Advertisement

Passivity-based Nonlinear Control for a Ballbot to Balance and Transfer

  • Van-Thach Do
  • Soon-Geul LeeEmail author
  • Kwan-Woong Gwak
Article
  • 44 Downloads

Abstract

Ballbot is a robot that can transfer to a given position while maintaining a self-balanced upright posture on a spherical ball. This paper proposes a nonlinear control of a ballbot using three omnidirectional wheels in the driving mechanism. Assuming a small swing angle for balance, the full dynamics of the ballbot can be decomposed into three, which are two underactuated dynamics for two orthogonal vertical planes and the fully actuated dynamics for one horizontal plane. The passivity of closed-loop systems of vertical planes is derived from the modified potential energy function. The proposed controller is designed to control the balancing and transferring of the system based on Lyapunov theory and the passivity of the system. A proportional-derivative feedforward controller is applied to regulate the heading motion in the horizontal plane. Experiments are performed with a real ballbot system to validate the effectiveness of system modeling and to show the controllability of the proposed algorithm.

Keywords

Ballbot decoupled dynamics nonlinear control passivity-based control underactuated system 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. [1]
    J. Moreno, E. Clotet, R. Lupiañez, M. Tresanchez, D. Martínez, T. Pallejá, J. Casanovas, and J. Palacín, “Design, implementation and validation of the three-wheel holonomic motion system of the assistant personal robot (APR),” Sensors (Switzerland), vol. 16, no. 10, pp. 1658–1678, 2016.CrossRefGoogle Scholar
  2. [2]
    M. Komori, K. Matsuda, T. Terakawa, F. Takeoka, H. Nishihara, and H. Ohashi, “Active omni wheel capable of active motion in arbitrary direction and omnidirectional vehicle,” J. Adv. Mech. Des. Syst. Manuf., vol. 10, no. 6, Pages JAMDSM0086, 2016.Google Scholar
  3. [3]
    T. F. Bastos-Filho, F. A. Cheein, S. M. T. Muller, W. C. Celeste, C. Cruz, D. C. Cavalieri, M. Sarcinelli-Filhom, P. F. S. Amaral, E. Perez, C. M. Soria, and R. Carelli, “Towards a new modality-independent interface for a robotic wheelchair,” IEEE Trans. Neural Syst. Rehabil. Eng., vol. 22, no. 3, pp. 567–584, 2014.CrossRefGoogle Scholar
  4. [4]
    P. Oryschuk, A. Salerno, A. M. Al-Husseini, and J. Angeles, “Experimental validation of an underactuated twowheeled mobile robot,” IEEE/ASME Trans. Mechatronics, vol. 14, no. 2, pp. 252–257, 2009.CrossRefGoogle Scholar
  5. [5]
    A. Kilin, P. Bozek, Y. Karavaev, A. Klekovkin, and V. Shestakov, “Experimental investigations of a highly maneuverable mobile omniwheel robot,” Int. J. Adv. Robot. Syst., vol. 14, no. 6, pp. 1–9, 2017.CrossRefGoogle Scholar
  6. [6]
    T. Lauwers, G. Kantor, and R. Hollis, “One is enough,” Proc. of 12th Int’l Symp. on Robotics Research, Robot. Res., pp. 1–10, 2005.Google Scholar
  7. [7]
    K. Sukvichai and M. Parnichkun, “Double-level ball-riding robot balancing: From system design, modeling, controller synthesis, to performance evaluation,” Mechatronics, vol. 24, no. 5, pp. 519–532, 2014.CrossRefGoogle Scholar
  8. [8]
    C. K. Chan and C. C. Tsai, “Direct adaptive recurrent interval type 2 fuzzy neural networks control using for a ball robot with a four-motor inverse-mouse ball drive,” Proc. of Int. Conf. Adv. Robot. Intell. Syst. ARIS 2013, pp. 5–10, 2013.Google Scholar
