  Spacecraft relative motion planning is concerned with the design and
execution of maneuvers relative to a nominal target. These types of maneuvers
are frequently utilized in missions such as rendezvous and docking, satellite
inspection and formation flight where exclusion zones representing spacecraft
or other obstacles must be avoided. The presence of these exclusion zones leads
to non-linear and non-convex constraints which must be satisfied. In this
paper, a novel approach to spacecraft relative motion planning with obstacle
avoidance and thrust constraints is developed. This approach is based on a
graph search applied to a virtual net of closed (periodic) natural motion
trajectories, where the natural motion trajectories represent virtual net nodes
(vertices), and adjacency and connection information is determined by
conditions defined in terms of safe, positively-invariant tubes built around
each trajectory. These conditions guarantee that transitions from one natural
motion trajectory to another natural motion trajectory can be completed without
constraint violations. The proposed approach improves the flexibility of a
previous approach based on the use of forced equilibria, and has other
advantages in terms of reduced fuel consumption and passive safety. The
resulting maneuvers, if planned on-board, can be executed directly or, if
planned off board, can be used to warm start trajectory optimizers to generate
further improvements.
