Voronoi-Based Satellite-Swarm Reconfiguration near the Earth–Moon L₂ Point

This study investigates planar Voronoi-based satellite-swarm reconfiguration near the Earth–Moon $L_2$ point under the Circular Restricted Three-Body Problem. Numerical simulations with linearized and nonlinear dynamics show that geometrically equivalent spatial distributions can require substantially different control effort and convergence time depending on their orientation. To account for this directional dependence, a finite-time energy-weighted Voronoi metric is constructed from the controllability Gramian of the linearized dynamics. As the finite-time horizon increases, the direction associated with the minimum eigenvalue of the energy metric approaches the projected unstable direction, and the resulting Voronoi partition becomes increasingly anisotropic with reduced closed-loop control effort in the tested configurations. These results illustrate how local dynamics can be incorporated into planar swarm spatial allocation near $L_2$.