RISK-BASED MULTIOBJECTIVE PATH PLANNING AND DESIGN OPTIMIZATION FOR UNMANNED AERIAL VEHICLES

Safe operation of unmanned aerial vehicles (UAVs) over populated areas requires reducing the risk posed by a UAV if it crashed during its operation. We considered several types of UAV risk-based path planning problems and developed techniques for estimating the risk to third parties on the ground. The path planning problem requires making trade-offs between risk and flight time. Four optimization approaches for solving the problem were tested; a network-based approach that used a greedy algorithm to improve the original solution generated the best solutions with the least computational effort. Additionally, an approach for solving a combined design and path planning problems was developed and tested. This approach was extended to solve robust risk-based path planning problem in which uncertainty about wind conditions would affect the risk posed by a UAV.

Motion Planning and Controls with Safety and Temporal Constraints

Motion planning, or trajectory planning, commonly refers to a process of converting high-level task specifications into low-level control commands that can be executed on the system of interest. For different applications, the system will be different. It can be an autonomous vehicle, an Unmanned Aerial Vehicle(UAV), a humanoid robot, or an industrial robotic arm. As human machine interaction is essential in many of these systems, safety is fundamental and crucial. Many of the applications also involve performing a task in an optimal manner within a given time constraint. Therefore, in this thesis, we focus on two aspects of the motion planning problem. One is the verification and synthesis of the safe controls for autonomous ground and air vehicles in collision avoidance scenarios. The other part focuses on the high-level planning for the autonomous vehicles with the timed temporal constraints. In the first aspect of our work, we first propose a verification method to prove the safety and robustness of a path planner and the path following controls based on reachable sets. We demonstrate the method on quadrotor and automobile applications. Secondly, we propose a reachable set based collision avoidance algorithm for UAVs. Instead of the traditional approaches of collision avoidance between trajectories, we propose a collision avoidance scheme based on reachable sets and tubes. We then formulate the problem as a convex optimization problem seeking control set design for the aircraft to avoid collision. We apply our approach to collision avoidance scenarios of quadrotors and fixed-wing aircraft. In the second aspect of our work, we address the high level planning problems with timed temporal logic constraints. Firstly, we present an optimization based method for path planning of a mobile robot subject to timed temporal constraints, in a dynamic environment. Temporal logic (TL) can address very complex task specifications such as safety, coverage, motion sequencing etc. We use metric temporal logic (MTL) to encode the task specifications with timing constraints. We then translate the MTL formulae into mixed integer linear constraints and solve the associated optimization problem using a mixed integer linear program solver. We have applied our approach on several case studies in complex dynamical environments subjected to timed temporal specifications. Secondly, we also present a timed automaton based method for planning under the given timed temporal logic specifications. We use metric interval temporal logic (MITL), a member of the MTL family, to represent the task specification, and provide a constructive way to generate a timed automaton and methods to look for accepting runs on the automaton to find an optimal motion (or path) sequence for the robot to complete the task.

