Non-linear Model Predictive Control for space debris removal missions

Abstract: The rapidly increasing amounts of space debris orbiting Earth is threatening to reach a critical level, where the near-Earth environment becomes so overfilled with junk that many missions simply become unfeasible. Long-term active debris removal operations appear to be a necessity, but due to the scale of the problem this will likely be an expensive affair spanning decades or even centuries. Many of the mission-related costs can be significantly reduced by making use of a smaller spacecraft, such as the rapidly developing CubeSat standard. An issue with this approach is the limited actuation capabilities, as that makes it very difficult to perform orbital maneuvers in a fuel-efficient manner. Rather than making a few high-impulse thrusts over the course of the mission, the thrust must be applied continuously for several hundred hours. This thesis attempts to solve the problem by using a non-linear Model Predictive Control strategy to implement an Orbital and Attitude Control system for a small satellite. This was done in MATLAB, using the fast-NMPC package MATMPC recently developed by Yutao Chen at Padova University. The controller was tested in a realistic model of the near-Earth environment, where disturbances such as drag and gravitational perturbations are simulated. It was shown through simulations that this method can successfully be used to perform a fuel-efficient rendezvous maneuver with an uncontrollable object, a critical step in any Active Debris Removal operation. Using a 4 kg CubeSat with a 30 µN thruster mounted on each of its six surfaces, the total mass consumption for a phasing maneuver of 10 degrees at 300 km altitude was less than 0.1% of the spacecraft mass. This assumes an Isp of 1,150 s, which is the specific impulse of the S-iEPS Electrostatic thruster flown on the Aero-Cube-8 IMPACT mission. This is made possible through prediction horizons spanning several days, which in turn forces the controller to operate at sampling rates as low as 1/100 Hz due to the computational load. Fully realizing the potential of this technique would likely require the inclusion of a low-level controller that uses the generated trajectories as input values, as this would negate many of the issues associated with a heavy computational load. The urgency of the space debris problem, and the endless list of other CubeSat applications that would benefit from a flexible and fuel-efficient AOCS, makes this an interesting to topic to consider for further research.