Modeling and Control for Spacecraft Relative Pose Motion by Using Twistor Representation

A novel approach toward the modeling and control problems of spacecraft relative translation and rotation by using twistors is presented. A twistor can be used as a complementary representation to dual quaternions for the modeling and control problem of combined spacecraft attitude and position relative motion. Just as the dual quaternion, the twistors not only provide a uniform representation for the combined spacecraft rotational and translational motion but also avoid the normalization constraint resulted from the dual-quaternion representation. The proposed controller avoids the inconvenient computation of the logarithm of dual quaternion in the dual-quaternion-based controller, whereas the control performance is acceptable. Furthermore, the twistor-based spacecraft attitude and position motion model can also be used to design state estimators or other advanced controllers.