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 submanifolds upon which the system has a different set of equations of motion. For such systems, then, considering controllability is difficult because of the discontinuous form of the equations of motion. We present two alternative forms of the controllability test. The first, analogous to Chow’s theorem, is based upon a construction involving distributions. The second, uses tools from exterior differential systems and is based upon a constrution which uses the derived flag.