A robust semi-analytic method to solve the minimum [formula omitted] two-impulse rendezvous problem

Abstract

A novel semi-analytic approach is developed to determine the minimum ΔV for a two-impulse rendezvous and validated both empirically and analytically. A previously published closed-form ΔV estimate and the Lambert minimum energy transfer is used to establish upper and lower bounds of the minimum ΔV 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 ΔV 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 ΔV. This approach will work for both coplanar and non-coplanar 3D geometries for any orbit type.