A space-discretized mixed-integer linear model for air-conflict resolution with speed and heading maneuvers

International audienceAir-conflict resolution is a bottleneck of air traffic management that will soon require powerful decision-aid systems to avoid the proliferation of delays. Since reactivity is critical for this application, we develop a mixed-integer linear model based on space discretization so that complex situations can be solved in near real-time. The discretization allows us to model the problem with finite and potentially small sets of variables and constraints by focusing on important points of the planned trajectories, including the points where trajectories intersect. A major goal of this work is to use space discretization while allowing velocity and heading maneuvers. Realistic trajectories are also ensured by considering speed vectors that are continuous with respect to time, and limits on the velocity, acceleration, and yaw rate. A classical indicator of economic efficiency is then optimized by minimizing a weighted sum of fuel consumption and delay. The experimental tests confirm that the model can solve complex situations within a few seconds without incurring more than a few kilograms of extra fuel consumption per aircraft

Real-Time Obstacle and Collision Avoidance System for Fixed-Wing Unmanned Aerial Systems

The motivation for the research presented in this dissertation is to provide a two-fold solution to the problem of non-cooperative reactive mid-air threat avoidance for fixed-wing unmanned aerial systems. The first phase is an offline UAS trajectory planning designed for an altitude-specific mission. The second phase leans on the results produced during the first phase to provide intelligent, real-time, reactive mid-air threat avoidance logic. That real-time operating logic provides a given fixed-wing UAS with local threat awareness so it can get a feel for the danger represented by a potential threat before using results produced during the first phase to require aircraft rerouting. The first original contribution of this research is the Advanced Mapping and Waypoint Generator (AMWG), a piece of software which processes publicly available elevation data in order to only retain the information necessary for a given altitude-specific flight mission. The AMWG is what makes systematic offline trajectory possible. The AMWG first creates altitude groups in order to discard elevations points which are not relevant to a specific mission because of the altitude flown at. Those groups referred to as altitude layers can in turn be reused if the original layer becomes unsafe for the altitude range in use, and the other layers are used for altitude re-scheduling in order to update the current altitude layer to a safer layer. Each layer is bounded by a lower and higher altitude, within which terrain contours are considered constant according to a conservative approach involving the principle of natural erosion. The AMWG then proceeds to obstacle contours extraction using threshold and edge detection vision algorithms. A simplification of those obstacle contours and their corresponding free space zones counterparts is performed using a fixed -tolerance Douglas-Peucker algorithm. This simplification allows free space zones to be described by vectors instead of point clouds, which enables UAS point location. The resulting geometry is then processed through a vertical trapezoidal decomposition where for each vertex defining a contour a vertical line is drawn, and the results of this decomposition is a set of trapezoidal cells. The cells corresponding to obstacle contours are then removed from the original trapezoidal decomposition in order to solely retain the obstacle-free trapezoidal cells. After decomposition, cells sharing part of a common edge are considered from a graph theory perspective so it becomes possible to list all acyclic paths between two cells by applying a depth first search (DFS) algorithm. The final product of the AWMG is a network of connected free space trapezoidal cells with embedded connectivity information referred to as the Synthetic Terrain Avoidance (STA network). The walls of the trapezoidal cells are then extruded as the AWMG essentially approximates a three-dimensional world by considering it as a stratification of two-dimensional layers, but the real-time phase needs 3D support. Using the graph conceptual view and the depth first search algorithm, all the connected cell sequences joining the departure to the arrival cell can be listed, a capability which is used during aircraft rerouting. By connecting two adjacent cells' centroids to their common midpoint located on the shared edge, the resulting flying legs remain within the two cells. The next step for paths between two cells is to be converted into flyable paths, and the conversion uses main and fallback methods to achieve that. The preferred method is the closed-form Dubins paths method involving the design of sequences of arc circle-straight line-arc circle (CLC) in order to account for the minimum radius turn constrain of the UAS. An additional geometric transformation is developed and applied to the initial waypoints used in the Dubins method so the flying leg directions are respected which is not possible by using the Dubins method alone. When consecutive waypoints are too close from one another, a condition called the Dubins condition cannot be respected, and the UAS trajectory design switches to the numerical integration of a system of ordinary differential equations accounting for the minimum turning constraint. Using the Dubins method and the ODE method makes it possible for the AWMG to design flyable offline trajectories accounting for the lateral dynamic of the fixed-wing UAS. The second original contribution of this research is the development and demonstration of the Double Dispersion reduction RRT (DDRRT), an algorithm which employs two new developed logic schemes respectively referred to as Punctual Dispersion Reduction (PDR), and Spatial Dispersion Reduction exploration (SDR). The DDRRT is employed during the real-time in-flight phase where it initially assumes a perfect terrain and no unpredictable threat, consequently following a 100% adaptive goal biasing toward the next waypoint in its list. When a threat such as an unpredicted obstacle is detected, the (PDR) acknowledges the fact that the DDRRT tree branches have met an obstacle and the its goal-biasing toward the next waypoint is decreased. If the PDR keeps decreasing, the DDRRT develops awareness of its surrounding obstacles by relaxing its PDR and switching to SDR which has the effect of increasing the dispersion of its branches, but keeping their extension bounded by the cell containing the last good position of the UAS, Csafe. If a number of branches reach a limit proportional to the Csafe and its relative area, then the STA network is queried for alternative rerouting. The two phases provide real-time reactive mid - air threat avoidance scenarios with the ability for a UAS to develop local and realistic threat awareness before considering intelligent rerouting. Either the local exploration of the DDRRT is successful before reaching a maximum number of points, or the STA Network is required to find another route

