Bicycle dynamics and control: adapted bicycles for education and research

In this paper, the dynamics of bicycles is analyzed from the perspective of control. Models of different complexity are presented, starting with simple ones and ending with more realistic models generated from multibody software. Models that capture essential behavior such as self-stabilization as well as models that demonstrate difficulties with rear wheel steering are considered. Experiences using bicycles in control education along with suggestions for fun and thought-provoking experiments with proven student attraction are presented. Finally, bicycles and clinical programs designed for children with disabilities are described.

[1]  T. Murakami,et al.  Self sustaining bicycle robot with steering controller , 2004, The 8th IEEE International Workshop on Advanced Motion Control, 2004. AMC '04..

[2]  Robin S. Sharp,et al.  The Stability and Control of Motorcycles , 1971 .

[3]  R. Klein,et al.  Adapted Bicycles for Teaching Riding Skills , 2005 .

[4]  Robert Schwarz.  ACCIDENT AVOIDANCE CHARACTERISTICS OF UNCONVENTIONAL MOTORCYCLE CONFIGURATIONS , 1979 .

[5]  Reinhold von Schwerin.  MultiBody System SIMulation - Numerical Methods, Algorithms, and Software , 1999, Lecture Notes in Computational Science and Engineering.

[6]  R.E. Klein.  Using bicycles to teach system dynamics , 1989, IEEE Control Systems Magazine.

[7]  S. W..  On Some Key Issues in the Windsurfer Approach to Adaptive Robust Control , .

[8]  Richard E. Klein.  Novel Systems and Dynamics Teaching Techniques using Bicycles , 1988, 1988 American Control Conference.

[9]  Anders Lennartsson,et al.  Efficient multibody dynamics , 1999 .

[10]  Iven M. Y. Mareels,et al.  On some key issues in the windsurfer approach to adaptive robust control , 1995, Autom..

[11]  C. Koenen,et al.  The dynamic behaviour of a motorcycle when running straight ahead and when cornering , 1983 .

[12]  P. A. J. Ruijs,et al.  Research in Lateral Dynamics of Motorcycles , 1985 .

[13]  J. W. Humberston.  Classical mechanics , 1980, Nature.

[14]  T. Mckeown.  Mechanics , 1970, The Mathematics of Fluid Flow Through Porous Media.

[15]  J. Lowell,et al.  The stability of bicycles , 1982 .

[16]  Pan Zhenkuan,et al.  Dynamics of flexible multibody systems with tree topologies , 1992 .

[17]  N. H. Getz.  Control of balance for a nonlinear nonholonomic non-minimum phase model of a bicycle , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[18]  G. Stein,et al.  Respect the unstable , 2003 .

[19]  D. Kirshner.  Some nonexplanations of bicycle stability , 1980 .

[20]  Y. Henaff.  Dynamical stability of the bicycle , 1987 .

[21]  Karl J. Åström,et al.  Limitations on control system performance , 1997, 1997 European Control Conference (ECC).

[22]  Tom D. Crouch,et al.  The Bishop’s Boys: A Life of Wilbur and Orville Wright by Tom Crouch (review) , 1991, Technology and Culture.

[23]  Leonard Krasner,et al.  Behavior modification: What it is and how to do it. , 1979 .

[24]  Stephen P. Boyd,et al.  Future directions in control in an information-rich world , 2003 .

[25]  I. Neĭmark,et al.  Dynamics of Nonholonomic Systems , 1972 .

[26]  A. I. Krauter.  Steady-State Cornering of Two-Wheeled Vehicles , 1973 .

[27]  Barry Craig Mears.  OPEN LOOP ASPECTS OF TWO WHEELED VEHICLE STABILITY CHARACTERISTICS , 1989 .

[28]  Jared R. Leadbetter,et al.  Control in an Information Rich World Report of the Panel on Future Directions in Control , Dynamics , and Systems , 2002 .

[29]  A. Letov.  Stability of an automatically controlled bicycle moving on a horizontal plane , 1959 .

[30]  D. Herlihy.  Bicycle: The History , 2004 .

[31]  Martin Lesser.  The analysis of complex nonlinear mechanical systems : a computer algebra assisted approach , 1995 .

[32]  Lee Howard Laiterman.  Theory and applications of rear-wheel steering in the design of man-powered land vehicles. , 1977 .

[33]  Hilding Elmqvist,et al.  The New Modelica MultiBody Library , 2003 .

[34]  G. Franke,et al.  An advanced model of bicycle dynamics , 1990 .

[35]  Robin S. Sharp.  The Dynamics of Single Track Vehicles , 1976 .

[36]  Simos A. Evangelou,et al.  Advances in the Modelling of Motorcycle Dynamics , 2004 .

[37]  Arend L. Schwab,et al.  Benchmark results on the linearized equations of motion of an uncontrolled bicycle , 2005 .

[39]  A. Bryson.  Applied Linear Optimal Control: Examples and Alogrithms , 2002 .

[40]  K. I. T. Richardson.  The gyroscope applied , 1954 .

[41]  R. H. HOUSMAN.  “Bicycles and Tricycles” , 1897, Nature.

[42]  Martin Otter,et al.  Modelica-a language for physical system modeling, visualization and interaction , 1999, Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design (Cat. No.99TH8404).

[43]  Richard M. Murray,et al.  Panel on Future Directions in Control, Dynamics, and Systems , 2000 .

[44]  Jerrold E. Marsden,et al.  Control for an autonomous bicycle , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[45]  Jerrold E. Marsden,et al.  The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems , 1997 .

[46]  Thomas R. Kane,et al.  Fundamental kinematical relationships for single-track vehicles , 1975 .

[47]  F. Klein,et al.  Über die Theorie des Kreisels , 1897 .

[48]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[49]  Sangduck Lee,et al.  Self stabilizing strategy in tracking control of unmanned electric bicycle with mass balance , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[50]  Hans B. Pacejka,et al.  Tire and Vehicle Dynamics , 1982 .

[51]  Hiroyasu Fu,et al.  Fundamental Characteristics of Single-Track Vehicles in Steady Turning , 1965 .

[52]  John Liesegang,et al.  Dynamics of a bicycle: Nongyroscopic aspects , 1978 .

[53]  D. E. Jones.  The stability of the bicycle , 1970 .

[54]  David H. Weir,et al.  Lateral-Directional Motorcycle Dynamics and Rider Control , 1978 .

[55]  Robin S. Sharp,et al.  A Motorcycle Model for Stability and Control Analysis , 2001 .

[56]  Ronald L. Huston,et al.  Dynamics of Multibody Systems , 1988 .

[57]  Archibald Sharp,et al.  Bicycles and Tricycles: An Elementary Treatise on Their Design and Construction , 1977 .

[58]  R. E. Klein.  THE UNIVERSITY OF ILLINOIS BICYCLE PROJECT , 1992 .