Shaping low-thrust multi-target visit trajectories via theory of functional connections

Abstract

This paper proposes a shaping method via theory of functional connections (TFC) to solve the coplanar low-thrust multi-target visit problems under the J2 perturbation. Three types of targets are considered including ground targets, space targets, and hybrid ground-space targets. The visit constraints for the ground and space targets under the linear J2-perturbed model are transformed into those under the two-body model with a correction term, which avoids directly solving the transfer trajectories with the J2 effect. Then, a unified shaping method via the TFC is proposed for the three types of targets. The multi-target visit problem is transformed into a nonlinear programming problem that analytically satisfies the initial conditions and the multi-target visit constraints. Several numerical examples show that the proposed method can realize rapid optimization for the whole transfer trajectories. Furthermore, the solved trajectories are successfully applied to the initial guess estimation of the Gauss pseudospectral method for further optimization.