Near-Optimal Feedback Rendezvous in Elliptic Orbits Accounting for Nonlinear Differential Gravity

Abstract

DOI: 10.2514/1.26650 This paper presents a novel approach to the design of near-optimal feedback control laws, for minimum-fuel rendezvous between satellites in elliptic orbits of arbitrary eccentricity. The rendezvous problem for the nonlinear differential gravity model is solved by the application of neighboring optimal feedback control methodology used in conjunction with a nominal trajectory, obtained by solving the related minimum-fuel feedback control problem for the linear Tschauner–Hempel equations, analytically. This novel closed-form solution is used to determine the best values of the final true anomaly by examining its effect on the cost to go for rendezvous. The neighboring feedback controllawaccountingfornonlineardifferentialgravityisobtainedbyusingageneralizedsweepmethod,validwhen the reference solution does not satisfy the first-order necessary conditions for optimality, exactly. Several numerical examples are analyzed to demonstrate the efficacy of the method.