Synthesis of Nominal Reorientation Trajectories of a Small Satellite in Case of Failure of One Actuator

The paper devotes to the development of the approach for synthesis of reorientation trajectory of a small satellite. We consider the nanosatellite angular motion described by the kinematic quaternion equations. The aerodynamic and gravitational disturbance torques are taken into account in the angular motion model. Reorientation of a small satellite occurs from some initial position. In addition, the final angular velocity components do not exceed 0.1 °/s. The control program is given as the even Fourier series. The even Fourier series were chosen due to they can describe a complex dependency accurately. The coefficients of the even Fourier series are defined by the differential evolution algorithm. Previously, this approach has shown its efficiency for the cases of normal operation of the actuators. The paper presents the approach of synthesis of reorientation trajectory in case of failure of the actuator. The problem of reorientation reduces to optimization problem of searching of 34 coefficients of the even Fourier series that provided the achievement of the desired boundary conditions. The numerical results are given that approved the possibility of solution of the reorientation problem of small satellite in case of failure of the actuator. To compare the control programs, research was made between the cases of normal operation of the actuator and failure of the actuator. The value of the control torque differs by the order of magnitude in case of failure of the actuator. Despite this, its value is achievable for the magnetic coils.