Optimization Techniques for Long Term Active Debris Removal Mission Design Applications

Abstract

Debris in Low Earth Orbit (LEO) poses a great risk to humanity’s access to space in the coming years. Seemingly the only way to prevent a full scale catastrophe rendering LEO unusable is to begin a series of active debris removal (ADR) missions. An approach for designing a series of active debris removal missions is presented in this thesis. This approach has multiple steps and begins with a large list of high risk, high mass debris objects. The first stage of the planning process entails the use of clustering algorithms to partition a large catalogue of orbits into groups of user defined sizes. It is shown that this operation is tantamount to histogram analysis in non-Euclidean spaces.

The second stage of the approach then solves a dynamic traveling salesman problem to compute an order of visitation through each cluster. Lastly, a novel trajectory optimization technique is presented, using Chebyshev polynomials to approximate the dynamics of the system (rather than the states, which is typical). This technique is then used to further optimize the solution of the dynamic traveling salesman problem in order to arrive at a locally optimal solution to each multi-rendezvous problem.