  We propose a method to compute approximate solutions to the minimum-fuel
far-field rendezvous problem for thrust-vectoring spacecraft. It is well-known
that the use of linearized spacecraft rendezvous equations may not give
sufficiently accurate results for far-field rendezvous. In particular, as the
distance between the active and the target spacecraft becomes significantly
greater than the distance between the target spacecraft and the center of
gravity of the planet, the accuracy of linearization-based control design
approaches may decline substantially. In this paper, we use a nonlinear state
space model which corresponds to more accurate description of dynamics than
linearized models but at the same time poses the known challenges of nonlinear
control design. To overcome these challenges, we utilize a Koopman operator
based approach with which the nonlinear spacecraft rendezvous dynamics is
lifted into a higher dimensional space over which the nonlinear dynamics can be
approximated by a linear system which is more suitable for control design
purposes than the original nonlinear model. An Iteratively Recursive Least
Squares (IRLS) algorithm from compressive sensing is then used to solve the
minimum fuel control problem based on the lifted linear system. Numerical
simulations are performed to show the efficacy of the proposed Koopman operator
based approach.
