The objective of this dissertation is to develop nonlinear tracking control laws that can stabilize all the states of general planar and spatial models of underactuated vehicles, regardless of their physical nature (air, sea, land). The method relies on the generation of feasible trajectories and a velocity coordinate transformation that can be applied to any underactuated vehicle, whether modeled as a planar or spatial rigid body. In the future, these methods can be extended in order to control a network of heterogeneous underactuated vehicles.

In the first part of this work, we develop backstepping and sliding mode controllers to track a generic underactuated planar vehicle along feasible trajectories, implement and simulate the controllers for a marine surface vessel model, and validate their performance with experiments. It is also shown that the control laws are robust with respect to unknown but bounded uncertainties and disturbances. The tracking controller design is made possible by taking the set of position / orientation and velocity states and transforming them into a smaller set of error states. The controllers derived herein can be applied to mobile robots, aircraft moving in the vertical plane, and surface vessels.

In the second part of this work, we extend this concept into three-dimensional space. First, we design controllers for a fully-actuated generic vehicle model, prove stability, and simulate it. Next, we develop nonlinear controllers that can stabilize the error dynamics of any three-dimensional vehicle with one translational degree of underactuation. Finally, we develop a backstepping control law to stabilize a generic three-dimensional vehicle with two translational degrees of underactuation, apply it to autonomous underwater vehicle and multirotor models, simulate it, and validate it with multirotor experiments.