[论文解读] Families of Two-Impulse Optimal Rendezvous Transfers Between Elliptic Orbits

Beom Park, Kathleen C. Howell+2 more|arXiv (Cornell University)|Mar 12, 2026

Spacecraft Dynamics and Control被引用 0

一句话总结

这篇论文表明，在椭圆轨道之间的两冲量最优会和- rendezvous 转移形成连续的一参数族；它利用角变量的连续化来揭示全局解结构并与 porkchop 图相连。

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.

研究动机与目标

• Motivate understanding of fuel-optimal TIOTs between general elliptic orbits.
• Reveal the global organization of TIOT solutions beyond isolated optima.
• Develop a continuation framework to trace one-dimensional families of TIOTs.
• Link geometric families to traditional porkchop plots for practical mission design.

提出的方法

• Enforce a subset of first-order optimality conditions to reduce the search to a one-parameter continuation problem.
• Represent the problem in angular (mean anomaly) and temporal (T, t) domains to trace families.
• Use a two-equation stationary condition F(X)=0 with a remaining degree of freedom for continuation.
• Employ a pseudo-arclength continuation scheme with an arclength constraint to traverse the family.
• Classify stationary points via Hessian-based criteria to distinguish minima, maxima, and saddles.
• Compute gradients and Hessians via state transition matrices along Lambert arcs and use Primer Vector Theory as a complementary optimality check.

实验结果

研究问题

• RQ1 How are TIOTs between elliptic orbits organized beyond isolated local minima?
• RQ2 Can we identify continuous families of TIOTs by enforcing only a subset of optimality conditions?
• RQ3 What is the relationship between angular-domain asymptotics and temporal-domain representations for TIOTs?
• RQ4 How do TIOT families evolve as orbital geometry varies, including emergence, coalescence, and disappearance of branches?

主要发现

• TIOTs between elliptic orbits form continuous one-parameter families rather than isolated solutions.
• Enforcing two optimality conditions and using continuation reveals connectivity among optima and links to porkchop plots.
• Asymptotic (t → ∞) analyses provide seeds that initiate and seed continuation of TIOT families.
• Parabolic Lambert arcs characterize asymptotic limits that seed families in both angular and temporal domains.
• Families exhibit merging, emergence, and disappearance as orbital geometry changes, enabling a global map of the TIOT solution landscape.
• The framework supports identification of robust and near-optimal transfers around a nominal trajectory.