Adaptive Control of Nonlinear Attitude Motions Realizing Linear Closed Loop Dynamics

Abstract

An adaptive attitude control law is presented that realizes linear closed-loop dynamics in the attitude error vector. The modified Rodrigues parameters (MRPs) are used as the kinematic variables since they are nonsingular for all possible rotations. The desired linear closed-loop dynamics can be of either PD or PID form. Only a crude estimate of the moment of inertia matrix is assumed to be known. An open-loop nonlinear control law is presented which yields linear closed-loop dynamics in terms of the MRPs. An adaptive control law is developed which asymptotically enforces these desired linear closed-loop dynamics in the presence of large inertia and external disturbance model errors. Since the unforced closed-loop dynamics are nominally linear, standard linear control methodologies can be employed to satisfy design requirements. The adaptive control law is shown to track the desired linear performance asymptotically without requiring a priori knowledge of either the inertia matrix or external disturbance.