POSITIVE FILTERED P_N METHOD FOR LINEAR TRANSPORT EQUATIONS AND THE ASSOCIATED OPTIMIZATION ALGORITHM

We propose a positive, accurate moment closure for linear kinetic transport equations based on a filtered spherical harmonic (FP_N) expansion in the angular variable. The FP_N moment equations are accurate approximations to linear kinetic equations, but they are known to suffer from the occurrence of unphysical, negative particle concentrations. The new positive filtered P_N (FP_N+) closure is developed to address this issue. The FP_N+ closure approximates the kinetic distribution by a spherical harmonic expansion that is non-negative on a finite, predetermined set of quadrature points. With an appropriate numerical PDE solver, the FP_N+ closure generates particle concentrations that are guaranteed to be non-negative. Under an additional, mild regularity assumption, we prove that as the moment order tends to infinity, the FP_N+ approximation converges, in the L2 sense, at the same rate as the FP_N approximation; numerical tests suggest that this assumption may not be necessary. By numerical experiments on the challenging line source benchmark problem, we confirm that the FP_N+ method indeed produces accurate and non-negative solutions. To apply the FP_N+ closure on problems at large temporal-spatial scales, we develop a positive asymptotic preserving (AP) numerical PDE solver. We prove that the propose AP scheme maintains stability and accuracy with standard mesh sizes at large temporal-spatial scales, while, for generic numerical schemes, excessive refinements on temporal-spatial meshes are required. We also show that the proposed scheme preserves positivity of the particle concentration, under some time step restriction. Numerical results confirm that the proposed AP scheme is capable for solving linear transport equations at large temporal-spatial scales, for which a generic scheme could fail. Constrained optimization problems are involved in the formulation of the FP_N+ closure to enforce non-negativity of the FP_N+ approximation on the set of quadrature points. These optimization problems can be written as strictly convex quadratic programs (CQPs) with a large number of inequality constraints. To efficiently solve the CQPs, we propose a constraint-reduced variant of a Mehrotra-predictor-corrector algorithm, with a novel constraint selection rule. We prove that, under appropriate assumptions, the proposed optimization algorithm converges globally to the solution at a locally q-quadratic rate. We test the algorithm on randomly generated problems, and the numerical results indicate that the combination of the proposed algorithm and the constraint selection rule outperforms other compared constraint-reduced algorithms, especially for problems with many more inequality constraints than variables.

Development of Planning And Evaluation Models For Superstreets

Despite the extensive implementation of Superstreets on congested arterials, reliable methodologies for such designs remain unavailable. The purpose of this research is to fill the information gap by offering reliable tools to assist traffic professionals in the design of Superstreets with and without signal control. The entire tool developed in this thesis consists of three models. The first model is used to determine the minimum U-turn offset length for an Un-signalized Superstreet, given the arterial headway distribution of the traffic flows and the distribution of critical gaps among drivers. The second model is designed to estimate the queue size and its variation on each critical link in a signalized Superstreet, based on the given signal plan and the range of observed volumes. Recognizing that the operational performance of a Superstreet cannot be achieved without an effective signal plan, the third model is developed to produce a signal optimization method that can generate progression offsets for heavy arterial flows moving into and out of such an intersection design.

Mission and Scenario Planning for Unmanned Aerial Vehicles (Path Planning and Collision Avoidance Systems)

As unmanned autonomous vehicles (UAVs) are being widely utilized in military and civil applications, concerns are growing about mission safety and how to integrate dierent phases of mission design. One important barrier to a coste ective and timely safety certication process for UAVs is the lack of a systematic approach for bridging the gap between understanding high-level commander/pilot intent and implementation of intent through low-level UAV behaviors. In this thesis we demonstrate an entire systems design process for a representative UAV mission, beginning from an operational concept and requirements and ending with a simulation framework for segments of the mission design, such as path planning and decision making in collision avoidance. In this thesis, we divided this complex system into sub-systems; path planning, collision detection and collision avoidance. We then developed software modules for each sub-system

Defining the Resolution of a Network for Transportation Analyses: a New Method to Improve Transportation Planning Decisions

Travel demand models are important tools used in the analysis of transportation plans, projects, and policies. The modeling results are useful for transportation planners making transportation decisions and for policy makers developing transportation policies. Defining the level of detail (i.e., the number of roads) of the transport network in consistency with the travel demand model’s zone system is crucial to the accuracy of modeling results. However, travel demand modelers have not had tools to determine how much detail is needed in a transport network for a travel demand model. This dissertation seeks to fill this knowledge gap by (1) providing methodology to define an appropriate level of detail for a transport network in a given travel demand model; (2) implementing this methodology in a travel demand model in the Baltimore area; and (3) identifying how this methodology improves the modeling accuracy. All analyses identify the spatial resolution of the transport network has great impacts on the modeling results. For example, when compared to the observed traffic data, a very detailed network underestimates traffic congestion in the Baltimore area, while a network developed by this dissertation provides a more accurate modeling result of the traffic conditions. Through the evaluation of the impacts a new transportation project has on both networks, the differences in their analysis results point out the importance of having an appropriate level of network detail for making improved planning decisions. The results corroborate a suggested guideline concerning the development of a transport network in consistency with the travel demand model’s zone system. To conclude this dissertation, limitations are identified in data sources and methodology, based on which a plan of future studies is laid out.