Trajectory tracking control of spatial underactuated vehicles

A common approach to control of underactuated vehicles is a prelude to cooperative control of heterogeneous networks. This article presents a novel nonlinear trajectory tracking control framework for general three-dimensional models of underactuated vehicles with twelve states and four control inputs, including underwater, air, and space vehicles. Given a desired reference trajectory for four of the six degrees of freedom, feasible state trajectories are generated using the second-order nonholonomic constraints in the vehicle equations of motion. A novel transformation is then introduced to formulate the error dynamics in a simplified form. The error dynamics is stabilized using a traditional nonlinear control approach. The control law is shown to uniformly asymptotically stabilize all six pose states assuming bounded unknown uncertainties and disturbances. Adaptation of the method to underwater vehicles is presented along with simulation under highly nonlinear conditions. The approach is also applied to quadrotors and both simulation and experimental results are presented.