Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-15T22:42:11.246Z Has data issue: false hasContentIssue false
  • English
  • Français

A Lyapunov controller for self-balancing two-wheeled vehicles

Published online by Cambridge University Press:  05 March 2014

A. Maddahi ,
A. H. Shamekhi  and
A. Ghaffari
A. Maddahi
Affiliation:
Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran
A. H. Shamekhi*
Affiliation:
Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran
A. Ghaffari
Affiliation:
Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran
*
*Corresponding author. E-mail: shamekhi@kntu.ac.ir
Get access Rights & Permissions [Opens in a new window]

Summary

Segway is a self-balancing motorized two-wheeled vehicle which is able to carry the human body. The main issue in design of such a vehicle is to choose a stable control system capable of keeping the rider close to the upright position over smooth and non-smooth surfaces. This work extends the research previously performed by the authors for design of a controller, using the feedback linearization technique, to increase the stability of a two-wheeled vehicle carrying human. This paper investigates the design and validation of a controller for an inertial mobile vehicle using the Lyapunov's feedback control design technique. The system equations of motion are derived followed by finding the Lyapunov function required to design the controller. Owing to the discontinuity, originating from a sign function in the control law, the proposed control system is discontinuous. Therefore, the existence, continuity, and uniqueness of the solution are proven utilizing the Filippov's solution. Afterwards, the asymptotic stability of the control system is proven using the extensions of Lyapunov's stability theory to nonsmooth systems, and LaSalle's invariant set theorem. Finally, the effectiveness of the proposed control system is validated using simulation studies. Results confirm that the controller keeps the system stable while provides good position tracking responses.

Keywords

SegwayTwo-wheeled vehicleFilippov's solutionLyapunov controller
Type
Articles
Information
Robotica , Volume 33 , Issue 1 , January 2015 , pp. 225 - 239
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Maddahi, Y., Sepehri, N., Maddahi, A. and Abdolmohammadi, M., “Calibration of wheeled mobile robots with differential drive mechanisms: An experimental approach,” J. Robotica 30 (6), 1029–1039 (2012).CrossRefGoogle Scholar
2.Maddahi, Y., Maddahi, A. and Hosseini Monsef, S. M., “Design improvement of wheeled mobile robots: Theory and experiment,” J. World Appl. Sci. 16 (2), 263–274 (2012).Google Scholar
3.Segway Inc. Segway homepage. http://www.segway.com.Google Scholar
4.Saifizul, A. A., Zainon, Z., Abu Osman, N. A., Azlan, C. A. and Ungku Ibrahim, U. F. S., “Intelligent control for self-erecting inverted pendulum via adaptive neuro-fuzzy inference system,” Am. J. Appl. Sci. 3 (4), 1795–1802 (2006).Google Scholar
5.Mills, A., Wills, A. and Ninness, B., “Nonlinear Model Predictive Control of an Inverted Pendulum,” American Control Conference (2009) pp. 2335–2340.Google Scholar
6.Pathak, K., Franch, J. and Agrawal, S. K., “Velocity Control of a Wheeled Inverted Pendulum by Partial Feedback Linearization,” IEEE Conference on Design and Control, Atlantis (2004) pp. 3962–3967.Google Scholar
7.Iida, S. and Yuta, S., “Control of a Vehicle Subsystem for an Autonomous Mobile Robot with Power Wheeled Steering”, Proceedings of IEEE International Workshop on Intelligent Motion Control (1990) pp. 859–866.Google Scholar
8.Ha, Y. and Yuta, S., “Trajectory tracking control for navigation of an inverted pendulum type self-contained mobile robot,” J. Robot. Auton. Syst. 17, 65–80 (1996).Google Scholar
9.Grasser, F., D'Arrigo, A., Colmbi, S. and Rufer, A. C., “JOE: A mobile inverted pendulum,” IEEE Trans. Ind. Electron. 49 (1), 107–114 (2002).Google Scholar
10.Lee, H. J. and Jung, S., “Gyro Sensor Drift Compensation by Kalman Filter to Control a Mobile Inverted Pendulum Robot System,” IEEE International Conference on Industrial Technology, Gippsland (2009) pp. 1–6.Google Scholar
11.Azizan, H., Jafarinasab, M., Behbahani, S. and Danesh, M., “Fuzzy Control Based on LMI Approach and Fuzzy Interpretation of the Rider Input for Two Wheeled Balancing Human Transporter,” IEEE Conference on Control and Automation, Xiamen, China (2010) pp. 192–197.Google Scholar
12.Tsai, C., Huang, H. C. and Lin, S. C., “Adaptive neural network control of a self-balancing two-wheeled scooter,” IEEE Trans. Ind. Electron. 57, 1420–1428 (2010).Google Scholar
13.Vermeiren, L., Dequidt, A., Guerra, T. M., Tirmant, H. R. and Parent, M., “Modeling, control and experimental verification on a two-wheeled vehicle with free inclination: An urban transportation system,” J. Control Eng. Pract. 19, 744–756 (2011).Google Scholar
14.Aracil, J., Acosta, J. and Gordillo, F., “A Controller for Swinging-up and Stabilization the Inverted Pendulum,” Proceeding of the 17th World Congress, IFAC, Korea (2008).Google Scholar
15.Maddahi, A. and Shamekhi, A. H., “Controller design for two-wheeled self-balancing vehicles using feedback linearisation technique,” Int. J. Veh. Syst. Modelling Test. 8 (1), 38–54 (2013).CrossRefGoogle Scholar
16.Zarei-nia, K., Sepehri, N. and Wu, C. Q., “A Lyapunov controller for stable haptic manipulation of hydraulic actuators,” Int. J. Robust Nonlinear Control 22, 241–261 (2012).Google Scholar
17.Filippov, A. F., “Differential equations with discontinuous right-hand side,” Am. Math. Soc. Transl. 42, 199–231 (1964).Google Scholar
18.Filippov, A. F., “Differential equations with second members discontinuous on intersecting surfaces,” Differ. Equ. 15, 1292–1299 (1980).Google Scholar
19.Wu, Q. and Sepehri, N., “On Lyapunov's stability analysis of non-smooth systems with applications to control engineering,” Int. J. Non-Linear Mech. 36 (7), 1153–1161 (2001).Google Scholar
20.Shevitz, D. and Paden, B., “Lyapunov stability theory of non-smooth systems,” IEEE Trans. Autom. Control 39 (9), 1910–1914 (1994).Google Scholar
21.Wu, Q., Sepehri, N. and Thornton-Trump, A. B., “An extended integral method to derive Lyapunov functions for nonlinear systems,” Int. J. Control 62 (3), 717–736 (1995).Google Scholar
22.Slotine, J. J. and Li, W., Applied Nonlinear Control (Prentice-Hall Inc., Englewood Cliffs, NJ, 1991).Google Scholar
23.LaSalle, J., “Some extensions of Liapunov's second method,” IRE Trans. Circuit Theory 7 (4), 520–527 (1960).Google Scholar