Optimal multi-target rendezvous planning for active debris removal

Abstract

Active debris removal (ADR) has received considerable attention in recent years with rapidly increasing space debris in Earth orbit. Multi-target rendezvous planning, which determines the targets to visit, their visiting orders, and associated trajectories simultaneously, is a key component of ADR mission design. Solving the optimal multi-target rendezvous problem is very challenging because it involves two different types of optimizations – combinatorial optimization and trajectory optimization – and the size of search space exponentially increases with the number of debris.

This thesis formulates an optimal multi-target rendezvous problem that considers the profit-based debris selection and the use of multiple chaser spacecraft. The objective of the problem is to determine a set of rendezvous sequences and associated trajectories that maximizes total profit collected by multiple spacecraft with limited fuel capacity and mission duration. A two-phase framework is developed to solve the proposed optimal multi-target rendezvous problem. In the first phase of the framework, a series of trajectory optimization problems for all departure/arrival debris pairs are solved to generate the elementary solutions, a database of rendezvous trajectories. The second phase combines the elementary solutions prepared in the first phase to obtain the final solution of the problem. A new variant of the travelling salesman problem (TSP) is introduced to find the optimal rendezvous sequence and associated cost using elementary solutions, and a column generation technique is applied to explore the routes (rendezvous sequences) that are relevant to the optimization problem. The validity of the proposed problem formulation and the optimization framework is demonstrated through two realistic ADR case studies.