Control of a slow-moving space crane as an adaptive structure

If we assume that the space crane is a statically determinate truss with length-adjustable bars and take as controls the length adjustments of these bars, the computation of the incremental controls corresponding to the motion of a payload along a trajectory is given in terms of the inverse-transpose of matrix B of the joint equilibrium equations Bs = p, where s lists the bar forces and p the nodal loads. An algorithm with 0(w2) computational complexity and 0(/z) storage demand is used for obtaining the inverse of the wth-order sparse matrix B. The compensation of the controls for elastic deformations and support movements is shown. The crane is assumed to be moving sufficiently slowly so that no vibratory motion is created during its maneuver. To simplify the computations, a zero-acceleration field is assumed in the workspace of the space crane. It is shown that the computations may be done automatically and in real time by an attached processor once the characteristics of the crane's maneuver are keyed in.