Practical considerations using transverse function methods on underactuated reaction wheel controlled spacecraft

This paper investigates the practical considerations for implementing an underactuated transverse function- based control law using only two reaction wheels. Previous investigations into transverse functions have looked at implementing these control laws for the underactuated problem but have yet to fully consider what may be required to run these control laws long term fora realistic mission and have primarily dismissed the increased control efforts needed from the remaining actuators. This paper first shows the effects of neglecting momentum dumping for both the transverse function approach and a previously published Singular Nonlinear Quaternion (SNLC) -based controller. This paper then outlines a control strategy using magnetic torque devices to dump momentum and help maintain the conditions needed to maintain the assumptions used by these underactuated systems. With adequately sized magnetic torque-based angular momentum management techniques, both the SNLC and Transverse function-based approaches produce acceptable results. However, the Transverse function- based method allows for a systematic setting of the allowable error bound, a desirable trait in a potentially compromised system where a trade-off in performance could extend the system's longevity. The paper then investigates improving the transverse function methods by minimizing the control effort the remaining wheels need by slowly changing the setpoint of the desired error bound when the desired orientation is far from the current orientation. This strategy helped power consumption on the wheels and allowed large manoeuvres before the remaining actuators became saturated. Transverse function-based controllers also perform well with uncertain spacecraft parameters, as shown through a Monte Carlo analysis.