Stabilization of Autonomous Vehicles with Nonholonomic Constraints: Open Problems and Future Directions

This position paper focuses on the problem of stabilization of underactuated and nonholonomic autonomous vehicles at a given posture. The stabilization problem for those systems represents a challenge for nonlinear control theory because the linearization of such systems is not controllable. In fact, as shown by Brockett [6], for this class of systems there does not exist a continuously differentiable, time invariant, state feedback control laws which asymptotically stabilizes those systems to an equilibrium point.