Optimal tracking and formation keeping near a general Keplerian orbit under nonlinear perturbations

•Develop a nonlinear feedback controller for optimal spacecraft formation keeping.•Analyze the cost/accuracy of spacecraft formation keeping in various situations.•Demonstrate the utility of higher order tracking controllers in feedback sense.•Extend the applicability of generating functions into a kind of soft-constraint type problems.

This study presents a semi-analytic approach for optimal tracking and formation keeping with high precision. For a continuous-thrust propulsion system, optimal formation keeping problems near a general Keplerian orbit are formulated with respect to a reference trajectory which is an explicit function of time. A nonlinear optimal tracking control law is then derived in generic form as a function of the states by employing generating functions in the theory of Hamiltonian systems. 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 controller in the Earth-centered inertial frame, a variety of nonlinear perturbations can be incorporated easily without complicated coordinate transformations. Numerical experiments demonstrate that the nonlinear tracking control logic achieves superior tracking accuracy and cost reduction by accommodating higher-order nonlinearities.