Addendum to “Universal covering of driftless control systems”

Abstract

Covering space for monotonic homotopy of trajectories of control systems without drift vector field was considered in [2]. More precisely, we initially proved that for a given initial state x ? M, the covering space Γ(Σ, x) by equivalent classes of monotonically homotopic trajectories of a driftless control system Σ coincides with the simply connected universal covering manifold of M. In this brief note, we improve upon some aspects of the paper [2] by providing an explicit construction of a contractible trajectory of Σ that was needed therein.