Continuous Path Following Control for Underactuated Systems With Bounded Actuation

Abstract

There exist many systems in our daily lives which are underactuated, subject to limits in actuation and which must navigate in constrained spatial environments. Furthermore, these systems can be described in uniform relative degree strict feedback form. Foremost among these are wheeled vehicles like passenger cars. Systems which navigate the physical environment often must follow precise geometric paths, but do not need to traverse the path at a specific speed profile. Hence we will utilize a path following approach, whereby path speed is considered an additional control degree of freedom. For such systems we present a control design method which will follow an arbitrary path with bounded error. The path following error itself is controllable. We then investigate conditions under which zero path following error is possible. Finally, we develop path speed limit conditions for a given path which guarantee zero path following error with control actions restricted to feasible values.