The capture control of test mass by means of the electrostatic suspensions is crucial for drag-free spacecraft. The test mass must be released to the cage center of the inertial sensor accurately and quickly. This paper proposes a minimum-time capture control method for the test mass release phase of drag-free spacecraft. An analytical solution of optimal control is derived based on Pontryagin’s minimum principle and the linearized dynamics model of the test mass during the release phase. The parameters of the analytical solution are initially guessed with an approximate linear solution of the test mass dynamics model and are slightly modified by using differential correction. Compared with the exact numerical solution by the hp -adaptive pseudospectral method, the analytical solution is proved to be minimum-time. Numerical simulation shows that the proposed control method quickly captures the test mass to the cage center of the inertial sensor. The capture time to stabilization is only half that of the traditional controller.

This paper presents a general analytical method to describe the center manifolds of collinear libration points in the restricted three-body problem (RTBP). It is well known that these center manifolds include Lissajous orbits, halo orbits, and quasi-halo orbits. Previous studies have traditionally treated these orbits separately by iteratively constructing high-order series solutions using the Lindstedt–Poincaré method. Instead of relying on resonance between their frequencies, this study identifies that halo and quasi-halo orbits arise due to intricate coupling interactions between in-plane and out-of-plane motions. To characterize this coupling effect, a novel concept, coupling coefficient [ ], is introduced in the RTBP, incorporating the coupling term [ ] in the [ ]-direction dynamics equation, where [ ] represents a formal power series concerning the amplitudes. Subsequently, a uniform series solution for these orbits is constructed up to a specified order using the Lindstedt–Poincaré method. For any given paired in-plane and out-of-plane amplitudes, the coupling coefficient [ ] is determined by the bifurcation equation [ ]. When [ ], the proposed solution describes Lissajous orbits around libration points. As [ ] transitions from zero to nonzero values, the solution describes quasi-halo orbits, which bifurcate from Lissajous orbits. Particularly, halo orbits bifurcate from planar Lyapunov orbits if the out-of-plane amplitude is zero. The proposed method provides a unified framework for understanding these intricate orbital behaviors in the RTBP.

Proximate spacecraft formation flying has many applications in high accurate earth observation and astronomy. In comparison to conventional or electronic thrust, Coulomb thrust has obvious advantages in close-formation control, such as fast throttling, nearly propellantless features and no thruster plume impingement. This paper presents the concept of charged-spacecraft formation and deployment, also investigates the Coulomb-force control for desired spacecraft formations. It is assumed that the charged chief spacecraft has several controllable charged spheres distributed around it and deputies are charged spheres. The deputies are deployed from the chief spacecraft to the desired formation orbits under the active charge control. In order to deploy these deputies subject to the constraints on the limited controllable charges, the transition trajectories are planned by using pseudo-spectral discretization method. Then a charge feedback controller is designed to track the transition trajectories and the desired formation. Numerical simulation results show that one or more deputies can be deployed by controlling the limited charge of the chief spacecraft.