A two-step formation-keeping control methodology is proposed that includes both attitude and orbital control requirements in the presence of uncertainties. Based on a nominal system model that provides the best assessment of the real-life uncertain environment, a nonlinear controller that satisfies the required attitude and orbital requirements is first developed. This controller allows the nonlinear nominal system to exactly track the desired attitude and orbital requirements without making any linearizations/approximations. In the second step, a new additional set of closed-form additive continuous controllers is developed. These continuous controllers compensate for uncertainties in the physical model of the satellite and in the forces to which it may be subjected. They obviate the problem of chattering. The desired trajectory of the nominal system is used as the tracking signal, and these controllers are based on a generalization of the concept of sliding surfaces. Error bounds on tracking due to the ...

This paper presents an analytic solution to the optimal reconfiguration problem of satellite formation flying in J₂ orbital perturbation. Continuous and variable low-thrust accelerations are represented by the Fourier series, and initial and final boundary conditions are used to establish the constraints on the thrust functions. The thrust functions are implemented by optimal Fourier coefficients that minimize the cost during the maneuver. The analytic solution composed of these Fourier coefficients are simply represented in a closed form, and no approximation is needed. Numerical simulations are conducted to visualize and compare the results obtained in this paper with those of previous papers with no perturbations. The analytic solution developed in this paper is more accurate in that the general behavior of the optimal control history and reconfiguration trajectories are easily calculated even in the presence of the J₂ potential disturbance. The analytic solution is useful for designing a reconfiguration controller for satellite formation flying under J₂ orbital perturbation.