Scheduling Autonomous Vehicle Platoons Through an Unregulated Intersection

We study various versions of the problem of scheduling platoons of autonomous vehicles through an unregulated intersection, where an algorithm must schedule which platoons should wait so that others can go through, so as to minimize the maximum delay for any vehicle. We provide polynomial-time algorithms for constructing such schedules for a k-way merge intersection, for constant k, and for a crossing intersection involving two-way traffic. We also show that the more general problem of scheduling autonomous platoons through an intersection that includes both a k-way merge, for non-constant k, and a crossing of two-way traffic is NP-complete

Optimal scheduling of connected and autonomous vehicles at a reservation-based intersection.

Reservation-based intersection control has been evaluated with better performance over traditional signal controls in terms of intersection safety, efficiency, and emission. Controlling connected and autonomous vehicles (CAVs) at a reservation-based intersection in terms of improving intersection efficiency is performed via two factors: trajectory (speed profile) and arrival time of CAVs at the intersection. In an early stage of the reservation-based intersection control, an intersection controller at the intersection may fail to find a feasible solution for both the trajectory and arrival time for a CAV at a certain planning horizon. Leveraging a deeper understanding of the control problem, reservation-based intersection control methods are able to optimize both trajectory and arrival time simultaneously while overcoming the infeasible condition. Furthermore, in order to achieve real-time control at the reservation-based intersection, a scheduling problem of CAV crossing the intersection has been widely modeled to optimize the intersection efficiency. Efficient solution algorithms have been proposed to overcome the curse of dimensionality. However, a control methodology consisting of trajectory planning and arrival time scheduling that can overcome the infeasible condition has not been explicitly explained and defined. Furthermore, an optimal control framework for joint control of the trajectory planning and arrival time scheduling in terms of global intersection efficiency has not been theoretically established and numerically validated; and mechanisms of how to reduce the time complexity meanwhile solving the scheduling problem to an optimal solution are not fully understood and rigorously defined. In this dissertation, a control method that eliminates the infeasible problem at any planning horizon is first explicitly explained and defined based on a time-speed-independent trajectory planning and scheduling model. Secondly, this dissertation theoretically defines the optimal control framework via analyzing various control methods in terms of intersection capacity, throughput and delay. Furthermore, this dissertation theoretically analyzes the mechanism of the scheduling problem and designs an exact algorithm to further reduce the time complexity. Through theoretical analyses of the properties of the scheduling problem, the reasons that the time complexity can be reduced are fundamentally explained. The results first validate that the defined control framework can adapt to extremely high traffic demand scenarios with feasible solutions at any planning horizon for all CAVs. Under extensive sensitivity analyses, the theoretical definition of the optimal control framework is validated in terms of maximizing the intersection efficiency. Moreover, numerical examples validate that a proposed scheduling algorithm finds an optimal solution with lower computation time and time complexity

Efficient Algorithms for Coordinated Motion in Shared Spaces

The steady development of autonomous systems motivates a number of interesting algorithmic problems. These systems, such as self-driving cars, must contend with far more complex and dynamic environments than factory floor robots of the past. This dissertation seeks to identify optimization problems that are simple enough to analyze formally, yet realistic enough to contribute to the eventual design of systems extant in real-world, physical spaces. With that in mind, this work examines three problems in particular: automated vehicles and unregulated traffic crossings, a smart network for city-wide traffic flow, and an online organizational scheme for automated warehouses. First, the Traffic Crossing Problem is introduced, in which a set of n axis-aligned vehicles moving monotonically in the plane must reach their goal positions within a time limit and subject to a maximum speed limit. It is shown that this problem is NP-complete and efficient algorithms for two special cases are given. Next, motivated by a problem of computing a periodic schedule for traffic lights in an urban transportation network, the problem of Circulation with Modular Demands is introduced. A novel variant of the well-known minimum-cost circulation problem in directed networks, in this problem vertex demand values are taken from the integers modulo λ, for some integer λ≥2. This modular circulation problem is solvable in polynomial time when λ=2, but the problem is NP-hard when λ≥3. For this case, a polynomial time approximation algorithm is provided. Finally, a theoretical model for organizing portable storage units in a warehouse subject to an online sequence of access requests is proposed. Complicated by the unknown request frequencies of stored products, the warehouse must be arranged with care. Analogous to virtual-memory systems, the more popular and oft-requested an item is, the more efficient its retrieval should be. Two formulations are considered, dependent on the number of access points to which storage units must be brought, and algorithms that are O(1)-competitive with respect to an optimal algorithm are given. Additionally, in the case of a single access point, the solution herein is asymptotically optimal with respect to density

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