Analytical solution of optimal reconfiguration for nonlinear relative motion

Linearization of relative motion model applied to large scale relative motion in elliptical orbit leads to low accuracy that can't meet mission requirement. An approximate analytical approach based on nonlinear relative motion model is proposed for solving large scale fuel optimal reconfiguration of spacecraft formation flying on arbitrary elliptical orbits. Firstly, the variational method is used to establish the mathematical model of the nonlinear optimal reconfiguration problem. Then an analytical open-loop optimal control law without special integrals is derived by using the perturbation method, taking the eccentric anomaly as the integral variable to avoid the special integrals under true anomaly domain. Simulations are carried out to verify effectiveness and advantage of the analytical open-loop optimal control based on nonlinear model. Results show that when the relative motion scale is larger, reconstruction errors of optimal control based on nonlinear relative motion model is decreased by 2 to 3 orders of magnitude while fuel consumption is approximately close compared with that based on linear relative motion model.