Families of Two-Impulse Optimal Rendezvous Transfers Between Elliptic Orbits

TL;DR

This paper introduces a family-based framework for analyzing fuel-optimal two-impulse rendezvous transfers between elliptic orbits, revealing continuous solution structures and their behavior under orbital variations.

Contribution

It re-parameterizes the problem to uncover continuous families of solutions, using numerical continuation and classification methods, providing a global view of the solution landscape.

Findings

Revealed continuous families of optimal solutions via numerical continuation.

Classified solution families using Hessian criteria and Primer Vector Theory.

Mapped solution structures onto porkchop plots to connect angular and temporal domains.

Abstract

The classical fuel-optimal two-impulse rendezvous problem between Keplerian orbits is revisited from a family-based perspective. Conventional approaches often yield isolated optimal solutions whose mutual relationships remain unclear; yet, when re-parameterized appropriately, seemingly unrelated optima are revealed to be connected members of continuous solution families. To expose this structure, the proposed framework enforces a subset of first-order necessary optimality conditions and traces the resulting one-parameter families via numerical continuation. The families are classified using Hessian-based criteria and Primer Vector Theory, and are projected onto porkchop plots to connect the angular and temporal domains. Representative case studies reveal the emergence, merging, and disappearance of locally optimal branches under variations in orbital geometry, supplying a global map of the solution landscape. This complementary perspective clarifies the robustness of optimal solutions and identifies alternative near-optimal transfers in the vicinity of a nominal trajectory.