While some of these problems are approximately solved by linearization-based techniques, our work focuses on the nonlinear features of these systems and on global robustness and performance issues. From a theoretical standpoint, autonomous vehicles are modeled as mechanical systems with symmetries . In particular for underwater and aerospace applications the classic Euler-Lagrange's equations provide us with simplified models that capture the relevant nonlinearities. A very useful feature of these systems is the presence of symmetries, that is the invariance of the equations of motion under an arbitrary translation and rotation. We believe that a proper understanding of the role of energy, conservation laws and forces will lead to powerful control strategies.
Station keeping in presence of actuation failure is for example one of the achieved goals.
We are currently investigating efficient motion planning strategies for underactuated systems. A promising direction is the study of relative equilibria, that is, steady motions for the unforced system. Some preliminary results are described here . A complete index of papers is available. We present a general framework for the control of Lagrangian systems with as many inputs as degrees of freedom.