Attitude Stabilization of a Satellite Having Only Electromagnetic Actuation Using Oscillating Controls

We consider the problem of attitude stabilization for a low Earth orbit satellite having only electromagnetic actuation. Such a satellite is not fully actuated, as the control torque is the cross-product of magnetic moment due to magnetorquers and the geomagnetic field. The aim of this work is to study whether oscillating controls can be designed such that a satellite actuated via magnetorquers alone can achieve full three-axis control irrespective of the position of the satellite. To this end, we propose considering oscillating feedback controls which generate the motion of the closed-loop system in the direction of appropriate Lie brackets. Simulation studies show that the proposed control scheme is able to stabilize the considered system.