Attitude control of underactuated spacecraft through flywheels motion using genetic algorithm with wavelet approximation

The optimal attitude control problem of a rigid spacecraft with flywheels that provide two control input is treated. In the case that the total angular momentum of the system is zero, the nonholonomic behavior of underactuated system is employed to develop the dynamical equations of the system. The problem of reorienting a rigid spacecraft is formulated as an optimal control problem for a drift free control system. The genetic algorithm is proposed to achieve angular rate input law of two flywheels and the optimal reorientation of a spacecraft. By use of the wavelet method, the control input law is approximated by the discrete orthogonal wavelets. The numerical simulation indicates that genetic algorithm and wavelet approximation are effective approaches to solve the optimal reorientation problem.