Robust nonlinear control of spacecraft formation flying using 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.