The snakeboard is shown to possess two decoupling vector fields, and to be kinematically controllable. Accordingly, the problem of steering the snakeboard from a given configuration at rest to a desired configuration at rest is posed as a constrained static nonlinear inversion problem. An explicit algorithmic solution to the problem is provided, and its limitations are discussed. An ad hoc solution to the nonlinear inversion problem is also exhibited.

This paper studies the mechanics of undulatory locomotion. This type of locomotion is generated by a coupling of internal shape changes to external non-holonomic constraints. Employing methods from geometric mechanics, the authors use the dynamic symmetries and kinematic constraints to develop a specialized form of the dynamic equations which govern undulatory systems. These equations are written in terms of physically meaningful and intuitively appealing variables that show the role of internal shape changes in driving locomotion.

Analysis and simulations are performed for a simplified model of a commercially available variant of the skateboard, known as the Snakeboard. 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 lies primarily in the way in which the nonholonomic constraints enter into the system. As a first step towards understanding systems represented by their model the authors present the equations of motion and perform some controllability analysis for the snakeboard. The authors also perform numerical simulations of possible gait patterns which are characteristic of snakeboard locomotion.>