Quaternion-Based Control Architecture for Determining Controllability/Maneuverability Limits

Abstract

Dynamic inversion has often been used in the simulation environment to rapidly prototype controls for the full flight envelope, because of its capacity for assessing a vehicle s maneuver performance and proper sizing of control surfaces. Generally, the architectures involve either a direct inversion of the entire set of equations of motion or a sequential set of inversions exploiting time scale separation in the vehicle dynamics where faster parameters are considered as controls for slower varying parameters. The proposed architecture builds on the latter using a quaternion formulation that provides singularity free tracking. Of interest, the proposed architecture simplifies the sequential approach by exploiting a simpler kinematic inversion in place of a more difficult inversion typically used. This kinematic relationship accurately describes the angular rate required to drive some reference frame of interest to a desired attitude at some desired quaternion error rate. A simple PID control is used to define the desired quaternion error rate. The paper develops the theoretical framework for the approach, and shows results in tracking a desired trajectory.