Floquet-based design and control approach to spacecraft formation flying in libration point orbits

Abstract

A method for spacecraft formation flying (SFF) design and control near libration point orbits was developed by making use of the Floquet theory for periodic orbits. Firstly, the Floquet theory used in libration point orbits was introduced and the coefficients of four Floquet periodic modes were proved to be nearly constant when the amplitude in z direction of earth-moon L1 halo orbits is less than 20000 km. On this basis, a configuration design approach to SFF in L1 halo orbits was proposed, and several types of special configurations were obtained with periodic mode 3 and mode 5 or mode 4 and mode 6. Then, in order to control the SFF configuration concisely, those coefficients of the 5 modes (except the stable one) must be kept constant. A stationkeeping method for SFF was developed, which controls 5 Floquet modes simultaneously. Finally, simulations showed that the Floquet-based approach of configuration design and control for SFF is effective, simple and convenient. The research may be of value for deep space explorations. circular restricted three body problem, spacecraft formation flying, Floquet modes, configuration design, formation control Citation: Meng Y H, Zhang Y D, Dai J H. Floquet-based design and control approach to spacecraft formation flying in libration point orbits. Sci China Tech Sci, 2011, 54: 758766,

Stationkeeping strategy for quasi-periodic orbit around Earth–Moon L2 point

“…9 Howell and Pernicka 10 employed a linear control strategy into the target point strategy, which achieved the optimal control result by adjusting the weight matrix. Derived from the invariant manifold theory, Simo et al 11 and Meng et al 12 applied the Floquet mode method to ensure the convergence of the trajectory. This type of method was successfully used in Sun-Earth libration point orbit stationkeeping strategies.…”

“…11 and Meng et al. 12 applied the Floquet mode method to ensure the convergence of the trajectory. This type of method was successfully used in Sun–Earth libration point orbit stationkeeping strategies.…”

A novel method of periodic orbit computation in circular restricted three-body problem

“…As Poincaré once said, periodic orbits are fundamental keys to understand the CRTBP dynamical system. In practical deep-space mission, periodic orbits are often considered as working orbits [3,4], therefore having great application value.…”