Title:

Uncertainty quantification and state estimation for complex nonlinear problems in space flight mechanics

The complex dynamics which describe the motion of a spacecraft far from a massive planetary body or in a highly perturbed environment close to minor celestial objects raises two fundamental but related problems. The first is represented by the difficulty to accurately predict the evolution of its orbit even over short period when its initial conditions are known with a small degree of confidence. The second is given by the need for precise real time estimation of the trajectory when the spacecraft orbits near the asteroid’s surface to avoid impacting on it. The main example of the first problem is the perturbed four body problem for the EarthSunMoon system. EarthSun Lagrangian Point Orbits (LPOs) are often selected for astrophysics and solar terrestrial missions while low cost missions aim at exploiting the so called Weak Stability Boundaries (WSB) to move at low propellant expense within the Earth sphere of influence. As current and future missions are planned to be placed on LPOs, it is a critical aspect to clear these regions at the end of operations to avoid damages to other spacecraft. For the second problem, we have a great number of asteroids and comets orbiting the inner solar system; they represent the socalled minor celestial objects which are very interesting for science since they preserve the remnants of the early formation of the planets and could shed light on the origins of life. At the same time they are very appealing for future commercial applications for the high content of precious ore. Among these celestial objects, the family of Near Earth Objects (NEOs) follows trajectories which lie close to, and sometimes cross, the Earth’s orbit. The impact hazard with the Earth has started to become considered as serious threat. Over the last three decades a number of missions have flown to and explored asteroids and comets, relying heavily on ground support with limited autonomy. In order to perform either asteroid’s exploration or collision hazard protection, autonomous navigation is needed, also to deal with the uncertain environment. Then the manipulation of asteroids’ orbit and attitude for deflection purposes is therefore required and an interesting problem to be studied. The aim of the research presented in this dissertation is to identify and develop methodologies for uncertainty propagation for spacecraft orbit and the application to orbit determination for complex nonlinear space mechanics problems, with particular care paid to the case of close proximity operations which are required when performing missions to minor celestial objects. The results are not limited only to this kind of problem but can be applied also to different scenarios. A first set of results focuses on the prediction of the trajectory evolution under initial condition uncertainties. The accuracy of the propagation of uncertainties is intimately related to the process of trajectory estimation, which relies on the use of the covariance matrix. The covariance matrix gives an idea of the dispersion of the spacecraft in terms of position and velocity. Different techniques to propagate the covariance matrix are used to predict the evolution of the trajectory when the initial conditions are known only to a certain degree of accuracy. They are compared under a highly nonlinear scenario where a spacecraft is injected into a disposal orbit towards an impacting trajectory with the Moon from a Lagrangian Point Orbit. A second set of results focuses on the identification of the estimation techniques applied to a single spacecraft. The estimation process performs well depending on the capability to propagate the covariance matrix and to incorporate the new information. A number of filtering techniques based on the Kalman and H∞ filters, employing different methods to handle the propagation of the covariance matrix, are presented and tested in typical nonlinear environments, i.e. a WSB transferan asteroid proximity, to draw precious information on their performance. The analyses demonstrate that only a hybrid Kalman H∞ filter can enable the spacecraft to estimate its trajectory with a good balance between accuracy and computational costs. Then this method is applied to the navigation of spacecraft formation about a NEO showing that the navigation performance is significantly improved by sharing relative information among the spacecraft and the overall system is shown to be faulttolerant. Finally the orbit’s and attitude manipulation of a small asteroid using a laser ablation system is analysed. An onboard state estimation and control algorithm is presented that simultaneously provides an optimal proximity control and control of the rotational motion of the asteroid. During the deflection, the proximity motion of the spacecraft is coupled with the orbital and rotational motion of the asteroid. The combination of the deflection acceleration, solar radiation pressure, and gravity field and plume impingement will force the spacecraft to drift away from the asteroid. In turn, a variation of the motion of the spacecraft produces a change in the modulus and direction of the deflection action which modifies the rotational and orbital motion of the asteroid.
