Controllability of affine nonlinear systems

The controllability of affine nonlinear systems is studied. The concept of controllability is defined by using the orbits of families of vector fields. A complete proof of the controllability criterion based on weakly positively Poisson stability of drift vector field is presented. Sufficient condition for systems on compact Riemann manifold with conservative drift vector field to be controllable is given, which is also necessary for analytic systems. Some equivalent conditions for weakly positively Poisson stability are proved. Finally, a sufficient condition for the controllability of general affine nonlinear systems is obtained by using the conservative field criterion, which is used to analyse the controllability of the underactuated spacecraft attitude control system.