Globally Stabilizing Proportional-Integral-Derivative Control Laws for Rigid-Body Attitude Tracking

摘要

ATTITUDE control of a rigid body has important applications tornaircraft and spacecraft. Various control laws have been devel-rnoped for pointing and slewing [1–17]. To enhance the flight envelopernof a spacecraft system, globally stabilizing control laws are widelyrndesired for attitude control.rnIn attitude control of a rigid-body, singular orientation and thernunwinding phenomenon are two major obstacles to designing arnglobally stabilizing control law [1]. Every three-parameter attitudernrepresentation has an associated singular orientation, including Eulerrnangles, Rodrigues parameters, and modified Rodrigues parametersrn[2]. Most of the control laws with the globally nonsingular four-rnparameter unit quaternion representation suffer the unwindingrnphenomenon. The unwinding phenomenonmeans that the bodymayrnstart at rest arbitrarily close to the desired final attitude and yet rotaternthrough large angles before coming to rest in the desired attitude [3].rnUsing rotation matrices directly could avoid the singularities andrnthe unwinding, such as in the continuous control laws proposed inrn[4–8]. These control laws, however, only achieve “almost“ globalrnresults, which seems to be the best possible in the sense that globalrnstabilization using smooth feedback is not achievable.