A theory of functional connections-based method for orbital pursuit-evasion games with analytic satisfaction of rendezvous constraints

Abstract

This study proposed an efficient approach to address the boundary constraints in the context of rendezvous with the noncooperative target within the vicinity of elliptical orbits. The problem was transformed into a two-point boundary value problem (TPBVP) constituted by series of boundary constraints and differential equation constraints by deriving the necessary conditions for the saddle-point strategy. The switching functions embedded with the boundary constraints equations were derived through the Theory of Functional Connections (TFC) to deal with the boundary constraints. Subsequently, the nested function structure with two levels was applied to be the free functions, which was involved in the constrainted expressions together with switching functions to treate the differential equation constraints. Simulation outcomes confirmed the superior computational efficiency of this method when compared to previous studies. Furthermore, a comprehensive analysis was undertaken to explore the impact of orbital eccentricity and true anomaly on the game's results, offering critical insights for enhancing spacecraft safety during on-orbit operations.