Optimal trajectory design for interception and deflection of Near Earth Objects

Many asteroids and comets orbit the inner solar system; among them Near Earth Objects (NEOs) are those celestial bodies for which the orbit lies close, and sometimes crosses, the Earth’s orbit. Over the last decades the impact hazard they pose to the Earth has generated heated discussions on the required measures to react to such a scenario. The aim of the research presented in this dissertation is to develop methodologies for the trajectory design of interception and deflection missions to Near Earth Objects. The displacement, following a deflection manoeuvre, of the asteroid at the minimum orbit intersection distance with the Earth is expressed by means of a simple and general formulation, which exploits the relative motion equations and Gauss’ equations. The variation of the orbital elements achieved by any impulsive or low-thrust action on the threatening body is derived through a semi-analytical approach, whose accuracy is extensively shown. This formulation allows the analysis of the optimal direction of the deflection manoeuvre to maximise the achievable deviation. The search for optimal opportunities for mitigation missions is done through a global optimisation approach. The transfer trajectory, modelled through preliminary design techniques, is integrated with the deflection model. In this way, the mission planning can be performed by optimising different contrasting criteria, such as the mass at launch, the warning time, and the total deflection. A set of Pareto fronts is computed for different deflection strategies and considering various asteroid mitigation scenarios. Each Pareto set represents a number of mission opportunities, over a wide domain of launch windows and design parameters. A first set of results focuses on impulsive deflection missions, to a selected group of potentially hazardous asteroids; the analysis shows that the ideal optimal direction of the deflection manoeuvre cannot always be achieved when the transfer trajectory is integrated with the deflection phase. A second set of results includes solutions for the deviation of some selected NEOs by means of a solar collector strategy. The semi-analytical formulation derived allows the reduction of the computational time, hence the generation of a large number of solutions. Moreover, sets of Pareto fronts for asteroid mitigation are computed through the more feasible deflection schemes proposed in literature: kinetic impactor, nuclear interceptor, mass driver device, low-thrust attached propulsion, solar collector, and gravity tug. A dominance criterion is used to perform a comparative assessment of these mitigation strategies, while also considering the required technological development through a technology readiness factor. The global search of solutions through a multi-criteria optimisation approach represents the first stage of the mission planning, in which preliminary design techniques are used for the trajectory model. At a second stage, a selected number of trajectories can be optimised, using a refined model of the dynamics. For this purpose, the use of Differential Dynamic Programming (DDP) is investigated for the solution of the optimal control problem associated to the design of low-thrust trajectories. The stage-wise approach of DDP is exploited to integrate an adaptive step discretisation scheme within the optimisation process. The discretisation mesh is adjusted at each iteration, to assure high accuracy of the solution trajectory and hence fully exploit the dynamics of the problem within the optimisation process. The feedback nature of the control law is preserved, through a particular interpolation technique that improves the robustness against some approximation errors. The modified DDP-method is presented and applied to the design of transfer trajectories to the fly-by or rendezvous of NEOs, including the escape phase at the Earth. The DDP approach allows the optimisation of the trajectory as a whole, without recurring to the patched conic approach. The results show how the proposed method is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution.