• inver over
• linear programming
• space debris
• travelling salesman problem

The Low Earth Orbit (LEO) region is getting more and more crowded by space
debris of all sizes. Random collisions between objects in space may cause a colli-
sional cascading effect, known as “Kessler Syndrome”, which would compromise
the utilization of operational orbits. Removing space debris actively from regions
with high object densities may be necessary and to fulfil this requirement many
Active Debris Removal (ADR) methods and mission designs have been proposed.
This thesis was carried out within the Swiss start-up ClearSpace, from the
EPFL’s Space Center (eSpace) in Lausanne, which is committed with the European
Space Agency (ESA) to the removal of an inactive ESA-owned object from LEO.
The problems addressed in this thesis concern the path optimization of single or
several spacecraft for multiple space debris removal to minimize the mission total
velocity change ∆V . The problem of choosing in which order to remove targeted
debris is a variant of the Travelling Salesman Problem (TSP), the substantial
differences are highlighted.
The path optimization problem is formulated as an integer linear programming
problem in the case of an ADR mission employing multiple spacecraft, while it is
solved by an adapted version of the inver-over algorithm when a single spacecraft
is involved in space debris removal.