Collinear invariant shapes for three-spacecraft Coulomb formations

This paper investigates invariant shape conditions for a three-craft collinear formation in deep space controlled solely by electrostatic Coulomb forces. Previous research shows that invariant shape solutions can exist under certain circumstances for a charged three-craft collinear configuration. This paper investigates the structure of the cluster shape solution space. The problem is examined from a mission design perspective, determining whether or not real charges can always be found that will yield a desired invariant collinear shape configuration. The paper proves that for any three-craft collinear invariant shape formations there always exists an infinite set of real open-loop charges that yield a shape equilibrium. Further, the null-space of the feasible charge solutions is analyzed, and a method for determining a charge-optimal solution is presented. The results are demonstrated through use of numerical simulations.

► Collinear invariant shape Coulomb formations. ► Formation geometry is specified to obtain charges. ► L∞-norm used to determine optimal charge configuration for desired shape.