Universal Covering of Driftless Control Systems

Abstract

Let M be a finite-dimensional manifold and Σ be a driftless control system on M of full rank. We prove that for a given initial state x � M, the covering space Γ(Σ, x) for a monotonic homotopy of trajectories of Σ which is recently constructed in [1] coincides with the simply connected universal covering manifold of M and that the terminal projection � x : Γ(Σ, x) � M given by � x ([�]) = �(1) is a covering mapping.