Holonomy orbits of the snake charmer algorithm

The snake charmer algorithm permits us to deform a piecewise smooth curve starting from the origin in R^d, so that its end follows a given path. When this path is a loop, a holonomy phenomenon occurs. We prove that the holonomy orbits are closed manifolds diffeomorphic to real Stiefel manifolds. A survey of the snake charmer algorithm is given in the paper.