  9. [9]
    C. C. Tsai, M. H. Juang, C. K. Chan, C. W. Liao, and S. J. Chan, “Self-balancing and position control using multiloop approach for ball robots,” Proc. of Int. Conf. Syst. Sci. Eng. ICSSE 2010, pp. 251–256, 2010.CrossRefGoogle Scholar
  10. [10]
    M. Kumagai, “Development of a ball drive unit using partially sliding rollers — An alternative mechanism for semiomnidirectional motion,” Proc. of IEEE/RSJ Int. Conf. Intell. Robot. Syst. IROS 2010, pp. 3352–3357, 2010.Google Scholar
  11. [11]
    M. Kumagai and T. Ochiai, “Development of a robot balancing on a ball,” Proc. of Int. Conf. on Control, Automation and Systems, pp. 433–438, 2008.Google Scholar
  12. [12]
    P. Fankhauser and C. Gwerder, Modeling and Control of a Ballbot, Eidgenössische Technische Hochschule Zürich, 2010.Google Scholar
  13. [13]
    P. Asgari, P. Zarafshan, and S. A. A. Moosavian, “Dynamics modelling and stable motion control of a ballbot equipped with a manipulator,” Proc. of Int. Conf. Robot. Mechatronics, ICRoM 2013, pp. 259–264, 2013.Google Scholar
  14. [14]
    U. Nagarajan, B. Kim, and R. Hollis, “Planning in highdimensional shape space for a single-wheeled balancing mobile robot with arms,” Proc. of IEEE Int. Conf. Robot. Autom., pp. 130–135, 2012.Google Scholar
  15. [15]
    D. B. Pham and S.-G. Lee, “Aggregated hierarchical sliding mode control for a spatial ridable ballbot,” Int. J. Precis. Eng. Manuf., vol. 19, no. 9, pp. 1291–1302, 2018.CrossRefGoogle Scholar
  16. [16]
    D. B. Pham, H. Kim, J. Kim, and S.- G. Lee, “Balancing and transferring control of a ball segway using a doubleloop approach [applications of control],” IEEE Control Syst., vol. 38, no. 2, pp. 15–37, 2018.MathSciNetCrossRefGoogle Scholar
  17. [17]
    D. B. Pham and S.-G. Lee, “Hierarchical sliding mode control for a two-dimensional ball segway that is a class of a second-order underactuated system,” J. Vib. Control, vol. 25, no. 1, pp. 72–83, Jan. 2019.MathSciNetCrossRefGoogle Scholar
  18. [18]
    T. B. Lauwers, G. A. Kantor, and R. L. Hollis, “A dynamically stable single-wheeled mobile robot with inverse mouse-ball drive,” Proc. of IEEE Int. Conf. Robot. Autom., vol. 2006, no. May, pp. 2884–2889, 2006.Google Scholar
  19. [19]
    C. H. Chiu and W. R. Tsai, “Design and implementation of an omnidirectional spherical mobile platform,” IEEE Trans. Ind. Electron., vol. 62, no. 3, pp. 1619–1628, 2015.CrossRefGoogle Scholar
  20. [20]
    H. Navabi, S. Sadeghnejad, S. Ramezani, and J. Baltes, “Position control of the single spherical wheel mobile robot by using the fuzzy sliding mode controller,” Adv. Fuzzy Syst., vol. 2017, pp. 1–10, 2017.MathSciNetCrossRefGoogle Scholar
  21. [21]
    Y. You, H.-M. Ha, Y.-K. Kim, and J.-m. Lee, “Balancing and driving control of a ball robot using fuzzy control,” Proc. of 12th Int. Conf. on Ubiquitous Robots and Ambient Intelligence (URAI), pp. 492–494, 2015.Google Scholar
  22. [22]
    R. Ortega and M. W. Spong, “Adaptive motion control of rigid robots: a tutorial,” PRoc of 27th Conf. on Decision and Control, no. 27, pp. 1575–1584, 1988.Google Scholar
  23. [23]
    N. Sun and Y. Fang, “New energy analytical results for the regulation of underactuated overhead cranes: an endeffector motion-based approach,” IEEE Trans. Ind. Electron., vol. 59, no. 12, pp. 4723–4734, 2012.CrossRefGoogle Scholar
