Optimal control of the low-energy transfer orbit in multi-body environment

This paper discussed the problem of low-energy transfer orbit optimization based on the patched manifolds and homotopic method with multi-body environment. A new integrative optimization method is proposed in this article. As a typical example, the Earth-Mars transfer orbit design is discussed in detail. The design process of the final orbit is composed of two steps. First is optimizing the parameters that describe the patching manifolds in circular restricted three-body problems until the least total absolute velocity increment has been got. Second is optimizing the low-thrust control laws of the transfer orbit employing the homotopic method with multi-body environment that transfers the fuel optimization problem to more easier solved one of energy optimization problem. The results showed that the parameters that describe the patching manifolds could be optimized by the genetic algorithm with a relatively high speed, the homotopic method with multi-body environment could get the optimal value that meet the first order optimality conditions, and the final fuel cost is much less than the optimal transfer in two-body problem(about 1.57km/s less of the total Δv). Therefore, the method proposed in this paper could effectively solve the low-energy optimal control problem in multi-body environment for the future deep space explorations.