Cross-track control of a slender, underactuated AUV using potential shaping

The three-dimensional directional stabilization problem is addressed for a slender autonomous underwater vehicle with three inputs: thrust, pitch moment, and yaw moment. The control law reshapes potential energy through feedback. Conditions for asymptotic stability are derived by applying Lyapunov's direct method to a control Lyapunov function constructed from the control-modified energy and other conserved quantities. Analysis proves asymptotic stability and suggests almost global convergence. The dynamic model requires minimal assumptions concerning the viscous force and moment, resulting in a directional controller that is inherently robust to uncertainty in these effects. The directional control algorithm is then extended by incorporating a line-of-sight guidance rule to enable cross-track control, or line following, although the extension requires an additional control moment about the roll axis. Spectral stability analysis provides sufficient conditions for local exponential stability and numerical simulations suggest that stability is almost globally asymptotic.