A robust semi-analytic method to solve the minimum ΔV two-impulse rendezvous problem. Issue 10 (15th May 2019)

• Record Type: Journal Article
• Authors: Koblick, Darin; Xu, Shujing
• Is Part Of: Advances in space research. Volume 63:Issue 10(2019)
• Page Start: 3358
• Page End: 3368
• Publication Date: 2019-05-15
• Subjects: Lambert's problem -- Minimum ΔV -- Non-coplanar Lambert transfer -- 3D minimum fuel rendezvous -- Optimal two-impulse rendezvous; Space sciences -- Periodicals; Astronautics -- Periodicals; Geophysics -- Periodicals; 500.505
• DOI: 10.1016/j.asr.2019.01.040
• Languages: English
• ISSNs: 0273-1177

Abstract

Highlights: Robust semi-analytical minimum ΔV approach for the rendezvous between any 3D orbit. Minimum total ΔV using this method less than or equal to other published results. Runtime improvement over fixed time solvers between one to two orders of magnitude. All singularities addressed for transfer angles between 0 and 360°. Abstract: A novel semi-analytic approach is developed to determine the minimum Δ V for a two-impulse rendezvous and validated both empirically and analytically. A previously published closed-form Δ V estimate and the Lambert minimum energy transfer is used to establish upper and lower bounds of the minimum Δ V transfer between two orbits. These bounds, in conjunction with the bisection method, operate on a nonlinear radical cost function to guarantee linear convergence. This approach has several real world applications including a low earth orbit (LEO) to highly elliptical orbit (HEO), and a HEO to retrograde geosynchronous orbit transfer. The minimum Δ V estimates are better than those reported in the existing literature, while run times improved as much as two orders of magnitude over a fixed time Lambert solver. All singularity cases were addressed such that any orbital geometry, including Hohmann and radial elliptic transfers, converged to the global minimum Δ V . This approach will work for both coplanar and non-coplanar 3D geometries for any orbit type.