Double-Loop Control with Hierarchical Sliding Mode and Proportional Integral Loop for 2D Ridable Ballbot

  • Dinh Ba Pham
  • Jaejun Kim
  • Soon-Geul LeeEmail author
  • Kwan-Woong Gwak
Regular Paper


In this study, we propose a nonlinear double-loop control system for a ridable ballbot. An improved nonlinear double-loop control technique based on double-loop control scheme and sliding mode technology is used, and the inner-loop consists of proportional–integral feedback plus feedforward control. A sliding mode control enables the ridable ballbot to balance and transfer on the floor. Feedforward compensation has been added for the stability of the ballbot. As a result, the control system can stabilize all state variables of the ballbot system despite the uncertainties of the system parameters such as model, friction, and external disturbances, and relatively large body inertia. Experiments demonstrate the effectiveness of the proposed control system and the performance validation of the nonlinear double-loop control.


Ridable ballbot Hierarchical sliding mode control Underactuated system Double-loop control system PI control 

List of symbols


Mass of the body


Mass of the ball


Moment of inertia of the ball

Ix, Iy

Moments of inertia of the body about the x- and y-axes


Distance from the mass center of the body to that of the ball


Radius of the ball


Radius of the omnidirectional wheel


Moment of inertia of each omnidirectional wheel


Zenith angle

xk, yk

Position of the ball

θx, θy

Roll and pitch angles of the body

τx, τy

Corresponding resultant toques of the motors to the x- and y-axes

brx, bry, bx, by

Friction factors


The gravity acceleration



This research was partly supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2019R1A2C2010195); and by the Ministry of Science and ICT, Korea, under the Grand Information Technology Research Center support program (IITP-2018-2015-0-00742) supervised by the IITP. It was also supported by the Senior-friendly Product R&D program funded by the Ministry of Health and Welfare through the Korea Health Industry Development Institute (KHIDI) (HI15C1027).


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Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringVietnam Maritime UniversityHai PhongVietnam
  2. 2.Korea Gas CorporationIncheonSouth Korea
  3. 3.School of Mechanical EngineeringKyung Hee UniversityYongin-siSouth Korea
  4. 4.School of Mechanical and Aerospace EngineeringSejong UniversitySeoulKorea

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