A novel low-thrust trajectory optimization approach based on virtual gravitational body

A novel approach based on virtual gravitational body (VGB) is proposed for low-thrust trajectory optimization in this paper. To represent the low-thrust trajectory in an analytical form, a VGB, whose gravity on the spacecraft is equivalent to the resultant of the Sun gravity and the low-thrust, is introduced. Firstly, it is assumed that the VGB stays stationary in each trajectory segment to recover the low-thrust. Secondly, to satisfy the low-thrust magnitude constraint, the VGB is further assumed to follow a uniform rectilinear motion in each segment. It can be proved that, in both cases, the low-thrust trajectory is still a conic arc when expressed in a translational reference frame centered at the VGB. Finally, the original optimal control problem is converted into a nonlinear programming problem, which could be solved very fast owing to the analytical nature of conic arcs. Compared with a spherical shaping approach, numerical results of the Earth to asteroid 1989ML rendezvous mission demonstrate the availability and high efficiency of this VGB based approach.