Uniformly semiglobally exponential stability of vector field guidance law and autopilot for path-following

A uniform semiglobal exponential stability (USGES) proof for a time-varying vector field guidance law used for path-following control of vehicles is presented. A sliding mode control is introduced for heading autopilot design and Lyapunov methods are used to derive the control law. The equilibrium point of the autopilot error dynamics is proven to be globally exponentially stable (GES). The main result is a time-varying vector field guidance law in cascade with the autopilot. A theorem ensures that the equilibrium point of the cascaded system is uniformly semiglobally exponentially stable. Both straight-line and curved-path path following scenarios are considered in the presence of ocean currents. Simulation studies are carried out to verify the theoretical results. The time-varying guidance laws can also be applied to vehicles in general such as aircraft, underwater vehicles, drones and autonomous vehicles