Study on Stability for Longitudinal Motion of Autonomous Underwater Vehicle

Although the equations describing the longitudinal motions of autonomous underwater vehicles are typically nonlinear, the linearized equations are still employed to design the depth controller by the traditional analysis methods in engineering for the sake of simplicity. The nonlinear systems limited in the longitudinal plane of the autonomous underwater vehicles are analyzed on center manifold through the bifurcation theory. The center manifolds are calculated and one-dimensional bifurcation equations on the center manifolds are obtained and analyzed. Based on the transcritical bifurcation diagram, we have found the mechanism of the attitude stability loss as well as the abnormal trajectory of autonomous underwater vehicles. Numerical simulation verifies the results.