Double integrator model and invariant manifold theory algorithm for an X4-AUV

Autonomous underwater vehicle (X4-AUV) with four inputs and 6 degrees of freedom (DOFs) is an underactuated system and has a nonholonomic features. There exist various studies on nonholonomic underatuated control so far, but most of them are confined into the case of systems with two inputs and therefore there are a few studies for the systems with three or more inputs. Control approaches for nonholonomic systems have utilized canonical forms. A nonholonomic double integrator model is the one of canonical forms for nonholonomic systems. In this paper an algorithm for an extended double integrator with four inputs is presented. Then a control law for an X4-AUV in extended double integrator model is derived using invariant manifold theory. It is expected that each state of the controlled object will be converge smoothly to the origin by using this type of control.