Far-Field Minimum-Fuel Spacecraft Rendezvous using Koopman Operator and $\ell_2/\ell_1$ Optimization

TL;DR

This paper introduces a novel Koopman operator-based method combined with IRLS optimization to solve the challenging minimum-fuel far-field spacecraft rendezvous problem using a nonlinear dynamic model.

Contribution

It presents a new approach that lifts nonlinear spacecraft dynamics into a higher-dimensional linear space for more accurate and effective control design.

Findings

Koopman operator effectively linearizes nonlinear spacecraft dynamics.

The method achieves near-optimal fuel efficiency in simulations.

The approach outperforms traditional linearization methods in accuracy.

Abstract

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.