Exponential stabilization of an underactuated autonomous surface vessel

This paper studies the problem of controlling the planar position and orientation of an autonomous surface vessel using two independent thrusters. It is first shown that although the system is not asymptotically stabilizable to a given configuration using a time-invariant continuous feedback, it is strongly accessible and small-time locally controllable at any equilibrium. Time-invariant discontinuous feedback laws are then constructed to asymptotically stabilize the system to the desired configuration with exponential convergence rates. A simulation example is included to demonstrate the results.