Research Of Relative Motion Control Near Perturbed Elliptical Reference Orbit

This dissertation focus on dynamics and control of the relative motion near ellipticalreference orbit. The research content is composed of six topics, namely nonlinear relativemotion dynamics, periodical conditions, perturbed optimal rendezvous, rendezvous usinghorizontal impulses, leader-follower formation and close-loop control for rendezvous. A-mong these topics, the former two topics are theoretical study of the relative motion dy-namics, and latter four topics are application of the relative motion control.In the research of relative motion dynamics, nonlinear relative dynamics models arederived using Lagrangian mechanics and Hamiltonian mechanics, respectively. In the t-wo nonlinear relative dynamics models, J2 perturbation and air drag are included, andthe atmosphere with exponential density is irrotational. The nonlinear dynamics derivedby Lagrangian mechanics is a set of second order differential equations independent ofthe right ascension of ascending node of reference orbit. The nonlinear relative dynam-ics derived by Hamiltonian mechanics is a set of first order di?erential equations withconcise form. Canonical variables in the second model have specific physical meaning.And the second model facilitates numerical propagation due to the concise form. Forthese two models, no approximations are applied in the derivation process, and evaluationof propagation error shows that these models can be used as high accuracy propagationmodels.In the research of periodic condition for relative motion, energy matching conditionin two-body problem is expressed in relative states at first. Based on the new form ofenergy matching condition, analytical periodical conditions are derived in six scenariosin which the initial relative motion are restricted. And then the impact of J2 perturbationon relative motion is considered, energy matching condition under J2 perturbation is pro-posed. Beyond energy matching condition, some periodic conditions exist for mean rela-tive motion. When J2 invariant condition or drift rate matching condition is used, residualrelative drift still exists between the reference and chaser. In order to decrease the residualrelative drift, a di?erential correction algorithm is proposed. Simulation results show that,the residual relative drift decreases greatly after one or two times correction.In the topics of perturbed optimal rendezvous near elliptical reference orbit, the sin- gularity of linear rendezvous is eliminated via treating the rendezvous in the view of iner-tial motion. From the standpoint of inertial motion, semi-revolution rendezvous schemeand complete-revolution rendezvous scheme are proposed. Based on these schemes, semi-revolution rendezvous optimization algorithm, complete-revolution rendezvous optimiza-tion algorithm and multi-revolution two-impulse rendezvous global optimization algorith-m are proposed. Further more, an iteration algorithm utilizing linear gradient is proposedto eliminate the impact of orbit perturbation on rendezvous. Simulation results show thatseveral iterations can make the terminal rendezvous error less than one meter.In the research of rendezvous using horizontal impulses, the feasibility of copla-nar relative motion control using horizontal impulses is proved at first. A three-impulsescheme for coplanar rendezvous is proposed subsequently. And then the su?cient andnecessary conditions for the solution of three-impulse coplanar rendezvous are derived.Based on the su?cient and necessary conditions, a solving algorithm for horizontal im-pulses is designed. Further more, an optimization algorithm is proposed for non-coplanarrendezvous using impulses in the horizontal plane. Finally, non-coupling iteration algo-rithm and coupling iteration algorithm are proposed to eliminate the impact of orbit per-turbation on rendezvous. Simulation results show that the total fuel consumption of three-impulse rendezvous scheme is not more than classical two-impulse rendezvous scheme.Hence high accuracy rendezvous with a target in elliptical orbit can be achieved usingimpulses in horizontal plane.In the research about initialization of formation and formation keeping, two method-s utilizing the energy matching condition under J2 perturbation to determine the relativestates are given at first. Then a new formation of accompanying fly is designed. Based onthe energy matching condition under J2 perturbation, two methods determining the ini-tial relative position and velocity are developed subsequently for accompanying ?y andcircum-?y. For real formation initialization, there is control error. In order to mitigatethe e?ect of initialization error, the analytical expression of formation keeping impulseis derived based on Lagrangian multiplier method, and an algorithm for seeking optimaltime of formation keeping maneuver is designed. Simulation results show that the newformation of accompanying fly is rational, the energy matching condition under J2 per-turbation can lead to stable formation, and the formation keeping maneuver can eliminatethe e?ect of initialization error. At last for the velocity closed-loop control of rendezvous, the expansion expressionof true anomaly and eccentric anomaly using mean anomaly as variable are adopted toget state transition matrix using time as independent variable. Based on the state tran-sition matrix in time domain, a velocity closed-loop on-o? control scheme is proposed.Then correction scheme in midcourse of rendezvous is developed. And an optimizationalgorithm used to calculate the time of midcourse correction is also designed. Simulationresults indicate that the algorithms proposed here can be used to perform rendezvous nearelliptical reference orbit.