Parametrized maneuvers for autonomous vehicles

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2004.Includes bibliographical references (p. 197-209).This thesis presents a method for creating continuously parametrized maneuver classes for autonomous vehicles. These classes provide useful tools for motion planners, bundling sets of related vehicle motions based on a low-dimensional parameter vector that describes the fundamental high-level variations within the trajectory set. The method follows from a relaxation of nonlinear parametric programming necessary conditions that discards the objective function, leaving a simple coordinatized feasible space including all dynamically admissible vehicle motions. A trajectory interpolation algorithm uses projection and integration methods to create the classes, starting from arbitrary user-provided maneuver examples, including those obtained from standard nonlinear optimization or motion capture of human-piloted vehicle flights. The interpolation process, which can be employed for real-time trajectory generation, efficiently creates entire maneuver sets satisfying nonlinear equations of motion and nonlinear state and control constraints without resorting to iterative optimization. Experimental application to a three degree-of-freedom rotorcraft testbed and the design of a stable feedforward control framework demonstrates the essential features of the method on actual hardware. Integration of the trajectory classes into an existing hybrid system motion planning framework illustrates the use of parametrized maneuvers for solving vehicle guidance problems. The earlier relaxation of strict optimality conditions makes possible the imposition of affine state transformation constraints, allowing maneuver sets to fit easily into a mixed integer-linear programming path planner.(cont.) The combined scheme generalizes previous planning techniques based on fixed, invariant representations of vehicle equilibrium states and maneuver elements. The method therefore increases the richness of available guidance solutions while maintaining problem tractability associated with hierarchical system models. Application of the framework to one and two-dimensional path planning examples demonstrates its usefulness in practical autonomous vehicle guidance scenarios.by Christopher Walden Dever.Ph.D

Fuel-efficient trajectories traffic synchronization

Continuous descent operations (CDOs) with required times of arrival (RTA) have been identified as a potential solution for reducing the environmental footprint of aviation in the terminal maneuvering area without compromising capacity. This paper assesses the feasibility of replacing current air traffic control sequencing and merging techniques, mainly based on path stretching and air holding, by a control based on RTA over metering fixes on known and fixed arrival routes. Because the remaining distance to the runway threshold is always known by the aircraft crew, this would allow engine-idle CDOs that do not require speed-brake usage and where only elevator control is used to meet the RTA. The assessment has been performed for Barcelona-El Prat Airport (Spain) using historical traffic demand data. The earliest and latest trajectories at a metering fix for each inbound aircraft were computed assuming engine-idle CDOs. Given the attainable RTA window for each aircraft, the aircraft sequencing problem was solved. The results show that assigning RTA allows optimizing the landing sequence when air traffic is low. For scenarios with high-traffic loads and late RTA assignments, path stretching still was found to be necessary. The minimum distance from the runway where inbound aircraft should receive the RTA to fully remove any radar vectoring was also analyzed. It was demonstrated that the assignment of RTA well before starting the descent would favor to enable full CDOs.Peer ReviewedPostprint (published version

