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Getting inspiration from the constraint forces in the classical mechanics, we presented the nonlinear control method of multiple spacecraft formation flying to accurately keep the desired formation arrays. Considering nonlinearity and perturbation, we changed the question of the formation array control to the Lagrange equations with the holonomic constraints and the differential algebraic equations (DAE), and developed the nonlinear control for design of the follower spacecraft tracking control laws by solving the DAE. Because of using the idea of the constraint forces, this approach can adequately utilize the characteristic of the dynamic equations, i.e., the space natural forces, and accurately keep the arbitrary formation array. Simulation results of the circular formation keeping with the linear and nonlinear dynamical equations were included to illuminate the control performance.satellite formation flying, array keeping, nonlinear control, Lagrangian systems, constraint forces

A robust nonlinear control method is presented for spacecraft precise formation flying. With the constraint forces and considering nonlinearity and perturbations, the problem of the formation keeping is changed to the Lagrange systems with the holonomic constraints and the differential algebraic equations (DAE). The nonlinear control laws are developed by solving the DAE. Because the traditional numerical solving methods of DAE are very sensitive to the various errors and the resulting control laws are not robust in engineering application, the robust control law designed method is further developed by designing the correct coefficients to correct the errors of the formation array constraints. A numeral study simulated the robustness of this method for the various errors in the formation flying mission, including the initial errors of spacecraft formation, the reference satellite orbit determination errors, the relative perturbation forces model errors, and so on. spacecraft formation flying, array keeping, nonlinear control, Lagrangian systems, constraint forces, robust Citation:Xing J J, Tang G J, Cheng W K, et al.

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