Optimal rendezvous guidance using linear quadratic control

Abstract

This paper handles with an energy optimal guidance law for rendezvous mission, based on linear quadratic control (LQC) problem. Rendezvous of two satellites are expressed by a nonlinear relative orbit dynamic model. The LQC problem minimizes integral of control input quadratic term with given final time and terminal states. A linear relative orbit dynamic, also called as the Clohessy-Wiltshire equation, is utilized as governing equation for optimal rendezvous guidance law. It is proven that renewing costates like an initial time is identical to propagating it from initial time to current time. Thus optimal guidance law can be formulated in state feedback form. To enhance computation efficiency, this work uses Taylor series expansion for the exponential of system matrix. The proposed algorithm is verified through nonlinear relative orbit simulations.