title: Stabilizing skateboard speed-wobble with reflex delay.
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.
authors.affiliation: Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary varszegi@mm.bme.hu.
authors.forename: Balazs
authors.identifier: 0000-0003-4713-5132
authors.initials: B
authors.lastname: Varszegi
authors.affiliation: MTA-BME Research Group on Dynamics of Machines and Vehicles, Budapest, Hungary.
authors.forename: Denes
authors.initials: D
authors.lastname: Takacs
authors.affiliation: Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary.
authors.forename: Gabor
authors.initials: G
authors.lastname: Stepan
authors.affiliation: Department of Engineering Mathematics, University of Bristol, Bristol, UK.
authors.forename: S John
authors.initials: SJ
authors.lastname: Hogan
mesh_terms: D006801:Humans; D008959:Models, Neurological; D012018:Reflex / Q000502:physiology*; D012861:Skating / Q000502:physiology*
keywords: human balancing; non-holonomic mechanics; skateboard; time delay