Motion measurement of a two-wheeled skateboard and its dynamical simulation

This study investigates the dynamics of the propulsion mechanism of a two-wheeled skateboard by measurements of human skateboard motion and computer simulations using a simplified model. This model expresses the board motion within the horizontal plane. The inputs of the model are the yaw moment about a vertical axis, horizontal force normal to the skateboard axis, and two-wheel orientations, while the outputs are the center of mass position in the horizontal plane and the board orientation. By selecting parameters of sinusoidal inputs to fit the measurement data, similar output data is obtained from the motion measurements and computer simulations. This result allows us to conclude that some sinusoidal motions and forces can robustly propel this type of skateboard.

[1]  James P. Ostrowski.  Steering for a class of dynamic nonholonomic systems , 2000, IEEE Trans. Autom. Control..

[2]  Joel W. Burdick,et al.  Geometric Perspectives on the Mechanics and Control of Robotic Locomotion , 1996 .

[3]  Francesco Bullo,et al.  Kinematic controllability and motion planning for the snakeboard , 2003, IEEE Trans. Robotics Autom..

[4]  Jerrold E. Marsden,et al.  Symmetries in Motion: Geometric Foundations of Motion Control , 1998 .

[5]  J. Grabowski,et al.  Nonholonomic Constraints: a New Viewpoint , 2008, 0806.1117.

[6]  Joel W. Burdick,et al.  Nonholonomic mechanics and locomotion: the snakeboard example , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[7]  T. Mestdag,et al.  A generalization of Chaplygin’s Reducibility Theorem , 2009, 0909.4018.

[8]  R. Ortega,et al.  A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints , 2010, Autom..

[9]  W. M. Oliva,et al.  A note on the conservation of energy and volume in the setting of nonholonomic mechanical systems , 2004 .

[10]  James P. Ostrowski,et al.  Motion planning for anguilliform locomotion , 2003, IEEE Trans. Robotics Autom..

[11]  Vijay Kumar,et al.  Optimal Gait Selection for Nonholonomic Locomotion Systems , 1997, Proceedings of International Conference on Robotics and Automation.

[12]  D. Iglesias,et al.  Momentum and energy preserving integrators for nonholonomic dynamics , 2007 .

[13]  Jerrold E. Marsden,et al.  Geometric mechanics, Lagrangian reduction, and nonholonomic systems , 2001 .

[14]  Joel W. Burdick,et al.  Control of biomimetic locomotion via averaging theory , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

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

[16]  Sonia Martinez,et al.  Symmetries in vakonomic dynamics: applications to optimal control , 2001 .

[17]  Juan Carlos Marrero,et al.  Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic Mechanics , 2008, 0801.4358.

[18]  Jerrold E. Marsden,et al.  Poisson reduction for nonholonomic mechanical systems with symmetry , 1998 .

[20]  Andrew D. Lewis,et al.  Simple mechanical control systems with constraints , 2000, IEEE Trans. Autom. Control..

[21]  Jorge Cortes,et al.  Motion Control Algorithms for Simple Mechanical Systems with Symmetry , 2003 .

[22]  D. Lefeber,et al.  Constraint Gradient Projective Method for Stabilized Dynamic Simulation of Constrained Multibody Systems , 2003 .

[23]  Francesco Bullo,et al.  On mechanical control systems with nonholonomic constraints and symmetries , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[24]  Tatsuo Narikiyo.  Control of underactuated mechanical systems via passive velocity field control: Application to snakeboard and 3D rigid body , 2009 .

[25]  Joel W. Burdick,et al.  The Geometric Mechanics of Undulatory Robotic Locomotion , 1998, Int. J. Robotics Res..

[26]  Ivan I. Kosenko,et al.  Multibody Systems Dynamics : Modelica Implementation and Bond Graph Representation , 2006 .

[27]  A. Asnafi,et al.  Some flower-like gaits in the snakeboard’s locomotion , 2007 .

[28]  J. Burdick,et al.  Controllability Tests for Mechanical Systems withSymmetries and ConstraintsJim , 1997 .

[29]  Kevin M. Lynch.  Optimal control of the thrusted skate , 2003, Autom..

[30]  Kevin M. Lynch,et al.  Minimum control-switch motions for the snakeboard: a case study in kinematically controllable underactuated systems , 2004, IEEE Transactions on Robotics.

[31]  P. Krishnaprasad,et al.  Nonholonomic mechanical systems with symmetry , 1996 .

[32]  Vijay Kumar,et al.  RoboTrikke: A Novel Undulatory Locomotion System , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[33]  M Hubbard.  Human control of the skateboard. , 1980, Journal of biomechanics.

[34]  Howie Choset,et al.  Towards automated gait generation for dynamic systems with non-holonomic constraints , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..