Rendezvous Maneuvers of Multiple Spacecraft Using Differential Drag Under J2 Perturbation

In this work, the residual atmospheric drag is exploited to perform rendezvous maneuvers among multiple spacecraft in low Earth orbits. These maneuvers are required, for instance, for autonomous on-orbit assembly. By varying the level of aerodynamic drag of each spacecraft, relative differential accelerations are generated among the spacecraft of the group and therefore their relative orbits are controlled. Each of the spacecraft is assumed to include a drag plate, which can be actively opened or closed, to vary the atmospheric drag. The recently developed Schweighart–Sedwick model is used to describe the relative dynamics of different spacecraft with respect to a circular orbit with the inclusion of J2 effects. Furthermore, the natural relative dynamics of each chaser with respect to the target is decoupled into a secular motion and a periodic oscillation. In particular, the following two-phase control method is proposed. First, the secular motion of each chaser is controlled via differential drag in order for the spacecraft to sequentially move from an arbitrary initial condition to a closed stable relative orbit around the target spacecraft. After the relative orbit stabilization, a relative eccentricity control is applied to each spacecraft to zero-out the semi-axis of the relative orbit around the target and to achieve the rendezvous condition. The control algorithm considers mutual constraints among the values of differential drag that the different spacecraft can experience. Potential collisions are avoided by changing the maneuvering initial time. The main advantage of the proposed technique is that it enables a fleet of spacecraft to rendezvous without propellant expenditure. Furthermore, no numerical optimization is needed, because the control policy is based on closed-form analytical solutions. The proposed technique was validated via numerical simulations.