Observer Design for an Inverted Pendulum with Biased Position Sensors

  • S. V. Aranovskiy
  • A. E. Biryuk
  • E. V. NikulchevEmail author
  • I. V. Ryadchikov
  • D. V. Sokolov


Inverted pendulums can be considered as an approximation for the stabilization problem for legged robots. In this paper we design a linear observer for a reaction wheel inverted pendulum under biased angle measurements. The reaction wheel is a flywheel that allows the free spinning motor to apply the control torque on the pendulum. In this paper we consider the stabilization problem in the presence of a constant unknown bias in the pendulum angle measurements; this problem has important practical implications, allowing for less precise sensor placement as well as a closer approximation for the control of legged robots. This paper provides a theoretical and experimental basis for the estimation of the velocities and the bias in the system.



This work is supported by the Ministry of Education and Science of the Russian Federation (GosZadanie grants no. 8.2321.2017/ПЧ and 8.8885.2017/8.9).


  1. 1.
    E. S. Briskin, Ya. V. Kalinin, A. V. Maloletov, and V. A. Shurygin, “Assessment of the performance of walking robots by multicriteria optimization of their parameters and algorithms of motion,” J. Comput. Syst. Sci. Int. 56, 334 (2017).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    S. I. Savin and L. Yu. Vorochaeva, “Control methods for in-pipe walking robots,” Cloud Sci. 5, 163 (2018).Google Scholar
  3. 3.
    A. A. Grishin, A. V. Lenskii, D. E. Okhotsimskii, D. A. Panin, and A. M. Formal’skii, “A control synthesis for an unstable object. An inverted pendulum,” J. Comput. Syst. Sci. Int. 41, 685 (2002).Google Scholar
  4. 4.
    C. A. Reshmin and F. L. Chernous’ko, “Time-optimal control of an inverted pendulum in the feedback form,” J. Comput. Syst. Sci. Int. 45, 383 (2006).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    E. Franco, A. Astolfi, and F. R. Baena, “Robust balancing control of flexible inverted-pendulum systems,” Mechanism Mach. Theory 130, 539–551 (2018).CrossRefGoogle Scholar
  6. 6.
    Y. Hua and Z. Yang, “Simple rotary inverted pendulum and the control device,” Appl. Mech. Mater. 851, 445–448 (2016).CrossRefGoogle Scholar
  7. 7.
    X. Chen, R. Yu, K. Huang, S. Zhen, H. Sun, and K. Shao, “Linear motor driven double inverted pendulum: a novel mechanical design as a testbed for control algorithms,” Simul. Model. Practice Theory 81, 31–50 (2018).CrossRefGoogle Scholar
  8. 8.
    J. Sánchez, S. Dormido, R. Pastor, and F. Morilla, “A Java/MATLAB-based environment for remote control system laboratories: illustrated with an inverted pendulum,” IEEE Trans. Educ. 47, 321–329 (2004).CrossRefGoogle Scholar
  9. 9.
    S. Chatterjee and S. K. Das, “An analytical formula for optimal tuning of the state feedback controller gains for the cart-inverted pendulum system,” IFAC-PapersOnLine 51, 668–672 (2018).CrossRefGoogle Scholar
  10. 10.
    J. J. Rubio, “Discrete time control based in neural networks for pendulums,” Appl. Soft Comput. 68, 821–832 (2018).CrossRefGoogle Scholar
  11. 11.
    A. Bellino, A. Fasana, E. Gandino, L. Garibaldi, and S. Marchesiello, “A time-varying inertia pendulum: analytical modelling and experimental identification,” Mech. Syst. Signal Proces. 47, 120–138 (2014).CrossRefGoogle Scholar
  12. 12.
    Z. Ping and J. Huang, “Approximate output regulation of spherical inverted pendulum by neural network control,” Neurocomputing 85, 38–44 (2012).CrossRefGoogle Scholar
  13. 13.
    M. Gajamohan, M. Merz, I. Thommen, and R. D’Andrea, “The subli: a cube that can jump up and balance,” in Proceedings of the 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems IROS (IEEE, Piscataway, 2012), pp. 3722–3727.Google Scholar
  14. 14.
    B. D. O. Anderson and J. B. Moore, Optimal Control: Linear Quadratic Methods (Dover, Mineola, 2007).Google Scholar
  15. 15.
    I. Ryadchikov, S. Sechenev, E. Nikulchev, M. Drobotenko, A. Svidlov, P. Volkodav, and R. Vishnykov, “Control and stability evaluation of the bipedal walking robot anywalker,” Int. Rev. Autom. Control 11, 160–165 (2018).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • S. V. Aranovskiy
    • 1
    • 2
  • A. E. Biryuk
    • 3
  • E. V. Nikulchev
    • 4
    Email author
  • I. V. Ryadchikov
    • 3
  • D. V. Sokolov
    • 5
  1. 1.CentraleSupelec-IETRCesson-SévignéFrance
  2. 2.ITMO UniversitySaint PetersburgRussia
  3. 3.Kuban State UniversityKrasnodarRussia
  4. 4.MIREA—Russian Technological UniversityMoscowRussia
  5. 5.Université de LorraineNancyFrance

Personalised recommendations