Dynamics and Bifurcations of Pursuit Guidance for Vehicle Path Keeping in the Dive Plane

Abstract

The problem of dynamic interactions between an orientation control law and pure pursuit guidance law for dive plane response of underwater vehicles is analyzed. A complete stability analysis is performed in order to evaluate regions of stable vehicle operations. It is shown that loss of stability can occur in either a static or dynamic way. In the first, a linearly increasing path deviation is observed, whereas in the second the loss of stability is accompanied by the generation of self-sustained oscillatory motions around the commanded path. Nonlinear analysis reveals the occurrence of both static and Poincaré-Andronov-Hopf bifurcations. Numerical experiments support the analytic predictions of the bifurcation analysis.