Constructing motion primitive sets to summarize periodic orbit families and hyperbolic invariant manifolds in a multi-body system

Motion Primitive Approach to Spacecraft Trajectory Design in a Multi-body System

“…The first step in the initial guess construction framework is to construct a library of motion primitives along with information approximating the regions of the phase space spanned by arcs with similar properties. Although the definition of a motion primitive depends on the application, this paper uses a similar definition to Frazzoli: a set of motion primitives is a finite set of arcs that sufficiently summarize the characteristics of part of the solution space [ 8 , 32 ]. In existing applications, motion primitives have been extracted using a variety of methods such as manual labeling, analytical approximations via basis functions, or clustering [ 8 , 25 , 28 , 39 ].…”

“…Then, an initial guess for a trajectory may be coarsely constructed from an ordered sequence of motion primitives within the library [ 8 , 22 , 41 ]. In the absence of general analytical expressions to describe the solution space and due to the significant burden of manual labeling, this paper uses a clustering-based approach that we have previously developed to extract a set of motion primitives that summarize periodic orbits and arcs along hyperbolic invariant manifolds in the CR3BP [ 32 ]. Although this subsection offers a brief overview of this procedure, additional details appear in Smith and Bosanac 2022 [ 32 ].…”

“…In this existing approach, two significant challenges emerge, particularly when designing maneuver-enabled, spatial trajectories: (1) visualizing and analyzing higher-dimensional datasets to manually select suitable arcs that form an initial guess for a nearby trajectory, and (2) manually constructing multiple geometrically distinct initial guesses to explore the solution space. Motivated by these challenges, Smith and Bosanac have recently introduced a motion primitive approach to spacecraft trajectory design in multi-body systems [ 30 – 32 ].…”

“…Inspired by their application to robotics, Smith and Bosanac have applied the concept of motion primitives to spacecraft trajectory design in a multi-body system. Specifically, we have formulated a consensus clustering procedure to numerically construct sets of motion primitives that summarize periodic orbit families and arcs along hyperbolic invariant manifolds based on geometry, stability, and energy in the Earth-Moon CR3BP [ 32 ]. We have then manually constructed sequences of motion primitives to produce coarse, primitive-based initial guesses that successfully enable the recovery of nearby natural and maneuver-enabled transfers between libration point orbits in the Earth-Moon CR3BP [ 30 ].…”

“…This paper presents a motion primitive framework for rapid and informed trajectory design in the Earth-Moon CR3BP with impulsive maneuvers. First, sets of motion primitives are constructed to summarize the fundamental geometry, stability, and/or energy characteristics of members of individual periodic orbit families and arcs along their hyperbolic invariant manifolds in the CR3BP [ 32 ]. These sets, along with a small number of representative trajectories with similar characteristics, form a motion primitive library.…”