Trajectory optimization with detection avoidance for visually identifying an aircraft

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2005.Includes bibliographical references (p. 115-118).Unmanned aerial vehicles (UAVs) play an essential role for the US Armed Forces by performing missions deemed as "dull, dirty and dangerous" for a pilot. As the capability of UAVs expand. they will perform a broader range of missions such as air-to-air combat. The focus of this thesis is forming trajectories for the closing phase of an air-to-air combat scenario. A UAV should close with the suspected aircraft in a manner that allows a ground operator to visually identify the suspected aircraft while avoiding visual/electronic detection from the other pilot. This thesis applies and compares three methods for producing trajectories which enable a visual identification. The first approach is formulated as a mixed integer linear programming problem which can be solved in real time. However, there are limitations to the accuracy of a radar detection model formed with only linear equations, which might justify using a nonlinear programming formulation. With this approach the interceptor's radar cross section and range between the suspected aircraft and interceptor can be incorporated into the problem formulation. The main limitation of this method is that the optimization software might not be able to reach online an optimal or even feasible solution. The third applied method is trajectory interpolation. In this approach, trajectories with specified boundary values and dynamics are formed offline; online, the method interpolates between the given trajectories to obtain similar maneuvers with different initial conditions and end- states. With this method, because the number of calculations required to produce a feasible trajectory is known, the amount of time to calculate a trajectory can be estimated.by Leonard N. Wholey.S.M

A Modular Approach to Large-scale Design Optimization of Aerospace Systems.

Gradient-based optimization and the adjoint method form a synergistic combination that enables the efficient solution of large-scale optimization problems. Though the gradient-based approach struggles with non-smooth or multi-modal problems, the capability to efficiently optimize up to tens of thousands of design variables provides a valuable design tool for exploring complex tradeoffs and finding unintuitive designs. However, the widespread adoption of gradient-based optimization is limited by the implementation challenges for computing derivatives efficiently and accurately, particularly in multidisciplinary and shape design problems. This thesis addresses these difficulties in two ways. First, to deal with the heterogeneity and integration challenges of multidisciplinary problems, this thesis presents a computational modeling framework that solves multidisciplinary systems and computes their derivatives in a semi-automated fashion. This framework is built upon a new mathematical formulation developed in this thesis that expresses any computational model as a system of algebraic equations and unifies all methods for computing derivatives using a single equation. The framework is applied to two engineering problems: the optimization of a nanosatellite with 7 disciplines and over 25,000 design variables; and simultaneous allocation and mission optimization for commercial aircraft involving 330 design variables, 12 of which are integer variables handled using the branch-and-bound method. In both cases, the framework makes large-scale optimization possible by reducing the implementation effort and code complexity. The second half of this thesis presents a differentiable parametrization of aircraft geometries and structures for high-fidelity shape optimization. Existing geometry parametrizations are not differentiable, or they are limited in the types of shape changes they allow. This is addressed by a novel parametrization that smoothly interpolates aircraft components, providing differentiability. An unstructured quadrilateral mesh generation algorithm is also developed to automate the creation of detailed meshes for aircraft structures, and a mesh convergence study is performed to verify that the quality of the mesh is maintained as it is refined. As a demonstration, high-fidelity aerostructural analysis is performed for two unconventional configurations with detailed structures included, and aerodynamic shape optimization is applied to the truss-braced wing, which finds and eliminates a shock in the region bounded by the struts and the wing.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111567/1/hwangjt_1.pd

Airborne Wind Energy - To fly or not to fly?

