and Experimental Results, IET Control Theory Appl., 2017, vol. 11, no. 4, pp. 541–549.

    Article  Google Scholar 

  33. Ivanov, A.P, On the Control of a Robot Ball Using Two Omniwheels, Regul. Chaotic Dyn., 2015, vol. 20, no. 4, pp. 441–428.

    Article  MathSciNet  MATH  Google Scholar 

  34. Reddy, B. S. and Ghosal, A, Asymptotic Stability and Chaotic Motions in Trajectory Following Feedback Controlled Robots, J. Comput. Nonlinear Dynam., 2016, vol. 11, no. 5, 051012, 11 pp.

    Article  Google Scholar 

  35. Ayati, M. and Khaki-Sedigh, A, Adaptive Control of Nonlinear in Parameters Chaotic Systems, Nonlinear Dyn. Syst. Theory, 2008, vol. 8, no. 2, pp. 123–135.

    MathSciNet  MATH  Google Scholar 

  36. Ayati, M. and Khaki-Sedigh, A, Adaptive Control of Nonlinear in Parameters Chaotic System via Lyapunov Exponents Placement, Chaos Solitons Fractals, 2009, vol. 41, no. 4, pp. 1980–1986.

    Article  MATH  Google Scholar 

  37. Ayati, M, Adaptive Fuzzy Control of Nonlinear in Parameters Uncertain Chaotic Systems Using Improved Speed Gradient Method, Circuits Syst. Signal Process., 2012, vol. 31, no. 3, pp. 911–926.

    Article  MathSciNet  MATH  Google Scholar 

  38. Yoshinaka, R., Kawashima, M., Takamura, Yu., Yamaguchi, H., Miyahara, N., Nabeta, K., Li, Yo., and Nara, Sh., Adaptive Control of Robot Systems with Simple Rules Using Chaotic Dynamics in Quasi-Layered Recurrent Neural Networks, in Computational Intelligence: Revised and Selected Papers of the International Joint Conference (IJCCI’2010, Valencia, Spain, 2010), K. Madani, A. Dourado Correia, A. Rosa, J. Filipe (Eds.), Stud. Comput. Intel., vol. 399, Berlin: Springer,2012, pp. 287–305.

    Chapter  Google Scholar 

  39. Mahmoodabadi, M. J., Maafi, R.A., and Taherkhorsandi, M, An Optimal Adaptive Robust PID Controller Subject to Fuzzy Rules and Sliding Modes for MIMO Uncertain Chaotic Systems, Appl. Soft Comput., 2017, vol. 52, Issue C, pp. 1191–1199.

    Article  Google Scholar 

  40. Fan, J., Zhang, Y., Jin, H., Wang, X., Bie, D., Zhao, J., and Zhu, Y, Chaotic CPG Based Locomotion Control for Modular Self-Reconfigurable Robot, J. Bionic Eng., 2016, vol. 13, no. 1, pp. 30–38.

    Article  Google Scholar 

  41. Kamaldar, M., Mahjoob, M. J., Haeri Yazdi, M., Vahid-Alizadeh, H., and Ahmadizadeh, S., A Control Synthesis for Reducing Lateral Oscillations of a Spherical Robot, in Proc. of the IEEE Internat. Conf. on Mechatronics (ICM, Istanbul, Turkey, 2011), pp. 546–551.

    Google Scholar 

  42. Kamaldar, M., Mahjoob, M. J., and Vahid-Alizadeh, H, Robust Speed Control of a Spherical Robot Using ARX Uncertain Modeling, in Proc. of the IEEE Internat. Symp. on Robotic and Sensors Environments (ROSE, Montreal, QC,Canada, 2011), pp. 196–201.

    Google Scholar 

  43. Vahid-Alizadeh, H. and Mahjoob, M. J, Effect of Incremental Driving Motion on a Vision-Based Path Planning of a Spherical Robot, in Proc. of the 2nd Internat. Conf. on Computer and Electrical Engineering (ICCEE’09, Dubai, United Arab Emirates, 2009), pp. 299–303.

    Google Scholar 

  44. Wang, L.-X., A Course in Fuzzy Systems and Control, Upper Saddle River,N.J.: Prentice Hall, 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Intelligent Machines (CIM), Department of Mechanical Engineering, McGill University, 817 Sherbrooke St. West, Montréal, QC, H3A 0C3, Canada

    Mehdi Roozegar

  2. Centre for Mechatronics and Intelligent Machines, School of Mechanical Engineering, University of Tehran, Kargar St. North, Tehran, Iran

    Mohammad J. Mahjoob

  3. School of Mechanical Engineering, University of Tehran, Kargar St. North, Tehran, Iran

    Moosa Ayati

Authors
  1. Mehdi Roozegar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad J. Mahjoob
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Moosa Ayati
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mehdi Roozegar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Roozegar, M., Mahjoob, M.J. & Ayati, M. Adaptive estimation of nonlinear parameters of a nonholonomic spherical robot using a modified fuzzy-based speed gradient algorithm. Regul. Chaot. Dyn. 22, 226–238 (2017). https://doi.org/10.1134/S1560354717030030

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

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

MSC2010 numbers

Keywords

Search

Navigation