Cross-coupling relative dynamics for on-orbit assembly in rotating frame of reference

Abstract

Dual numbers are applied in this paper to relative dynamics between rigid-flex combination systems. In space cooperative missions, the relative dynamic equations with engineering applicability require description in rotating frame of reference. Taking advantages of dual numbers which can represent spiral movement in a compact form with respect to the rotating frame, the dual vector, dual momentum, dual inertia operator, dual coupling coefficient operator and dual modal coordinates of flexible modules are derived. The algebra of dual numbers for rigid-flex combination system is further developed. On this basis, relative equations of motion between two rigid-flex combination systems in rotating frame of reference are proposed. The behaviors of relative dynamics present complex cross-coupling effects between attitude-orbit coupling and rigid-flex coupling. An on-orbit assembly mission of flexible modules via free flying robots is presented as an exemplary application of the cross-coupling relative dynamics. Ground testing results illustrate the cross-coupling effects on the six degree-of-freedom motion of rigid-flex combination system. Simulation results prove the engineering significance of the cross-coupling relative dynamic model.