Nonholonomic mechanics and locomotion: the snakeboard example

Abstract

Analysis and simulations are performed for a simplified model of a commercially available variant on the skateboard, known as the Snakeboard.1 Although the model exhibits basic gait patterns seen in a large number of locomotion problems, the analysis tools currently available do not apply to this problem. The difficulty is seen to lie primarily in the way in which the nonholonomic constraints enter into the system. As a first step towards understanding systems represented by our model we present the equations of motion and perform some controllability analysis for the snakeboard. We also perform some numerical simulations of the gait patterns.