AbstractsAstronomy & Space Science

Contemporary collision avoidance systems such as the Traffic Alert and Collision Avoidance System (TCAS) have proven their effectiveness in the Commercial Aviation (CA) industry within the last decade. Yet, TCAS and many systems like it represent attempts at collision avoidance that do not fully recognize the uncertain nature of a conflict event. Most systems circumvent probabilistic representation through simplifying approximations and pre-compiled notions of hazard space, since probabilistic representation of collision in three dimensions is considered to be an intractable problem. Recent developments by Kuchar and Yang[70] and Paielli and Erzberger[50] have shown that collision avoidance may be cast as a probabilistic state-space problem. Innovative solution approaches may then allow systems of this nature to probe collision risk in real-time, based on real-time state estimates. The research documented in this thesis further develops the probabilistic approach for the non-cooperative, two-vehicle problem as applied in real-time to autonomous aircraft. The research is kept in a general form, thereby warranting application to a wide variety of multi-dimensional collision avoidance applications and scenario geometries. The work primarily improves the state of the art through the creation of order reductive collision metrics in order to simplify the intractable problem of multi-dimensional collision risk calculation. As a result, a tractable, real-time, probabilistic algorithm is developed for the calculation of collision risk as a function of time. The collision avoidance problem is contextualized not only within the realm of recent research within the CA industry, but is also likened to such concepts as the first passage time problem encountered in physics, and the field of reliability theory often encountered in civil and mechanical engineering problems. Yang's method of solution, a piece-wise straight-line Monte-Carlo approach to state propagation, is extended with a model-predictive, finite horizon risk accumulation algorithm. Through this extension we are capable of modelling collision risk for linear(-ized), time-variant, dynamic vehicle models and control strategies. A strategy is developed whereby the advantage of delayed collision avoidance action is calculated and it is framed as an extension of the notion of system operating characteristics (SOCs). The complexity of the probabilistic representation is reduced by application of quadratic conflict metrics. The numerical complexity can be reduced from [Omicron](N2n) to [Omicron](Nlog2(N)) at each time step within a finite horizon time interval. Risk calculation errors due to numerical and stochastic approximations are quantified. An applicability test is also devised whereby a vehicle's dynamic model and control characteristics may be used to calculate risk error estimates before implementing the bulk of the algorithmic solution. Various other applications of the work, outside the scope of collision avoidance, are also identified.