  24. [24]
    N. Q. Hoang, S.-G. Lee, J. Kim, and B. S. Kim, “Simple energy-based controller for a class of underactuated mechanical systems,” Int. J. Precis. Eng. Manuf., vol. 15, no. 8, pp. 1529–1536, 2014.CrossRefGoogle Scholar
  25. [25]
    M. W. Spong, “Energy-based control for a class of underactuated mechanical systems,” IFAC World Congr., pp. 431–435, 1996.Google Scholar
  26. [26]
    W. Zhong and H. Rock, “Energy and passivity based control,” Proc. of IEEE Int. Conf. Control Appl., pp. 896–901, 2001.Google Scholar
  27. [27]
    R. Liu, J. Wu, and D. Wang, “Sampled-data fuzzy control of two-wheel inverted pendulums based on passivity theory,” Int. J. Control. Autom. Syst., vol. 16, no. 5, pp. 2538–2548, Oct. 2018.CrossRefGoogle Scholar
  28. [28]
    O. Penaloza-Mejia, C. P. Ojeda-Perez, and H. J. Estrada-Garcia, “Passivity-based tracking control of robot manipulators with torque constraints,” Proc. of IEEE/ASME Int. Conf. Adv. Intell. Mechatronics, AIM, pp. 947–952, 2016.Google Scholar
  29. [29]
    A. M. Khan, D.-W. Yun, M. A. Ali, K. M. Zuhaib, C. Yuan, J. Iqbal, J. Han, K. Shin, and C. Han, “Passivity based adaptive control for upper extremity assist exoskeleton,” Int. J. Control. Autom. Syst., vol. 14, no. 1, pp. 291–300, Feb. 2016.CrossRefGoogle Scholar
  30. [30]
    D. V. Thach, P. D. Ba, and S.-G. Lee, “Design of an energybased controller for a 2D ball segway,” Proc. of 17th Int. Conf. on Control, Automation and Systems (ICCAS), pp. 442–446, 2017.Google Scholar
  31. [31]
    Z.-P. Jiang and I. Marcels, “Robust nonlinear integral control,” IEEE Trans. Automat. Contr., vol. 46, no. 8, pp. 1336–1342, Aug. 2001.MathSciNetCrossRefGoogle Scholar
  32. [32]
    J. Yu, Y. Zhao, and Y. Wu, “Robust integral control for a class of nonlinear systems with unknown control coefficients,” J. Control Theory Appl., vol. 10, no. 3, pp. 359–364, 2012.MathSciNetCrossRefGoogle Scholar
  33. [33]
    H. Wu, “A new integral inequality and its applications to robust control problems of uncertain nonlinear systems,” Int. J. Robust Nonlinear Control, vol. 28, no. 15, pp. 4584–4603, 2018.MathSciNetzbMATHGoogle Scholar
  34. [34]
    D. V. Thach and S.-G. Lee, “LQG control design for a coupled ballbot dynamical system,” Proc. of 18th Int. Conf. on Control, Automation and Systems (ICCAS), pp. 666–670, 2018.Google Scholar
  35. [35]
    R. Olfati-Saber, “Nonlinear control and reduction of underactuated systems with symmetry.III. Input coupling case,” Proc. of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), pp. 3778–3783, 2001.Google Scholar
  36. [36]
    C. I. Byrnes, A. Isidori, and J. C. Willems, “Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems,” IEEE Trans. Automat. Contr., vol. 36, no. 11, pp. 1228–1240, 1991.MathSciNetCrossRefGoogle Scholar
  37. [37]
    J. C. Willems, “Dissipative dynamical systems part I: general theory,” Arch. Ration. Mech. Anal., vol. 45, no. 5, pp. 321–351, 1972.CrossRefGoogle Scholar
  38. [38]
    H. K. Khalil, Nonlinear Systems, 3rd ed., Prentice-Hall, Upper Saddle River, NJ, 2000.zbMATHGoogle Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.Kyung Hee UniversityYongin-si, Gyeonggi-doKorea
  2. 2.Department of Mechanical EngineeringSejong UniversitySeoulKorea

Personalised recommendations