An Integral Line-of-Sight Guidance Law with a Speed-dependent Lookahead Distance

This paper presents an algorithm that makes an underactuated marine vehicle follow a straight line path while in the presence of a constant ocean current. When following the path, the vehicle maintains a desired surge speed which is measured relative to the water, and which may be constant or time-varying. The algorithm is an integral line-of-sight guidance law where the lookahead distance is designed to depend linearly on the desired relative surge speed of the vehicle. This dependency makes it possible to keep the maneuvering demands of the vehicle limited, even when the vehicle surge speed is large. It is shown that if the desired relative surge speed is constant along the path, the resulting error dynamics has a uniformly semiglobally exponentially stable equilibrium at the origin, thus achieving the path following and velocity control objectives. Furthermore, in the case of a general, timevarying desired speed trajectory, it is shown that the solutions of the system remain bounded. The results are supported by simulations, as well as experiments with an unmanned surface vehicle.