Optimal open loop maneuver profiles for flexible spacecraft

Using the Calculus of Variations, optimal slewing profiles minimizing a structural e xcitation criterion are e stablished for a dynamically s imple spacecraft maneuvering between two quiescent states. Two problem types are considered. In the free end point problem, the structural deformation and its time derivative are unconstrained at maneuver's end. For the constrained end point problem, these variables a re r equired to vanish, which necessarily degrades the excitation criterion. Several figures are presented that illustrate both the n ature and the limitations inherent in maneuvering the spacecraft from one attitude state to another. For a given maneuver amplitude, en, the key parameter influencing structural e xcitation is the product of the maneuver time, Ta, and the lowest significant structural frequency, w. It is shown that when wTa 10, however, this penalty is fairly minor, and some reasonable control of terminal conditions is then practical. Thus it is generally d esirable that all maneuver times meet this criterion. When this is the case, it is possible to derive a normalized suboptimal slewing profile, F(x), applicable to a1 1 maneuvers. Given 0" and Ta, the commanded maneuver rate becomes e( t) = eO F(t/Ta)/Ta. Only a minor computational and memory burden is therefore necessary to perform almost optimal re-orientations.