A simple mechanical model of the skateboard–skater system is analyzed, in which a linear proportional-derivative (PD) controller with delay is included to mimic the effect of human control. The equations of motion of the nonholonomic system are derived with the help of the Gibbs–Appell method. The linear stability analysis of the rectilinear motion is carried out analytically in closed form. It is shown that how the control gains have to be varied with respect to the speed of the skateboard in order to stabilize the uniform motion. The critical reflex delay of the skater is determined as functions of the speed, position of the skater on the board, and damping of the skateboard suspension system. Based on these, an explanation is given for the experimentally observed dynamic behavior of the skateboard–skater system at high speed.
Stability of Damped Skateboards Under Human Control
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 21, 2016; final manuscript received March 20, 2017; published online May 4, 2017. Assoc. Editor: Bernard Brogliato.
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Varszegi, B., Takacs, D., and Stepan, G. (May 4, 2017). "Stability of Damped Skateboards Under Human Control." ASME. J. Comput. Nonlinear Dynam. September 2017; 12(5): 051014. https://doi.org/10.1115/1.4036482
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