Two-Dimensional Reachability of Low-Thrust Spacecraft

Reachability analysis is very useful and of great interest in various space missions. This correspondence proposes a method to compute the 2-D reachable set (RS) of low-thrust spacecraft with bounded control and limited fuel. For a class of smooth nonlinear affine-control systems, a two-step solving procedure is proposed to solve the boundary of 2-D RSs. By constructing a suitable homotopy, the connection between the homotopy path and the boundary of 2-D RSs is built. The proposed method is applied to investigate the 2-D orbital element RS of low-thrust spacecraft. In particular, both osculating and mean orbital elements are considered. The effectiveness and efficiency of the proposed method are demonstrated by numerical simulations and analyses.