# Constrained Spacecraft Relative Motion Planning Exploiting Periodic Natural Motion Trajectories and Invariance

## TL;DR

This paper introduces a novel spacecraft relative motion planning method that leverages periodic natural motion trajectories and invariance principles to ensure obstacle avoidance, fuel efficiency, and passive safety in complex mission scenarios.

## Contribution

It develops a graph search approach on a virtual net of periodic natural trajectories, enhancing flexibility and safety over previous methods based on forced equilibria.

## Key findings

- Reduces fuel consumption in maneuver planning.
- Ensures constraint satisfaction through invariant tubes.
- Improves safety and flexibility in trajectory design.

## Abstract

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.