Hamiltonian structure-based formation flight control along low-energy transfer trajectory

This paper studies the three-dimensional formation-flying problem in multibody regime using the Hamiltonian structure-preserving(HSP) control strategy.Alow-energy lunarhalo transfer orbit is chosen as the reference trajectory, which can represent the dramatically varying dynamics in the vast Earth–Moon region, and demonstrates much more complex environments than the vicinity of libration points. This trajectory exhibits time-varying topology of four different types, with two new ones: saddle × saddle × center and complex saddle × complex saddle × center (to the authors’ best knowledge, never studied in the literature). Stability transitions occur with a tremendous variation of the eigenvalues, bringing newchallenges to effective formation controller design. Toobtain boundedmotion, topology-typedependent HSP controller is proposed using the local stable/unstable manifolds. Difficulty arises in the transition regions, where close-to-zero real (complex) eigenvalues appear and require huge control gains, which may be infeasible for onboard computers. Accordingly, the controller is improved by considering additionally the local center manifold, andthe gains requiredare always lower than25.The controller is simple to implement because onlyposition information is required, and its validity and robustness in the presence of initial deviations and navigation errors are verified by Monte Carlo simulations.