Kinematics-based control of underactuated vehicles with four-inputs and six-states by applying invariant manifolds

In this paper, an invariant manifold approach is applied for controlling chained form systems with four inputs and six states. This type of systems includes VTOL (vertical take off and landing) aerial robots such as X4-flyer, AUVs (autonomous underwater vehicles) such as a longitudinal or lateral X4 -AUV, etc. The present underactuated control method is composed of a two step method: the first step is an attractive control to achieve an invariant manifold vector and the second step is a state feedback control to assure the asymptotic behavior of states constrained on each invariant manifold. Some simulations with changes in design parameters are given to demonstrate the effectiveness of the proposed method.