Connection vector fields for underactuated systems

In this paper, we build off results from geometric mechanics to gain fresh insight into the locomotion of underactuated systems. More specifically, we use the connection, which relates body velocity to internal shape changes, to create a set of vector fields on the shape space. Each of these fields corresponds to one component of the body velocity (forward, lateral, rotational), and together they highlight how a given shape change will move the system through ambient space. To demonstrate this approach, we use it to analyze the motion of several model systems, both simulated and physically instantiated.