Kybernetika 51 no. 1, 173-191, 2015

LQR and MPC controller design and comparison for a stationary self-balancing bicycle robot with a reaction wheel

Kiattisin KanjanawanishkulDOI: 10.14736/kyb-2015-1-0173

Abstract:

A self-balancing bicycle robot based on the concept of an inverted pendulum is an unstable and nonlinear system. To stabilize the system in this work, the following three main components are required, i. e., (1) an IMU sensor that detects the tilt angle of the bicycle robot, (2) a controller that is used to control motion of a reaction wheel, and (3) a reaction wheel that is employed to produce reactionary torque to balance the bicycle robot. In this paper, we propose three control strategies: linear quadratic regulator (LQR), linear model predictive control (LMPC), and nonlinear model predictive control (NMPC). Several simulation tests have been conducted in order to show that our proposed control laws can achieve stabilizaton and make the system balance. Furthermore, LMPC and NMPC controllers can deal with state and input constraints explicitly.

Keywords:

self-balancing bicycle robot, linear quadratic regulator, model predictive control

Classification:

49N05, 93C85

paper.pdf

References:

  1. F. Allgöwer, R. Findeisen and Z. K. Nagy: Nonlinear model predictive control: from theory to application. J. Chin. Inst. Chem. Eng. 35 (2004), 3, 299-315.   CrossRef
  2. A. V. Beznos, A. M. Formalsky, E. V. Gurfinkel, D. N. Jicharev, A. V. Lensky, K. V. Savitsky and L. S. Tchesalin: Control of autonomous motion of two-wheel bicycle with gyroscopic stabilization. In: Proc. International Conference on Robotics and Automation, Leuven 1998, pp. 2670-2675.   DOI:10.1109/robot.1998.680749
  3. T. Bui and M. Parnichkun: Balancing control of bicyrobo by particle swarm optimization-based structure-specified mixed h2/hinf control. Internat. J. Adv. Robot. Syst. 5 (2008), 4, 395-402.   DOI:10.5772/6235
  4. M. Defoort and T. Murakami: Second order sliding mode control with disturbance observer for bicycle stabilization. In: Proc. International Conference on Intelligent Robots and Systems, Nice 2008, pp. 2822-2827.   DOI:10.1109/iros.2008.4650685
  5. J. Gallaspy: Gyroscopic Stabilization of an Unmanned Bicycle. Master's Thesis, Auburn University, 1999.   CrossRef
  6. L. Keo and Y. Masaki: Trajectory control for an autonomous bicycle with balancer. In: Proc. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Xi'an 2008, pp. 676-681.   DOI:10.1109/aim.2008.4601741
  7. L. Keo and M. Yamakita: Control of an autonomous electric bicycle with both steering and balancer controls. Adv. Robot. 25 (2011), 1-22.   DOI:10.1163/016918610x538462
  8. S. Lee and W. Ham: Self-stabilizing strategy in tracking control of unmanned electric bicycle with mass balance. In: Proc. International Conference on Intelligent Robots and Systems, Lausanne 2002, pp. 2200-2205.   DOI:10.1109/irds.2002.1041594
  9. G. Lei, L. Qi-zheng, W. Shi-min and Z. Yu-feng: Design of linear quadratic optimal controller for bicycle robot, automation and logistics. In: Proc. International Conference on Automation and Logistics (ICAL), Shenyang 2009, pp. 1968-1972.   DOI:10.1109/ical.2009.5262628
  10. D. Q. Mayne, J. B. Rawlings, C. V. Rao and P. O. M. Scokaert: Constrained model predictive control: Stability and optimality. Automatica 36 (2000), 6, 789-814.   DOI:10.1016/s0005-1098(99)00214-9
  11. P. Pongpaew: Balancing Control of a Bicycle Robot by Centrifugal Force. Master's Thesis, Asian Institute of Technology, 2010.   CrossRef
  12. P. O. M. Scokaert and J. B. Rawlings: Constrained linear quadratic regulation. IEEE Trans. Automat. Control 43 (1998), 8, 1163-1169.   DOI:10.1109/9.704994
  13. Y. Tanaka and T. Murakami: Self sustaining bicycle robot with steering controller. In: Proc. IEEE International Workshop on Advanced Motion Control, Kawasaki 2004, pp. 193-197.   DOI:10.1109/amc.2004.1297665
  14. J. Yi, D. Song, A. Levandowski and S. Jayasuriya: Trajectory tracking and balance stabilization control of autonomous motorcycle. In: Proc. International Conference on Robotics and Automation, Orlando 2006, pp. 2583-2589.   DOI:10.1109/robot.2006.1642091