Kinematic mechanism and path planning of the Essboard

In this paper, we study the kinematic mechanism and path planning for a two-caster nonholonomic vehicle (the Essboard) which is a recent variant of skateboard. Different from the most studied Snakeboard, the Essboard consists of a torsion bar and two platforms, each of which contains a pedal and a caster. We first investigate the relationship between the tilt angles of the pedals and the wheel directions of the casters. This relationship reveals how to control the wheel directions by adjusting the tilt angles. Next, the rotational radius of the Essboard is derived for a given pair of tilt angles of both pedals. The rotational radius of the Essboard is much different than that of the Snakeboard. Then we develop a path-planning algorithm for the Essboard to move from a start position to the goal, using a series of consecutively connected arcs, which are tangent to each other at the connected points. It is shown from a kinematic point of view that the path planning of the Essboard can be solved by a series of pairs of pedals' tilt angles. Three experiments are conducted to confirm the correctness of the main results. The results in this paper are a foundation for further study of the Essboard.