Optimal formation keeping near a general keplerian orbit under nonlinear perturbations

This study presents a semi-analytic approach for optimal spacecraft formation keeping with high precision. For a continuous-thrust propulsion system, a nonlinear optimal tracking law is derived in generic form as an explicit function of the states by employing generating functions in the theory of Hamiltonian systems. Optimal formation keeping problems are formulated with respect to a time-varying reference trajectory on a finite time span to accommodate nonlinearities more precisely. The applicability of the overall process is not affected by the complexity of dynamics and the selection of coordinates. As it allows us to design a nonlinear optimal feedback control in the Earth-centered inertial frame, a variety of nonlinear perturbations can be incorporated without complicated coordinate transformations. Numerical experiments demonstrate that the nonlinear tracking control logic results in superior tracking accuracy and cost reduction by accommodating higher-order nonlinearities.