Development of a Real-Time Hierarchical 3D Path Planning Algorithm for Unmanned Aerial Vehicles

Unmanned aerial vehicles (UAVs) frequently operate in partially or entirely unknown environments. As the vehicle traverses the environment and detects new obstacles, rapid path replanning is essential to avoid collisions. This thesis presents a new algorithm called Hierarchical D* Lite (HD*), which combines the incremental algorithm D* Lite with a novel hierarchical path planning approach to replan paths sufficiently fast for real-time operation. Unlike current hierarchical planning algorithms, HD* does not require map corrections before planning a new path. Directional cost scale factors, path smoothing, and Catmull-Rom splines are used to ensure the resulting paths are feasible. HD* sacrifices optimality for real-time performance. Its computation time and path quality are dependent on the map size, obstacle density, sensor range, and any restrictions on planning time. For the most complex scenarios tested, HD* found paths within 10% of optimal in under 35 milliseconds.

Essays on Market Frictions and Securitization

This dissertation provides a novel theory of securitization based on intermediaries minimizing the moral hazard that insiders can misuse assets held on-balance sheet. The model predicts how intermediaries finance different assets. Under deposit funding, the moral hazard is greatest for low-risk assets that yield sizable returns in bad states of nature; under securitization, it is greatest for high-risk assets that require high guarantees and large reserves. Intermediaries thus securitize low-risk assets. In an extension, I identify a novel channel through which government bailouts exacerbate the moral hazard and reduce total investment irrespective of the funding mode. This adverse effect is stronger under deposit funding, implying that intermediaries finance more risky assets off-balance sheet. The dissertation discusses the implications of different forms of guarantees. With explicit guarantees, banks securitize assets with either low information-intensity or low risk. By contrast, with implicit guarantees, banks only securitize assets with high information-intensity and low risk. Two extensions to the benchmark static and dynamic models are discussed. First, an extension to the static model studies the optimality of tranching versus securitization with guarantees. Tranching eliminates agency costs but worsens adverse selection, while securitization with guarantees does the opposite. When the quality of underlying assets in a certain security market is sufficiently heterogeneous, and when the highest quality assets are perceived to be sufficiently safe, securitization with guarantees dominates tranching. Second, in an extension to the dynamic setting, the moral hazard of misusing assets held on-balance sheet naturally gives rise to the moral hazard of weak ex-post monitoring in securitization. The use of guarantees reduces the dependence of banks' ex-post payoffs on monitoring efforts, thereby weakening monitoring incentives. The incentive to monitor under securitization with implicit guarantees is the weakest among all funding modes, as implicit guarantees allow banks to renege on their monitoring promises without being declared bankrupt and punished.