Invariant manifold for extended nonholonomic double integrator systems

Nonholonomic underactuated systems are typically modelled as highly nonlinear ones, which becomes obvious as the dimension of the system increases. Since this system cannot be stabilized by a static continuous feedback with constant gains, there are several control methods by using a canonical form up to now such as a chained form, a power form, a goursat normal form and a double integrator model. In this paper, we consider extended nonholonomic double integrator systems obtained by extending the Brockett nonholonomic integrator in order to expand the application of underactuated control to control the system using invariant manifold approach.