An effective minimum-time orbital transfer design under continuous thrust

To achieve the optimal orbit transfer under continuous thrust, under the condition that the thrust size does not change, we design the optimal orbital transfer by taking minimum time and fuel consumption into account. Sections 1 and 2 of the full paper explain our minimum-time orbital transfer design, which is more effective than previous ones and whose core consists of; (1) we derive the state equations for describing the orbital transfer under continuous thrust; (2) we deduce two minimum-time guidance laws which are expressed as co-state variables, using the minimum-value principle and the bang-bang control principle respectively; the optimal control with the minimum-value principle can eliminate the singular interval which may occur with the bang-bang control principle; (3) as it is difficult to obtain the analytical solutions of the co-state variables, we use the genetic algorithm to optimize and solve them. Section 3 gives two numerical simulation examples of the transfer of circular orbits in the same plane by using the minimum-value principle and the bang-bang control principle respectively; the simulation results, presented in Figs. 2 through 7, and their analysis show preliminarily that the orbital transfers with both principles take nearly the same minimum time; however, the orbital transfer with the minimum principle is more fuelconserving.