Modelling and state feedback control of nonholonomic mechanical systems

The dynamics of nonholonomic mechanical systems is described by the classical Euler-Lagrange equations subjected to a set of nonintegrable constraints. It is shown that nonholonomic systems are strongly accessible whatever the structure of the constraints. They cannot be asymptotically stabilized by a smooth pure state feedback. However, smooth state feedback control laws can be designed which guarantee the global marginal stability of the system with the convergence to zero of an output function whose dimension is the number of degrees of freedom