Reduced Effort Control Laws for Underactuated Rigid Spacecraft

Abstract

A nonsmooth, time-invariant feedback control law can be used to rotate an axisymmetric rigid spacecraft to the zero equilibriumusingonly twocontroltorques.Thismethod,however, may requireasignie cantamountofcontrol effort, especially for initial conditions close to an equilibrium manifold corresponding to rotations about the unactuated principal axis.Acontrollawisproposedin thiswork thatreducesthecontroleffortrequired toperformrestto-restmaneuversforinitialconditionsclosetothisequilibrium manifold.Specie cally,thephasespaceofthesystem is divided into two parts, one corresponding to initial conditions producing large control effort (the “ bad” region ) and theothercorresponding to initialconditionsproducing small control signals (the“ good” region ). Theproposed control lawthen rendersthisundesirableequilibrium manifold unstable, driving the trajectoriesof theclosed-loop system into the good region, where the original control law is subsequently used. Numerical simulations indicate reduction of the control magnitude on theorder of 80 ‐90% for initial conditions close to theequilibrium manifold.