Controllability of kinematic control systems on stratified configuration spaces

This paper considers nonlinear kinematic controllability of a class of systems called stratified. Roughly speaking, such stratified systems have a configuration space which can be decomposed into sub-manifolds upon which the system has different sets of equations of motion. For such systems, considering the controllability is difficult because of the discontinuous form of the equations of motion. The main result in this paper is a controllability test, analogous to Chow's theorem, is based upon a construction involving distributions, and the extension thereof to robotic gaits.