Supervisory control of uncertain underactuated vehicles

In this paper, the author proposes a solution to the position tracking problem for fairly general class of underactuated autonomous vehicles that is applicable to motion in either two or three dimensional spaces. The tracking controller proposed yields global stability and exponential convergence of the position tracking error to a neighborhood of the origin that can be made arbitrarily small. The desired trajectory does not need to be a trimming trajectory and can be sufficiently smooth time-varying bounded curve, including the degenerate case of a constant trajectory (set-point). The control algorithm builds on iterative Lyapunov-based techniques, in particular, integrator backstepping. This is an important issue since the availability of a Lyapunov function suits the need of robust control designs in the presence of noise measurements, handed disturbances, and unmeasured thruster dynamics.