On the Integration of Unmanned Aerial Vehicles into Public Airspace

Unmanned Aerial Vehicles will soon be integrated in the airspace and start serving us in various capacities such as package delivery, surveillance, search and rescue missions, inspection of infrastructure, precision agriculture, and cinematography. In this thesis, motivated by the challenges this new era brings about, we design a layered architecture called Internet of Drones (IoD). In this architecture, we propose a structure for the traffic in the airspace as well as the interaction between the components of our system such as unmanned aerial vehicles and service providers. We envision the minimal features that need to be implemented in various layers of the architecture, both on the Unmanned Aerial Vehicle (UAV)'s side and on the service providers' side. We compare and contrast various approaches in three existing networks, namely the Internet, the cellular network, and the air traffic control network and discuss how they relate to IoD. As a tool to aid in enabling integration of drones in the airspace, we create a traffic flow model. This model will assign velocities to drones according to the traffic conditions in a stable way as well as help to study the formation of congestion in the airspace. We take the novel problem posed by the 3D nature of UAV flights as opposed to the 2D nature of road vehicles movements and create a fitting traffic flow model. In this model, instead of structuring our model in terms of roads and lanes as is customary for ground vehicles, we structure it in terms of channels, density and capacities. The congestion is formulated as the perceived density given the capacity and the velocity of vehicles will be set accordingly. This view removes the need for a lane changing model and its complexity which we believe should be abstracted away even for the ground vehicles as it is not fundamentally related to the longitudinal movements of vehicles. Our model uses a scalar capacity parameter and can exhibit both passing and blocking behaviors. Furthermore, our model can be solved analytically in the blocking regime and piece-wise analytically solved when in the passing regime. Finally, it is not possible to integrate UAVs into the airspace without some mechanism for coordination or in other words scheduling. We define a new scheduling problem in this regard that we call Vehicle Scheduling Problem (VSP). We prove NP-hardness for all the commonly used objective functions in the context of Job Shop Scheduling Problem (JSP). Then for the number of missed deadlines as our objective function, we give a Mixed Integer Programming (MIP) formulation of VSP. We design a heuristic algorithm and compare the quality of the schedules created for small instances with the exact solution to the MIP instance. For larger instances, these comparisons are made with a baseline algorithm

The non-injective hidden shift problem

In this work, we mostly concentrate on the hidden shift problem for non-injective functions. It is worthwhile to know that the query complexity of the non-injective hidden shift problem is exponential in the worst case by the well known bounds on the unstructured search problem. Hence, we can make this problem more tractable by imposing additional constraints on the problem. Perhaps the first constraint that comes to mind is to address the average case problem. In this work, we show that the average case non-injective hidden shift problem can be reduced to the injective hidden shift problem by giving one such reduction. The reduction is based on a tool we developed called injectivization. The result is strong in the sense that the underlying group can be any finite group and that the non-injective functions for which we have defined the hidden shift problem can have range in an arbitrary finite set. Using this tool, we simplify the main result of a recent paper by about the hidden shift problem for Boolean-valued functions by reducing that problem to Simon's problem. They also posed an open question which is subject to personal interpretation. We answer the seemingly most general interpretation of the question. However, we use our own techniques in doing so (the authors ask if their techniques can be used for addressing that problem). Another constraint that one can consider is to have a promise on the structure of the functions. In this work we consider the hidden shift problem for c-almost generalized bent functions. A class of functions which we defined that includes the generalized bent functions. Then we turn our attention toward the generalized hidden shift problem which is easier than injective hidden shift problem and hence more tractable. We state some of our observations about this problem. Finally we show that the average classical query complexity of the non-injective hidden shift problem over groups of form (Z/mZ)^n when m is a constant is exponential, which also immediately implies that the classical average query complexity of the non-injective hidden shift problem is exponential. We also show that the worst-case classical query complexity of the generalized injective hidden shift problem over the same group is high, which implies that the classical query complexity of the hidden shift problem is high

A Density-Based and Lane-Free Microscopic Traffic Flow Model Applied to Unmanned Aerial Vehicles

In this work, we introduce a microscopic traffic flow model called Scalar Capacity Model (SCM) which can be used to study the formation of traffic on an airway link for autonomous Unmanned Aerial Vehicles (UAVs) as well as for the ground vehicles on the road. Given the 3D trajectory of UAV flights (as opposed to the 2D trajectory of ground vehicles), the main novelty in our model is to eliminate the commonly used notion of lanes and replace it with a notion of density and capacity of flow, but in such a way that individual vehicle motions can still be modeled. We name this a Density/Capacity View (DCV) of the link capacity and how vehicles utilize it versus the traditional One/Multi-Lane View (OMV). An interesting feature of this model is exhibiting both passing and blocking regimes (analogous to multi-lane or single-lane) depending on the set scalar parameter for capacity. We show the model has linear local (platoon) and asymptotic linear stability. Additionally, we perform numerical simulations and show evidence for non-linear stability. Our traffic flow model is represented by a nonlinear differential equation which we transform into a linear form. This makes our model analytically solvable in the blocking regime and piece-wise analytically solvable in the passing regime. Finally, a key advantage of using our model over an OMV model for representing UAV’s flights is the removal of the artificial restriction on passing via only adjacent lanes. This will result in an improved and more realistic traffic flow for UAVs

A Density-Based and Lane-Free Microscopic Traffic Flow Model Applied to Unmanned Aerial Vehicles

In this work, we introduce a microscopic traffic flow model called Scalar Capacity Model (SCM) which can be used to study the formation of traffic on an airway link for autonomous Unmanned Aerial Vehicles (UAVs) as well as for the ground vehicles on the road. Given the 3D trajectory of UAV flights (as opposed to the 2D trajectory of ground vehicles), the main novelty in our model is to eliminate the commonly used notion of lanes and replace it with a notion of density and capacity of flow, but in such a way that individual vehicle motions can still be modeled. We name this a Density/Capacity View (DCV) of the link capacity and how vehicles utilize it versus the traditional One/Multi-Lane View (OMV). An interesting feature of this model is exhibiting both passing and blocking regimes (analogous to multi-lane or single-lane) depending on the set scalar parameter for capacity. We show the model has linear local (platoon) and asymptotic linear stability. Additionally, we perform numerical simulations and show evidence for non-linear stability. Our traffic flow model is represented by a nonlinear differential equation which we transform into a linear form. This makes our model analytically solvable in the blocking regime and piece-wise analytically solvable in the passing regime. Finally, a key advantage of using our model over an OMV model for representing UAV’s flights is the removal of the artificial restriction on passing via only adjacent lanes. This will result in an improved and more realistic traffic flow for UAVs

Jobseekers Bill Notes on clauses, House of Commons

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