Turning dynamics and equilibrium of two-wheeled vehicles



The equations of motion of two-wheeled vehicles, e g bicycles or motorcycles, are developed by using Lagrange’s equations for quasi-coord mates The pure rolling constiatnts between the ground and the two wheels aie considered in the dynamical equations of the system For each wheel, two nonholonomic and two holonomic constraints are introduced in a set of differential-algebraic equations (DAE) The constraint Jacobian matrix is obtained by collecting all the constraint equations and converting them into the velocity form Equilibrium, an algorithm for searching for equilibrium points of two-wheeled vehicles and the associated problems are discussed Formulae foi calculating the radii of curvatures of ground-wheel contact paths and the reference point are also given

Key Words

Bicycle Dynamics Two-Wheeled Vehicle Nonholonomic Constraint Multibody 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alleyne, A and DePoorter, M, 1997, “Lateral Displacement Sensor Placement and Forwaid Velocity Effects on Stability of Lateral Control of Vehicles,”American Control Conference, Vol. 3, pp 1593–1597Google Scholar
  2. Amirouche, F M L, 1992, Computational Me- thods in Multibody Dynamics, Prentice-HallGoogle Scholar
  3. Baruh, H, 1999, Analytical Dynamics, Mc-Graw-HillGoogle Scholar
  4. Beznos, A V, Formal’sky, A M, Gurfinkel, E V, Jicharev, D N, Lensky, A V, Savitsky, K V and Tchesahn, L S, 1998, “Control of Autonomous Motion of Two-wheel Bicycle with Gyioscopic Stabilisation,”Proceedings of the 1998 IEEE Internationa! Conference on Robo- tics & Automation, Leuven, Belgium May, Vol 3, pp 2670–2675Google Scholar
  5. Chen, C and Tan, H S, 1998, “Steering Con- tiol of High Speed Vehicles Dynamic Look Ahead and Yaw Rate Feedback,”Proceedings of the 37th IEEE Conference on Decision & Control, Tampa, Floiida USAGoogle Scholar
  6. Feng, K T, Tan, H S and Tomizuka, M, 1998, “Automatic Steering Control of Vehicle Lateral Motion with the Effect of Roll Dyna- mics,”Proceedings of the American Control Con- ference, Philadelphia, PennsylvaniaGoogle Scholar
  7. Getz, N H, 1993, “Control of Nonholonomic Systems With Dynamically Decoupled Actua- tors,”Proceedings of the 32nd Conference on Decision and Control, San Antonio, TexasGoogle Scholar
  8. Getz, N H, 1994, “Control of Balance for a Nonlinear Nonholonomic Non-minimum Phase Model of a Bicycle,”Proceedings of the American Control Conference, Baltimore, MarylandGoogle Scholar
  9. Getz, N H, 1995, “Internal Eqtnlibiium Con- trol of a Bicycle,”Proceedings of the 34th Con- ference on Decision & Control, New Orleans, LA-December, Vol 4, pp 4286–4287Google Scholar
  10. Getz, N H and Hednck, J K, 1995, “An In- ternal Equilibrium Manifold Method of Trac- king for Nonlinear Nonmmimum Phase Sys- tems,”Proceedings of the American Control Con- ference, Seattle, WashingtonGoogle Scholar
  11. Getz, N H and Marsden, J E, 1995, “Control for an Autonomous Bicycle,”IEEE International Conference on Robotics and Automation, Vol 2, pp 1397–1402Google Scholar
  12. Indiven, G, 1999, “Kinematic Time-invariant Control of a 2D Nonholonomic Vehicle,”Procee- dings of the 38th IEEE Conference on Decision & Control, Vol 3, pp 2112–2117Google Scholar
  13. Lee, S and Ham, W, 2002, “Self Stabilizing Strategy in Tracking Control of Unmanned Electric Bicycle with Mass Balance,”IEEE/RSJ International Conference on Intelligent Robots and System, Vol 3, pp 2200–2205Google Scholar
  14. Suryanarayanan, S., Tomizuka, M and Weaver, M, 2002, “System Dynamics and Control of Bicycles at High Speeds,”American Control Conference, Vol 2, pp 845–850Google Scholar
  15. Yao, Y S and Chellappa, R, 1994, “Estimation of Unstabilized Components in Vehicular Motion,”Proceedings of the 12th IAPR International Conference on Computer Vision & Image Processing, Voi 1, pp 641–644Google Scholar
  16. Yavin, Y, 1997, “Navigation and Control of the Motion of a Riderless Bicycle by Using a Simplified Dynamic Model,”Mathematical and Computer Modelling, Vol 25, pp 67–74MATHCrossRefMathSciNetGoogle Scholar
  17. Yavin, Y, 1998, “Navigation and Control of the Motion of a Riderless Bicycle,”Compute Methods Appl Mech Engrg, 160, pp 193–202MATHCrossRefMathSciNetGoogle Scholar
  18. Yavin, Y, 1999, “Stabilization and Control of the Motion of an Autonomous Bicycle by Using a Rotor for the Tilting Moment,”Computer Methods in Applied Mechanics and Engineering, Vol 178, pp 233–243MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2005

Authors and Affiliations

  1. 1.Department of Mechanical and Automation EngineeringDa-Yeh UniversityChanghuaTaiwan

Personalised recommendations