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In this paper, the spacecraft formation flying using virtual structure algorithm is studied. In spacecraft formations flying, several small spacecraft have been used instead of employing a single one to achieve the same goal. In virtual structure method, the position and orientation of each spacecraft is measured with respect to the position and attitude of a virtual node in every moment. Two robust control methods are proposed to control formation. At first, the robust μ synthesis controller is used to attenuate the influence of the sensor noises, environment disturbances and parametric uncertainties but it is done with heavy computations. The second method is in the standard form of optimization problem. It is composed of state feedback controller and lyapanov stability theory. The LMI controller Computations are very efficient and the controller is robust against parametric uncertainties and most of the disturbances. The implementations of control methods on virtual center guarantees robust stability and performance. Concerning with Actuator constraints, Simulation example is provided to show the effectiveness of the proposed control schemes to track the desired attitude and position trajectories despite system uncertainties.

Keywords: Spacecraft formation flying, Virtual structure method, μ synthesis, Linear Matrix Inequality (LMI)

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