Research On Spiral Correction Algorithm Of Formation Flying Satellite Based On The Dual Quaternion

Satellite formation flying is a rising field with its better performance, more robust, betteradaptability, lower cost, getting more attentions in all countries. This thesis studies two basictheoretical issues involved in formation flying satellites: modeling and numerical computation ofsatellites’ relative position and attitude, the noncommutative error solution.In the description of general rigid body motion, dual quaternion is the most simple and effectivetool which can be applied in all rigid body kinematics (and dynamics). This thesis therefore builds aunified model of formation flying satellites based on dual quaternion which describes relative positionand attitude uniformly and establishes two relative kinematics equations of the Leader-Follower pairsatellites. Compared with conventional methods which usually separately describe rotation andtranslation of rigid body, the chief advantage in adopting a dual quaternion representation for a screwdisplacement lies in its simplicity and economy. It is particularly useful when performing severalsuccessive displacements or coordinate transformation as in the derivation of loop equations forspatial linkages.As the rigid body motion is non-exchangeable, the dual quaternion position and attitude model insatellite navigation introduces the so-called coning error and sculling error. Hence, this thesis designthe spiral correction algorithm based on a typical spiral motion, then demonstrate its consistency andcompare its accuracy with the traditional coning correction and sculling correction. Unlike traditionalalgorithms, the spiral correction algorithm doesn’t have to design two sets of coefficients respectivelyfor updating satellite’s attitude and position or velocity, thus it greatly reduces the computational costand complexity of the algorithm, enabling that the follow-up control or measurement system hasbetter real-time. It provides a theoretical basis of the model this thesis addresses.Besides, the precision and real-time of spiral correction algorithms with different subsamplings arecompared and numerical simulations show advantages and prospects of the dual quaternion positionand attitude model and spiral correction algorithm.