Reachable Set of Spacecraft with Finite Thrust Based on Grid Method

Reachable sets are sets of position states that the spacecraft can reach from its initial state under mass and time constraints. In this study, a method to solve the reachable set of spacecraft with finite thrust is proposed. Solving reachable sets can be transformed into solving its boundary surface using the distance fields over grids method. A grid is established to represent the boundary surface, and each node on the grid can be determined by an optimal control problem. A modified sequential convex programming with nonlinear dynamic correction is used to solve optimal control problems with a theoretical proof of convergence. Moreover, the symmetry plane of the reachable set is found to reduce the computation in applications. The method is tested with two types of orbits, namely, geosynchronous and highly elliptical orbits, and the properties of the spacecraft's reachability in two orbits are obtained. Numerical simulations show that the proposed method can succeed in solving reachable sets under mass and time constraints in two types of initial orbits even when a long period is considered.