ATTITUDE ERROR KINEMATICS: APPLICATIONS IN CONTROL
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abstract
Several attitude error representations are presented for describing the tracking orientation error kinematics. Compact forms of attitude error kinematics are derived for each representation. The attitude error is initially defined as rotational error between the current and the reference orientation. The development of nonlinear kinematic models enables arbitrarily large relative rotations and rotation rates for several standard attitude representations. An optimal tracking control is developed where the optimal control is calculated by optimizing a universal quadratic penalty function. An open-loop optimal nonlinear control spacecraft maneuver is solved first for reference motion. The tracking error is defined yielding a nonlinear error dynamics in a compact form. Two distinct approaches to attitude error kinematics are presented. The first one is that the reference and current angular velocity vectors are defined in the same axes frame while in the second one is defined in the different attitude axes frame. By utilizing several attitude error kinematics methodologies to describe the spacecraft rotation error, we introduce a universal quadratic penalty function of tracking errors that is consistent in each of the coordinate choices and removes the dependency on the attitude coordinate choice.
