A GENERIC OPTIMAL CONTROL TRACKING SOLUTION FOR VARIOUS ATTITUDE ERROR PARAMETRIZATIONS
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A generic optimal tracking control is developed where the optimal control is calculated by optimizing a universal quadratic penalty function. Several attitude error representations are presented for describing the tracking orientation error kinematics. Compact forms of attitude error equation are derived for each case. The attitude error is initially defined as the quaternion (rotation) error between the current and the reference orientation. Transformation equations are presented that enable the development of nonlinear kinematic models that are valid for arbitrarily large relative rotations and rotation rates. The nonlinear error for the equation of motion is retained, yielding a tensor-based series solution for the Co-State as a function of error dynamics. By utilizing several attitude error kinematics 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-i.e. a quadratic penalty on the MRPs error is clearly not "the same" physically as a quadratic penalty on the classical Rodrigues parameters. We utilize this universal attitude error measure expressed through approximate transformations as a positive function of each of the coordinate choices. This allows for a universal solution to many spacecraft optimal control problems and removes the dependency on the attitude coordinate choice. 2013 2013 California Institute of Technology.
