Combined Optimal Low-Thrust and Stable-Manifold Trajectories to the Earth-Moon Halo Orbits

Abstract

In this paper we incorporate the low-thrust propulsion in the stable manifold technique to design transfer trajectories to the halo orbits around L 1 and L 2 of the Earth-Moon system. The problem is stated in an optimal control scheme and solved using direct transcription and collocation; the dynamics is discretized over an uniform time grid using a sixth-order linear multi-point method. The resulting transfers are made up by a spiral arc that targets a piece of the stable manifold associated to the final orbit. Thanks to the generality of this approach, halo-to-Moon transfers are also computed combining unstable manifolds and low-thrust. Furthermore, complete Earth-to-Moon transfers via halos can also be constructed. Results show the feasibility of this kind of transfers requiring moderate propellant mass fractions and feasible times of flight.

Optimal Control and Applications to Aerospace: Some Results and Challenges

“…[214,203,215,216]). In [203,217,218,219], the authors combine the use of low-thrust propulsion with the use of the nice properties of invariant manifolds of periodic orbits around Lagrange points in order to design low-cost trajectories for space exploration. Their techniques consist of stating an optimal control problem that is numerically solved using either a direct or an indirect transcription, carefully initialized with the trajectories of the previously studied system (with no thrust).…”

Transfers to distant periodic orbits around the Moon via their invariant manifolds

“…Its stable manifold does not reach the Earth at a sufficiently low altitude to permit a direct insertion from a parking orbit. When a continuously propelled arc is introduced, it is possible to raise the initial orbit to place the spacecraft on the DPO stable manifold [14]. Thus, the initial part of the transfer is an orbit belonging to EðI=TÞðtÞ.…”

“…This can be done in a deterministic fashion [13]. Using DPO's intrinsic dynamics to design low-energy lunar transfers mimics the technique already established in literature, with the exception that the invariant manifolds associated to the DPO are exploited in place of those associated to the libration point orbits [8,10,11,14,15]. This approach is also used in Mingotti and Gurfil [18] to design transfers to DPO around Mars (with and without lunar gravity assists).…”

“…This is done by spiraling around the Earth up to reach a point that lies on the stable manifold. This strategy recalls that already formulated to design low-thrust transfers to halo orbits in the Earth-Moon system [14].…”

“…to design low-thrust, stable-manifold interior trajectories to final DPO around the Moon in analogy with low-thrust transfers to halos [14].…”