The problem here considered is the control of the orientation of a satellite with two control torques only, whereas nominal full actuation requires three independent torque actuators. This corresponds to the degraded situation when one of these actuators fails and one still wishes to orientate the satellite by tracking a given reference orientation trajectory. A specificity of this system with respect to control, beyond the fact that it does not satisfy Brockett’s condition at fixed orientations and cannot exactly track most reference orientation trajectories, is that, by contrast with other man-made vehicles, it is not subjected to environmental dissipative forces. In other words its momentum is constant when no control is applied. The only way to reduce (or augment) its momentum is via the injection of control energy. The importance of this fact can be appreciated when knowing that natural energy dissipation usually facilitates the control design. The single transverse function feedback controller used for the simulation video achieves practical stabilization of any reference orientation trajectory and asymptotically stabilizes fixed desired orientations. Concerning this latter case, the slow rate of convergence observed in the video is related to the fact that the feedback control law is differentiable everywhere.

The reference frame is yellow coloured, and the satellite’s frame is in red. The lengths of the gas jets shown in the video are proportional to the control torques applied to the satellite.

To watch the video click here