Cislunar Pursuit-Evasion Game on Periodic and Quasi-Periodic Orbits
Cislunar spacecraft operate in nonlinear and unstable environments that make defensive maneuver planning difficult. We formulate cislunar spacecraft pursuit and evasion as a zero-sum differential game in the circular restricted three-body problem. Each spacecraft controls its thrust and reference orbit phase, enabling motion along periodic orbits and across quasi-periodic tori while remaining near the reference. We solve the game using a constrained discrete-time differential dynamic programming method that enforces hard input constraints. We propose a shared time regularization to synchronize both spacecraft while refining the discretization near close lunar passages. Numerical results on periodic and quasi-periodic orbits show that phase control improves maneuvering flexibility while limiting departure from the reference orbit. The discrete-time method also provides a large computational advantage over a continuous-time formulation. Comparisons between quasi-halo and quasi-near-rectilinear halo orbits show that close lunar passages create larger escape opportunities but also increase the sensitivity of the encounter. These results show that reference orbit geometry is an important part of defensive cislunar mission design.