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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Modeling and Nonlinear Control of a Two-Wheeled Self Balancing Human Transporter

Journal of Applied Nonlinear Dynamics 10(1) (2021) 29--45 | DOI:10.5890/JAND.2021.03.002

Saransh Jain$^1$, Mohit Makkar$^1$ , Sarthak Jain$^1$, Deepak Unune$^2$

$^1$ Department of Mechanical-Mechatronics Engineering, The LNM Institute of Information Technology Jaipur, 302031, India

$^2$ Department of Materials Science and Engineering, University of Sheffield, INSIGNEO Institute for in silico Medicine, The Pam Liversidge Building, Sheffield, S1 3JD, United Kingdom

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The two-wheeled self-balancing human transporters (TW-SBHT) are being widely used in transportation nowadays owing to their advantages such as energy saving, environmental protection, simple structure, and flexible operation. The modelling and control of TW-SBHT have emerged as one of the trending research areas in the field of control system design of mobile robots. Being a complex and nonlinear system, the control problem of TW-SBHT is a challenging task and needs to be effectively tackled to achieve the control objectives of maintaining uniform speed and dynamic stability. Though linear control strategies for TW-SBHT have been already proposed in the literature, they cannot offer an effective control for large external disturbances. Therefore, in this work, a non-linear control i.e. State-Dependent Riccati Equation (SDRE) has been implemented for effective control of TW-SBHT and its performance is compared with the linear controls including Proportional-Integral-Derivative (PID) and Linear-Quadratic Regulator (LQR) techniques. Initially, the more accurate model of TW-SBHT has been derived by applying the suitable modifications in existing models. Then, the application of SDRE for control of TW-SBHT has been presented and its performance is compared with linear control strategies.


  1. [1] Shimizu, Y. and Shimada, A. (2010), Direct tilt angle control on inverted pendulum mobile robots, In 2010 11th IEEE International Workshop on Advanced Motion Control (AMC) (pp. 234-239), IEEE.
  2. [2] Lin, S.C. and Tsai, C.C. (2008), Development of a self-balancing human transportation vehicle for the teaching of feedback control, IEEE Transactions on Education, 52(1), 157-168
  3. [3] Lupian, L.F. and Avila, R. (2008), Stabilization of a wheeled inverted pendulum by a continuous-time infinite-horizon LQG optimal controller, In 2008 IEEE Latin American Robotic Symposium, 65-70.
  4. [4] Huang, J., Guan, Z.H., Matsuno, T., Fukuda, T., and Sekiyama, K. (2010), Sliding-mode velocity control of mobile-wheeled inverted-pendulum systems, IEEE Transactions on robotics, 26(4), 750-758.
  5. [5]  Irfan, S., Mehmood, A., Razzaq, M.T., and Iqbal, J. (2018), Advanced sliding mode control techniques for inverted pendulum: Modelling and simulation, Engineering Science and Technology, an international journal, 21(4), 753-759.
  6. [6]  Lin, S.C., Tsai, C.C., and Huang, H.C. (2011), Adaptive robust self-balancing and steering of a two-wheeled human transportation vehicle, Journal of Intelligent and Robotic Systems, 62(1), 103-123.
  7. [7]  Kim, S. and Kwon, S. (2017), Nonlinear optimal control design for underactuated two-wheeled inverted pendulum mobile platform, IEEE/ASME Transactions on Mechatronics, 22(6), 2803-2808.
  8. [8]  Xu, J.X., Guo, Z.Q., and Lee, T.H. (2013), Design and implementation of integral sliding-mode control on an underactuated two-wheeled mobile robot, IEEE Transactions on Industrial Electronics, 61(7), 3671-3681.
  9. [9]  Li, Z. and Yang, C. (2011), Neural-adaptive output feedback control of a class of transportation vehicles based on wheeled inverted pendulum models, IEEE Transactions on Control Systems Technology, 20(6), 1583-1591.
  10. [10]  Huang, C.H., Wang, W.J., and Chiu, C.H. (2010), Design and implementation of fuzzy control on a two-wheel inverted pendulum, IEEE Transactions on Industrial Electronics, 58(7), 2988-3001.
  11. [11]  Jadlovska, S. and Sarnovsky, J. (2013), Application of the state dependent Riccati equation method in nonlinear control design for inverted pendulum systems, In 2013 IEEE 11th International Symposium on Intelligent Systems and Informatics (SISY), 209-214.
  12. [12]  Cimen, T. (2012), Survey of state dependent Riccati equation in nonlinear optimal feedback control synthesis, Journal of Guidance, Control, and Dynamics, 35(4), 1025-1047.
  13. [13]  Yamamoto, Y. (2008), NXTway-GS Model-Based Design-Control of self-balancing two-wheeled robot built with LEGO Mindstorms NXT. Cybernet Systems Co., Ltd.
  14. [14]  Arvidsson, M. and Karlsson, J. (2012), Design, construction and verification of a self-balancing vehicle.
  15. [15]  Kim, S. and Kwon, S. (2015), Dynamic modeling of a two-wheeled inverted pendulum balancing mobile robot, International Journal of Control, Automation and Systems, 13(4), 926-933.
  16. [16]  van Rensburg, R., Steyn, N., Trenoras, L., Hamam, Y., and Monacelli, E. (2017), Stability and enhancement analysis of a modelled self-balancing verticalized mobility aid using optimal control techniques, African Journal of Science, Technology, Innovation and Development, 9(1), 93-109.
  17. [17]  Batmani, Y., Davoodi, M., and Meskin, N. (2016), Nonlinear suboptimal tracking controller design using state dependent Riccati equation technique, IEEE Transactions on Control Systems Technology, 25(5), 1833-1839.
  18. [18]  Prach, A.N.N.A. (2015), Faux Riccati equation techniques for feedback control of nonlinear and time-varying systems(Doctoral dissertation, PhD. Thesis. School of Natural and Applied Sciences. Aerospace Engineering. Middle East Technical University).