Orbit design and control for periodically revisiting multiple formation satellites

In the formation flying mission, the periodic revisit of multiple formation satellites can provide periodic surveillance of satellite status, e.g., on-orbit inspection. This paper studies the orbit design problem and the single-impulse control problem for periodically revisiting multiple formation satellites. Two periodic revisit conditions under the J2 perturbation are considered: the J2 invariant orbit and the same mean semi-major axis. By analyzing the numbers of free variables and constraint equations, the maximum numbers of revisiting satellites are obtained for both the coplanar and non-coplanar cases. A hybrid method is proposed by combining the state transition matrix and the second-order state transition tensor, which are used to solve the required velocity vector and to propagate the relative state vector, respectively. The original multi-dimensional nonlinear equation is reduced into a one-or two-dimensional equation, which is solved by numerical methods. Several numerical examples show that the revisit orbit drifts after 30 revolutions by the proposed method for the coplanar and non-coplanar cases are less than 0.3 km and 4.5 km, respectively.(c) 2023 Elsevier Masson SAS. All rights reserved.