An Application of Rapidly Expanding Random Trees to Spacecraft Rendezvous

The need for spacecraft autonomy continues to grow as the number of satellites increase and spacecraft architectures for distant worlds are created. This work investigates the capability of Rapidly expanding Random Trees (RRT) to provide autonomous rendezvous trajectories for satellites in Earth and cislunar orbits. A combinatorial algorithm, Shooter RRT* (S-RRT*), uses an RRT to choose target nodes through a differential correction scheme that generates trajectories and estimated costs. The S-RRT* can execute fast and optimal path-planning in a nonlinear environment as a preliminary guidance algorithm. The S-RRT* is validated using a Linear Quadratic Regulator fed RRT* algorithm (LQR-RRT*) in the Clohessy-Wiltshire (CW) equations of motion and is extended in the cislunar environment leveraging the Circular Restricted Three-Body Problem (CR3BP) dynamics. This study shows that S-RRT* can generate more optimal paths than LQR-RRT* with the same number of samples. Additionally, the investigation demonstrates that the S-RRT* can deliver a near-optimal trajectory in an NRHO rendezvous with a relatively small number of samples.