Constant speed gaits should work across all speeds

Abstract

The Stokesian form of the reconstruction equation of Geometric Mechanics arises when the contact forces are so large compared to body inertia that the group momentum decays almost instantaneously. As special case of this occurs when body velocity is constant. In that case it can be shown that for a variety of types of contact friction, as long as all contacts use the same type of friction, time-rescaling the body shape change would produce a geometrically identical motion at a re-scaled speed. The implication of this observation is that if an animal or robot managed to discover a pattern of shape-changes which produces a constant velocity motion, that pattern could be used for every speed. The limiting factor would not be interaction with the environment -- it would be the ability of the body to change its own shape at the desired rates.