Research On Quaternions-based Orbit Dynamics And Control Of Spacecraft

Complex space mission put stringent demands on orbit elements, orbit propagationand control. Traditional orbit elements have several disadvantages in orbit modeling andorbit propagation. The Kepler orbit elements have singular points where the equationsare degenerate and Gaussian perturbation equation contains a lot of trigonometricfunctions which reduce the efficiency of orbit calculations. Cartesian coordinates havethe loss of geometrical clarity. In this thesis we use a set of orbit elements based on thenormalized quaternions, norm of the radius vector, radial velocity and angular velocityto describe spacecraft orbit. Compared with the Cartesian coordinates or the classicalorbital element, this set of orbit elements is singularity-free and efficient. The problemsof orbit propagation, orbit optimization and orbit control are discussed. The maincontents of this thesis are as follows:Considering the analogy between orbital dynamics and rigid body dynamics,quaternions can be used to describe the angels between the orbit plan and ECIcoordinate system. From the perspective of improving the performance of the traditionalorbital elements, groups of orbit elements consist of quaternions are studied. Thecorresponding orbital dynamics and kinematics equations are derived. The conversionbetween Kepler orbital elements, Cartesian coordinates and the quaternions based orbitelements is given.The efficiency and precision of the quaternion based orbit elements in the orbitpropagation are explored. Compared with the results of Cartesian coordinates, theformer has higher accuracy without complicating the computing. J2disturbing force,finite thrust, and orbit eccentricity have no significant influence on the performance ofthe orbit propagation results. Increase the integration step size, the propagation accuracyof quaternion-based orbit elements is still higher than the Cartesian coordinates, and theadvantage is more obvious.A continuous finite-thrust rendezvous of two spacecraft trajectory optimizationproblem using quaternion-based model is considered. Time-optimal orbital rendezvoussolutions are obtained using hp Adaptive pseudospectral method. Compared with thetraditional orbital elements, the efficiency of the trajectory optimization usingquaternions is lower than in Cartesian coordinates, but still better than the Kepler orbitelements.A closed-loop feedback-driven control law suitable for the quaternion-basedfinite-thrust spacecraft rendezvous problem is designed based on Lyapunov stabilitytheory. In order to reduce the time and fuel consumption, the gains in the control law areoptimized. Simulation results indicate that the rendezvous problem can be solved under conditions of finite thrust.