Dynamics of damped skateboards under human control

[+] Author and Article Information
Balazs Varszegi

Department of Applied Mechanics Budapest University of Technology and Economics and MTA-BME Lendulet Human Balancing Research Group, Budapest, Hungary

Denes Takacs

MTA-BME Research Group on Dynamics of Machines and Vehicles Budapest, Hungary

Gabor Stepan

Department of Applied Mechanics Budapest University of Technology and Economics Budapest, Hungary

1Corresponding author.

ASME doi:10.1115/1.4036482 History: Received September 21, 2016; Revised March 20, 2017


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 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, the position of the skater on the board and the 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.

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