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Satellites flying in close proximity can provide many advantages over a single monolithic system.However, the balance between minimising fuel and maintaining safe trajectories creates the inevitable dilemma of trading fuel for safety or vice versa to preserve formation life. Multi-satellite trajectory planning for proximity operations is traditionally completed days or weeks in advance of a manoeuvre due to the complex dynamics of relative motion. Allowing satellite formations the flexibility to perform path-planning operations on-board each spacecraft can significantly reduce the ground operations burden and increase the responsiveness of a formation to reconfiguration events. To meet rapid manoeuvre requirements for future multi-satellite missions, collision-free path-planning and execution must be completed on-board a satellite. This thesis presents a novel approach for real-time multi-satellite collision avoidance path-planning and execution which can be implemented autonomously on-board individual spacecraft in a formation. A systematic study of the effects of perturbations during optimal reconfiguration and a heuristic model of reconfiguration in relative motion creates a basis for building multi-satellite collision-free trajectory planning and control tools. Utilising an analytic reconfiguration model, a new semi-analytic collision identification approach is developed which increases the dimensional understanding and allows for focused collision avoidance planning. Implementation of this approach in conjunction with a sequential pareto-optimal trajectory deviation strategy to produces an innovative collision avoidance path-planner. A new analytic model predictive control system is developed which implements collision-free manoeuvre plans in the presence of perturbations and other uncertainties. Additionally, approaches are presented for extending the heuristic motion model. A new relative motion model is developed including J2 perturbations and using cylindrical coordinates which allows for higher-fidelity modelling of long-duration, large-separation relative motion. Such models further decrease fuel usage during the execution of multi-satellite collision-free reconfiguration. I Comparisons with traditional methods demonstrate a substantially reduced computational burden allowing these to be the first such path-planning tools to be validated on spacecraft hardware. Controller demonstration also shows a dramatic decrease in fuel usage when compared with traditional analytic controllers at nearly equal computation time. Satellite hardware testing validates that both the semi-analytic collision avoidance and analytic model predictive controller are real-time solutions to safe on-orbit formation reconfiguration. Keywords: Collision Avoidance; Formation Flying; Optimal Control; Model Predictive Control; J2 Linearized Relative Motion Email: lsauter@alum.mit.edu

This thesis considers two systems: a dumb-bell satellite which is a system of two point masses connected by a massless rigid rod, and a gyrostat consisting of a dumbbell satellite with a gyroscope attached. Stability of relative equilibria of the dumbbell satellite in two dimensions is studied, where two types of relative equilibrium are obtained, which correspond to two orientations: radial and tangential. The only relative equilibrium which is found to be stable is the radial position, and this stability is only satisfied when the length of the dumb-bell satellite is smaller than the radius of the orbit. The reduced energy-momentum method is used through the augmented Hamiltonian.

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This thesis reports on the application of network theory to data representing space debris in Low Earth Orbit. The research was designed with a view to developing a targeted approach to Active Debris Removal (ADR). The need for remediation, via ADR, of the space debris environment is regarded as the only means by which we can control the growth of the future debris population to maintain use of Earth orbit. A targeted approach to ADR is required to remove the objects that pose the greatest risk in terms of the creation of further debris by explosions or collisions in the future. Methods of determining target criteria are debated in the literature. Network theory is introduced here as an alternative method that, unlike other methods, does not treat debris-producing events in isolation and examines the role of objects in series of conjunctions. The research involved using networks to represent various aspects of the space debris environment. Network theory analysis was carried out on the datasets to determine specific characteristics such as the presence of clustering and the extent of disassortative mixing. Once general characteristics of the 'space debris networks' were determined, two case studies were used as preliminary investigations to assess the use of network theory for targeting objects for removal. The research shows that network theory can be used to determine that `space debris networks' are robust and disassortative. Although there are limitations due to the uncertainties in the data used to create the networks, the findings suggest that careful development and application of target criteria would result in successful ADR.

Three fundamental tether motions were considered for payload orbital transfer with tethers: hanging, prograde libration and prograde motorised spin. The symmetrical double-ended motorised spinning tether performed best and was most efficient, improving by two orders of magnitude on the librating tether which in turn improved on the hanging tether by roughly a factor of two. An upper payload using long tethers with a motorised tether on a circular orbit can be transferred from a low to a geostationary Earth orbit by employing relatively high motor torque and a safety factor on the tether strength close to unity. Two common literature results, the constant efficiency index of seven for a hanging tether upper payload release and the maximum efficiency index of fourteen for an upper payload released from a prograde librating tether, were found to be a lower bound and quite readily breached, respectively. Orbit circularisation through tether release was found to be feasible with retrograde librating tethers. When the point of release does not occur along the local vertical then a non-optimum release of the payload was found to severely reduce the performance of payload transfer with tethers. Consequently, a very precise and accurately timed release is important for the success of payload orbital transfer with tethers since missing the point of release by a single degree with a spinning tether, say, can cause the payload to miss its required target. The best design for the outrigger system to provide the necessary resistive torque is to utilise the gravity gradient and tap the outrigger system within the gravitational potential well. In this manner the outrigger tether length can be significantly reduced and the outrigger end masses can be minimised, thus saving valuable launch mass and cost, as well as exposing less tether surface area to the space environment. With current materials the maximum ?V to be expected with a motorised tether is between 600-1400 m/s depending on the tether length and payload mass. The duration of the spin-up lasts approximately between half and a full Earth day but may vary by an hour, say, depending on the initial conditions and orbit eccentricity. Ensuring the motor torque axis remains perpendicular to the orbital plane was found to be vital otherwise the spin-up time is greatly increased. The motorised tether has the ability to shift the datum of a hanging tether, which may have useful applications in Earth monitoring or tethered Interferometry. Out-of-plane initial angular displacements or the motor torque axis not remaining perpendicular to the orbital plane caused the motorised tether to precess. Furthermore, the motion of the motorised tether with a constant motor torque was found to be regular, but quasi-periodic, which implies that the payload cannot be reliably delivered at perigee along the local vertical.