Control property of the spacecraft attitude underactuated by wheels

Small-time local controllability (STLC) and stabilizability of the spacecraft attitude underactuated by reaction wheels (RWs) were investigated with the wheel speeds as control inputs. Firstly, with the wheel speeds being treated as inputs, the conservation constraint of the total angular momentum of the spacecraft and RWs was directly brought into the dynamics of the system. Then nonlinear controllability and stabilizability theory were utilized to analyze the control property of this dynamics with one and two RWs respectively. The results show that the STLC of the spacecraft attitude is possible only when two non-coaxial RWs are available. Simultaneously, the system cannot be asymptotically stabilized by a time-invariant smooth feedback, but it still can be asymptotically stabilized at least by a piecewise continuous feedback. Accordingly, a nonsmooth control law based on quaternion was constructed to stabilize the spacecraft attitude with wheel speeds under the saturation limits, which not only confirms the theoretical outcomes but also is practically useful.