Analytical optimal solutions of impulsive out-of-plane rendezvous around elliptic orbits

Abstract

This paper focuses on the fixed-time minimum-fuel out-of-plane rendezvous between close elliptic orbits of an active spacecraft, with a passive target spacecraft, assuming a linear impulsive setting, and a Keplerian relative motion. It is shown that the out-of-plane Keplerian relative dynamics are simple enough to allow for an analytical solution of the problem reviewed. The different optimal solutions, for different durations of the rendezvous, are obtained via the analysis of the optimal conditions expressed in terms of the primer vector. A numerical example illustrate sthese results.

Analytical Solutions for Impulsive Elliptic Out-of-Plane Rendezvous Problem via Primer Vector Theory

“…Due to space constraints, only the proof of the first proposition is given in the Appendix. The other proofs follow the same lines and may be found in the technical note [8].…”

“…Finally, two realistic examples illustrate these results. Note that a preliminary version of this paper has been presented at the IFAC World Congress [7] in which results are stated without any proof and degenerate cases are not explored.…”

A Minimum-Fuel Fixed-Time Low-Thrust Rendezvous Solved with the Switching Systems Theory

“…To this end, spacecraft are equipped with electric and/or chemical thrusters, and studies about effective numerical solutions for minimum-fuel rendezvous problems, dating back to the sixties, 5,12) are still on progress nowadays for both types of propulsion. 4,6,14) When using chemical thrusters, the thrusts are so high that the thrusting durations are short in comparison to the orbital period and the thrusts can therefore be idealised as impulsive manoeuvres (instantaneous change of velocity without change of position). As opposed to chemical thrusters, electric thrusters require a longer thrusting duration leading to the low-thrust class of rendezvous problems.…”