Dynamics of multibody vehicles and their formulation as nonlinear control systems

We develop equations of motion for multibody vehicles that can be used for nonlinear system analysis and control design. A multibody vehicle consists of a base body that can undergo general motion in three dimensions, as well as a finite number of body interconnections that can deform relative to the base body and hence define the shape of the multibody. A Lagrangian development leads to equations of motion that are expressed in terms of the locked inertia and the mechanical connection. We show that the equations of motion can be written in terms of the base body translational and angular momentum (or equivalently the base body translational and angular velocities) and generalized coordinates for the shape. The coupling between the base body translational and rotational dynamics and the shape dynamics is made clear in this formulation. We define several fundamental categories of underactuated control problems, based on specific control actuation assumptions