Stretching and Restoring Directions as a Basis for Relative Trajectory Design

As traffic in cislunar space grows and missions become increasingly complex, effective understanding of relative motion between spacecraft is paramount. Additional tools are necessary to more accurately determine favorable relative behaviors in a multi-body gravitational environment. In this investigation, relative states are characterized as linear combinations of principal stretching and restoring directions to introduce techniques for relative trajectory design in the circular restricted three-body problem. These dynamically-informed directions form sets of orthonormal vector bases employed to describe and design spacecraft motion relative to a reference trajectory. Properties unique to 3x3 subsets of the state transition matrix are exploited to derive methodologies for two relative motion applications. First, the formulation is presented from a spacecraft loitering perspective, providing a framework to methodically determine ballistic relative trajectory options for visiting spacecraft. Secondly, modifications are introduced for flexible maneuver planning in a collision avoidance scenario. The two methodologies are assessed for a variety of test cases along four different periodic orbits in the Earth-Moon system.