Position Control of Rolling Skateboard

A simple mechanical model of the skateboard-skater system is analyzed, in which the skater tries to follow a straight line by the board. The human control is considered by means of a linear delayed PD controller. The equations of motion of the non-holonomic system are derived with the help of the Gibbs-Appell method. The linear stability of the system is given analytically. The effect of the re?ex delay of the skater on the stability is investigated. It is shown that in case of zero re?ex delay, the motion along a straight line is unstable while non-zero re?ex delay can provide stable motion for some speci?c speed ranges.