Stabilizing skateboard speed-wobble with reflex delay

Balazs Varszegi; Denes Takacs; Gabor Stepan; John Hogan

doi:10.1098/rsif.2016.0345

Stabilizing skateboard speed-wobble with reflex delay

Balazs Varszegi, Denes Takacs, Gabor Stepan, John Hogan

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

A simple mechanical model of the skateboard–skater system is analysed, in which the effect of human control is considered by means of a linear proportional-derivative (PD) controller with delay. The equations of motion of this non-holonomic system are neutral delay-differential equations. A linear stability analysis of the rectilinear motion is carried out analytically. It is shown how to vary the control gains with respect to the speed of the skateboard to stabilize the uniform motion. The critical reflex delay of the skater is determined as the function of the speed. Based on this analysis, we present an explanation for the linear instability of the skateboard–skater system at high speed. Moreover, the advantages of standing ahead of the centre of the board are demonstrated from the viewpoint of reflex delay and control gain sensitivity.

Original language	English
Article number	20160345
Number of pages	9
Journal	Journal of the Royal Society Interface
Volume	13
Issue number	121
Early online date	17 Aug 2016
DOIs	https://doi.org/10.1098/rsif.2016.0345
Publication status	Published - Aug 2016

Research Groups and Themes

Engineering Mathematics Research Group

Keywords

nonholonomic mechanics
human balancing
skateboard
time delay

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10.1098/rsif.2016.0345

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abstract = "A simple mechanical model of the skateboard–skater system is analysed, in which the effect of human control is considered by means of a linear proportional-derivative (PD) controller with delay. The equations of motion of this non-holonomic system are neutral delay-differential equations. A linear stability analysis of the rectilinear motion is carried out analytically. It is shown how to vary the control gains with respect to the speed of the skateboard to stabilize the uniform motion. The critical reflex delay of the skater is determined as the function of the speed. Based on this analysis, we present an explanation for the linear instability of the skateboard–skater system at high speed. Moreover, the advantages of standing ahead of the centre of the board are demonstrated from the viewpoint of reflex delay and control gain sensitivity.",

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AU - Varszegi, Balazs

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Y1 - 2016/8

N2 - A simple mechanical model of the skateboard–skater system is analysed, in which the effect of human control is considered by means of a linear proportional-derivative (PD) controller with delay. The equations of motion of this non-holonomic system are neutral delay-differential equations. A linear stability analysis of the rectilinear motion is carried out analytically. It is shown how to vary the control gains with respect to the speed of the skateboard to stabilize the uniform motion. The critical reflex delay of the skater is determined as the function of the speed. Based on this analysis, we present an explanation for the linear instability of the skateboard–skater system at high speed. Moreover, the advantages of standing ahead of the centre of the board are demonstrated from the viewpoint of reflex delay and control gain sensitivity.

AB - A simple mechanical model of the skateboard–skater system is analysed, in which the effect of human control is considered by means of a linear proportional-derivative (PD) controller with delay. The equations of motion of this non-holonomic system are neutral delay-differential equations. A linear stability analysis of the rectilinear motion is carried out analytically. It is shown how to vary the control gains with respect to the speed of the skateboard to stabilize the uniform motion. The critical reflex delay of the skater is determined as the function of the speed. Based on this analysis, we present an explanation for the linear instability of the skateboard–skater system at high speed. Moreover, the advantages of standing ahead of the centre of the board are demonstrated from the viewpoint of reflex delay and control gain sensitivity.

KW - nonholonomic mechanics

KW - human balancing

KW - skateboard

KW - time delay

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DO - 10.1098/rsif.2016.0345

M3 - Article (Academic Journal)

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VL - 13

JO - Journal of the Royal Society Interface

JF - Journal of the Royal Society Interface

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ER -

Stabilizing skateboard speed-wobble with reflex delay

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