This thesis investigates crosswind Airborne Wind Energy Systems (AWESs) in terms of power production and potential role in future electricity generation systems. The perspective ranges from the small scale, modelling AWE as a single system, to the large, implementing AWESs in regional electricity systems. \ua0To estimate the AWES power production, the thesis provides a dynamic system model that serves as the basis for all the work. The model describes the flight dynamics of a rigid wing that is exposed to tether and aerodynamic forces controlled by flight control surfaces. Index-3 Differential Algebraic Equations (DAEs) based on Lagrangian mechanics describe the dynamics. \ua0This model is validated by fitting it to real flight measurements obtained with a pumping-mode AWES, the prototype AP2 by Ampyx Power. The optimal power production of an AWES depends on complex trade-offs; this motivates formulating the power production computation as an Optimal Control Problem (OCP). The thesis presents the numerical methods needed to discretize the OCP and solve the resulting Nonlinear Program (NLP). \ua0Large-scale implementation of AWESs raises challenges related to variability in power production on the time scale of minutes to weeks. For the former, we investigate the periodic fluctuations in the power output of a single AWES. These fluctuations can be severe when operating a wind farm and have to be considered and reduced for an acceptable grid integration. We analyse the option of controlling the flight trajectories of the individual systems in a farm so that the total power output of the farm is smoothed. This controlled operation fixes the system\u27s trajectory, reducing the ability to maximize the power output of individual AWESs to local wind conditions. We quantify the lost power production if the systems are controlled such that the total farm power output is smoothed. Results show that the power difference between the optimal and fixed trajectory does not exceed 4% for the systems modelled in the study.\ua0The variations in AWESs power production on the timescale of hours to weeks are particularly relevant to the interaction between AWE and other power generation technologies. Investigating AWESs in an electricity system context requires power-generation profiles with high spatio-temporal resolution, which means solving a large number of OCPs. In order to efficiently solve these numerous OCPs in a sequential manner, this thesis presents a homotopy-path-following method combined with modifications to the NLP solver. The implementation shows a 20-fold reduction in computation time compared to the original method for solving the NLP for AWES power optimization.\ua0 For large wind-data sets, a random forest regression model is trained to a high accuracy, providing an even faster computation.The annual generation profiles for the modelled systems are computed using ERA5 wind data for several locations and compared to the generation profile for a traditional wind turbine. The results show that the profiles are strongly correlated in time, which is a sobering fact in terms of technology competition. However, the correlation is weaker in locations with high wind shear.\ua0 \ua0The potential role of AWESs in the future electricity system is further investigated. This thesis implements annual AWE-farm generation profiles into a cost-optimizing electricity system model. We find that AWE is most valuable to the electricity system if installed at sites with low wind speed within a region. At greater shares of the electricity system, even if AWESs could demonstrate lower costs compared to wind turbines, AWE would merely substitute for them instead of increasing the total share of wind energy in the system. This implies that the economic value of an AWES is limited by its cost relative to traditional wind turbines

Advanced control for miniature helicopters : modelling, design and flight test

Unmanned aerial vehicles (UAV) have been receiving unprecedented development during the past two decades. Among different types of UAVs, unmanned helicopters exhibit promising features gained from vertical-takeoff-and-landing, which make them as a versatile platform for both military and civil applications. The work reported in this thesis aims to apply advanced control techniques, in particular model predictive control (MPC), to an autonomous helicopter in order to enhance its performance and capability. First, a rapid prototyping testbed is developed to enable indoor flight testing for miniature helicopters. This testbed is able to simultaneously observe the flight state, carry out complicated algorithms and realtime control of helicopters all in a Matlab/Simulink environment, which provides a streamline process from algorithm development, simulation to flight tests. Next, the modelling and system identification for small-scale helicopters are studied. A parametric model is developed and the unknown parameters are estimated through the designed identification process. After a mathematical model of the selected helicopter is available, three MPC based control algorithms are developed focusing on different aspects in the operation of autonomous helicopters. The first algorithm is a nonlinear MPC framework. A piecewise constant scheme is used in the MPC formulation to reduce the intensive computation load. A two-level framework is suggested where the nonlinear MPC is combined with a low-level linear controller to allow its application on the systems with fast dynamics. The second algorithm solves the local path planning and the successive tracking control by using nonlinear and linear MPC, respectively. The kinematics and obstacle information are incorporated in the path planning, and the linear dynamics are used to design a flight controller. A guidance compensator dynamically links the path planner and flight controller. The third algorithm focuses on the further reduction of computational load in a MPC scheme and the trajectory tracking control in the presence of uncertainties and disturbances. An explicit nonlinear MPC is developed for helicopters to avoid online optimisation, which is then integrated with a nonlinear disturbance observer to significantly improve its robustness and disturbance attenuation. All these algorithms have been verified by flight tests for autonomous helicopters in the dedicated rapid prototyping testbed developed in this thesis.EThOS - Electronic Theses Online ServiceGBUnited Kingdo