On the Global Behavior of a Geometric PDAV Controller by Means of a Geometrically Exact Linearization

Abstract

A complex motion encountered in a number of robotic, industrial, and defense applications is the motion of a rigid body when one of its body-fixed axes tracks a desired pointing direction while it rotates at high angular velocity around the pointing direction (PDAV); during this motion, high frequency precession/nutation oscillations arise. This work analyzes the global/local closed-loop (CL) behavior induced by a developed geometric, PDAV controller and studies the high frequency precession/nutation oscillations that characterize PDAV motions. This is done via geometrically exact linearization and via simulation techniques that amount to charting the smooth CL vector fields on the manifold. A method to quickly estimate the frequency of the precession/nutation oscillations is developed and can be used for sizing actuators. A thorough understanding of the behavior of the CL flow induced by the PDAV controller is achieved, allowing the control engineer to anticipate/have a rough estimate of the system CL response.