Far-Field Minimum-Fuel Spacecraft Rendezvous using Koopman Operator and l2/l1 Optimization

We propose a method to compute approximate solutions to the minimum-fuel far-field rendezvous problem for thrust-vectoring spacecraft. When the distance between the active and the target spacecraft is significantly greater than the distance between the target spacecraft and the center of gravity of the planet, linearization-based approximations of the nonlinear rendezvous dynamics may not be sufficiently accurate. For this reason, control methods that rely on such linearizations may not be appropriate for far-field rendezvous. In this paper, we address the control design problem based on a nonlinear state space model. To overcome the well-known challenges of nonlinear control design, we utilize a Koopman operator based approach in 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.