Spacecraft Attitude Control under Constrained Zones via Quadratically Constrained Quadratic Programming

This paper examines an optimal spacecraft attitude control problem in the presence of complicated attitude forbidden and mandatary 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 zones are 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). An iterative rank minimization approach is proposed to gradually approach to the optimal solution of nonconvex QCQP. Simulation results are presented to demonstrate the feasibility of proposed algorithm.