This paper examines an optimal spacecraft attitude control problem in the presence of complicated attitude forbidden zones. The objective is to design an optimal reorientation trajectory for a rigid body spacecraft under constraints, which is originally formulated as a nonlinear programming problem. The attitude forbidden zones are considered to prevent the light-sensitive instruments operated on-board from exposure to bright light while the mandatory zone to keep the communication instrument in certain zones to transmit and receive signals. When unit quaternions are used to represent the attitude of spacecraft, the dynamics and constraints are formulated as quadratic functions. By discretizing the reorientation trajectory into discrete nodes, the optimal attitude control problem can be formulated as general quadratically constrained quadratic programming (QCQP). Due to nonconvexity of general QCQP problems, the traditional semidefinite relaxation method can only obtain a bound on the optimal solution. In this paper, we proposed an iterative rank minimization approach to gradually reduce the gap between the bound and the optimal solution and will finally converges to the optima. Simulation results are presented to demonstrate the feasibility of proposed algorithm.
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