Missions to Near-Earth Objects (NEOs) are a growing trend in spaceflight. The interest for such bodies is not only justified by the threat that they represent for the Earth, but also because they are potential sources of extra-terrestrial materials, provide windows to the past of the Solar System and to planetary formation, and offer a good opportunity to demonstrate deep-space mission technologies.

The Asteroid Impact Mission (AIM) is the next European Space Agency mission to a NEO, which has among its main objectives the deployment of the Asteroid Spectral Imaging Mission Cubesat (ASPECT) in the vicinity of the binary asteroid Didymos during the Payload Delivery Phase (PDP). However, this deployment is affected by the uncertainties and errors coming from the strongly perturbed environment, the previous phase dispersions, and the navigation and command inaccuracies.

The objective of this thesis is therefore to assess the viability of the cubesat deployment in terms of the safety of the reference trajectories and the accuracy of the deployment conditions achieved.

The reference trajectories that target the cubesat’s commissioning orbit injection point were designed by implementing a two-arc hyperbolic trajectory design problem in a direct-shooting optimisation architecture in the commercial heuristics optimisation software known as Mixed Integer Distributed Ant Colony Optimization (MIDACO). These trajectories were obtained in an ideal, unperturbed scenario. The safety and accuracy of the trajectories obtained were tested in a series of Monte Carlo campaigns in which the uncertainties, errors and dispersions present in the system were used as Monte Carlo variables in a high-level Guidance, Navigation and Control (GNC) simulator implemented in Simulink 2016b.

After identifying the pericentre of the target Self-Stabilised Terminator Orbit (SSTO) as the best point to carry out the deployment, five different families of trajectories that bring the spacecraft within the safety deployment margins were found. The total velocity increment required for these trajectories were found to vary from 1.2 to 3.4 m/s. These relatively high velocity increments are caused by the combination of the constraints imposed in the design process that emanate from the mission operational requirements.

The first Monte Carlo set of simulations showed that the optimum number of guidance correction manoeuvres is assessed to be three. The timing of these manoeuvres is case dependent, but one correction must take place in the first arc flown, and the other two during the second arc and before the deployment.
Results of the second Monte Carlo campaign showed that the trajectories were unsafe according to the mission safety requirements on the minimum distance to the main asteroid and on the margin to the escape velocity. Of these two requirements, the escape velocity margin was the main cause of these safety violations, with several trajectories falling below the margin of 2 cm/s at certain epochs. This was due to the initial state vector dispersion coming from the previous phase and, to a lesser extent, due to the potential thrust failures.

In the final Monte Carlo campaign, the ASPECT injection success rates reached a maximum value of 75% for the trajectory that targets the SSTO with a semi-major axis equal to 5 km. The cause of this low success rate was attributed to a combination of high initial position dispersions and velocity navigation errors. Due to this velocity navigation inaccuracies, the corrections made by the guidance subsystem are not capable of compensating the dispersions in initial position. These corrections further deteriorate the final deployment conditions, since their calculation only takes into account deviations in position, and not in velocity.

The results of this study highlight the need of finding ways of reducing the position dispersion with respect to the nominal trajectory prior to the autonomous PDP. Furthermore, they indicate that the prediction of success rates can be improved by refining the navigation performance models, since these are considered conservative when compared to the real scenario.

Loss of Control is the primary contributor to aviation fatalities. To prevent this type of accident, flight envelope protection is considered to be a necessary development. The calculation of the Safe Flight Envelope provides a bound on the states that can safely be approached by the aircraft. Although theoretically accurate, some states may not be reachable under the influence of disturbances (e.g. turbulence). In this thesis a stochastic extension to the reachability analysis is applied to a simplified aircraft model. The probabilistic reachability analysis yields the transition probability from a state to the target set. By comparing the deterministic and probabilistic Safe Flight Envelope, it becomes clear that the Safe Flight Envelope can shrink considerably under the influence of turbulence. It is shown that for a 3 sigma (99.7%) confidence interval, the envelope can shrink by as much as 50.8% compared to the deterministic envelope. Furthermore, it is found that for high roll angles, some parts of the deterministic envelope have a 0% transition probability under the influence of turbulence, further emphasizing the importance of probabilistic envelopes.

A Hybrid Optimal Control (HOC) framework which can be used in conjunction with existing optimal control software is presented. By using hybrid optimal control theory, trajectory optimization problems for systems that are both discrete time and continuous time from a mathematical perspective can be solved. A case study on multi-aircraft formation flying for civil aviation is performed which demonstrates the capabilities of the designed method. Whilst previous research has dealt with either high accuracy trajectories for small formation flying problems or low accuracy modelling of very large formation flying trajectories, in this thesis HOC is used to achieve a high accuracy optimal trajectory for formations of three aircraft and larger. Given the number of flights that are performed every day, the impact of saving fuel just by optimizing their trajectories using formation flying can be significant on a global scale, both environmentally and economically.