Stabilizing skateboard speed-wobble with reflex delay

Balazs Varszegi, Denes Takacs, Gabor Stepan, John Hogan

Research output: Contribution to journalArticle (Academic Journal)peer-review

13 Citations (Scopus)
217 Downloads (Pure)


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 languageEnglish
Article number20160345
Number of pages9
JournalJournal of the Royal Society Interface
Issue number121
Early online date17 Aug 2016
Publication statusPublished - Aug 2016


  • nonholonomic mechanics
  • human balancing
  • skateboard
  • time delay


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