Two/three-spacecraft Electromagnetic Formation Relative Equilibrium And Dynamics Characteristics

With the development of the spacecraft on-orbit servicing technology,the use of multiple spacecraft formation coordinated flying to implement orbit control for a particular spatial object will become a new approach of space missions.In recent years,the research on spacecraft non-contacting internal forces which include the electromagnetic force,the Coulomb force and Flux-pinned effect force provides novel insight and a technological alternative of on-line orbit control,namely the use of internal forces among different satellites to accomplish non-contacting on-orbit operations,thus avoiding physical connection and improving on-line orbit manipulation safety.Electromagnetic Formation Flying(EMFF)is a novel technology that uses superconducting electromagnetic coils to provide electromagnetic forces/torques which can be used to control the relative position and attitude among different satellites in a formation.This concept could effectively address the issues of propellant consumption and plume contamination caused by conventional propellant approaches such as thrusters,and offer non-contacting continuous reversible and synchronous controllability.With the development of coordinated spacecraft formation technology,the EMFF technology increasingly turns into a research hotspot.In this field,abundant studies have been carried out home and abroad.Nevertheless,it is a challenge to investigate the dynamics and control of Electromagnetic Formation Flying because of the characteristics of electromagnetic internal force/ internal moment and the high nonlinearity/coupling of the dynamic equation.A lot of problems still remain to be solved.This paper mainly investigates the dynamics modeling,relative equilibrium analysis,stability analysis.(1)Relative equilibrium of spacecraft electromagnetic formation.The equilibrium problem can be translated to static formation maintenance,in which each spacecraft stay at a relatively unchanging position.In this paper,the relative trajectory and attitude motion dynamics model are derived by the vectorial mechanics approach based on Newton-Euler equations.The relative equilibrium for the vector mechanics model is analyzed and the necessary conditions for a circularly restricted static electromagnetic formation are derived.(2)Hamilton mechanics modol of spacecraft electromagnetic formation.The electromagnetic formation flying is subordinate to multi-spacecraft coordinated flying which involves complicated and correlative motions.These motions can be decomposed into two parts,one is the group motion of the formation flying itself and the other is the relative motion among member spacecraft of the electromagnetic formation system.Therefore,in order to clearly describe the dynamic characteristics of the formation itself and the relationship among each satellite,the method of analytical mechanics is used in this research.In this paper,the 6-DOF coupled nonlinear dynamic models by Hamiltonian method for the multi-spacecraft electromagnetic formation are obtained without earth perturbation.(3)Relative equilibrium and stability of spacecraft electromagnetic formation.Relative equilibrium and stability studies are fundamental to on-orbit flying of the static formation,which is closely related to the safe and stable flying of the spacecraft formation system.In this paper,the equilibrium solution and the magnetic dipole scheme of the given two/three spacecraft static formation are gained.Based on the equilibrium conditions and Hamilton dynamic models,the characteristics of stability of the equilibrium solution are investigated.