Unmanned vehicles formation control in 3D space and cooperative search

The first problem considered in this dissertation is the decentralized non-planar formation control of multiple unmanned vehicles using graph rigidity. The three-dimensional formation control problem consists of n vehicles operating in a plane Q and r vehicles that operate in an upper layer outside of the plane Q. This can be referred to as a layered formation control where the objective is for all vehicles to cooperatively acquire a predefined formation shape using a decentralized control law. The proposed control strategy is based on regulating the inter-vehicle distances and uses backstepping and Lyapunov approaches. Three different models, with increasing level of complexity are considered for the multi-vehicle system: the single integrator vehicle model, the double integrator vehicle model, and a model that represents the dynamics of a class of robotics vehicles including wheeled mobile robots, underwater vehicles with constant depth, aircraft with constant altitude, and marine vessels. A rigorous stability analysis is presented that guarantees convergence of the inter-vehicle distances to desired values. Additionally, a new Neural Network (NN)-based control algorithm that uses graph rigidity and relative positions of the vehicles is proposed to solve the formation control problem of unmanned vehicles in 3D space. The control law for each vehicle consists of a nonlinear component that is dependent on the closed-loop error dynamics plus a NN component that is linear in the output weights (a one-tunable layer NN is used). A Lyapunov analysis shows that the proposed distance-based control strategy achieves the uniformly ultimately bounded stability of the desired infinitesimally and minimally rigid formation and that NN weights remain bounded. Simulation results are included to demonstrate the performance of the proposed method. The second problem addressed in this dissertation is the cooperative unmanned vehicles search. In search and surveillance operations, deploying a team of unmanned vehicles provides a robust solution that has multiple advantages over using a single vehicle in efficiency and minimizing exploration time. The cooperative search problem addresses the challenge of identifying target(s) in a given environment when using a team of unmarried vehicles by proposing a novel method of mapping and movement of vehicle teams in a cooperative manner. The approach consists of two parts. First, the region is partitioned into a hexagonal beehive structure in order to provide equidistant movements in every direction and to allow for more natural and flexible environment mapping. Additionally, in search environments that are partitioned into hexagons, the vehicles have an efficient travel path while performing searches due to this partitioning approach. Second, a team of unmanned vehicles that move in a cooperative manner and utilize the Tabu Random algorithm is used to search for target(s). Due to the ever-increasing use of robotics and unmanned systems, the field of cooperative multi-vehicle search has developed many applications recently that would benefit from the use of the approach presented in this dissertation, including: search and rescue operations, surveillance, data collection, and border patrol. Simulation results are presented that show the performance of the Tabu Random search algorithm method in combination with hexagonal partitioning

Lorenz-Mie theory for 2D scattering and resonance calculations

This PhD tutorial is concerned with a description of the two-dimensional generalized Lorenz-Mie theory (2D-GLMT), a well-established numerical method used to compute the interaction of light with arrays of cylindrical scatterers. This theory is based on the method of separation of variables and the application of an addition theorem for cylindrical functions. The purpose of this tutorial is to assemble the practical tools necessary to implement the 2D-GLMT method for the computation of scattering by passive scatterers or of resonances in optically active media. The first part contains a derivation of the vector and scalar Helmholtz equations for 2D geometries, starting from Maxwell's equations. Optically active media are included in 2D-GLMT using a recent stationary formulation of the Maxwell-Bloch equations called steady-state ab initio laser theory (SALT), which introduces new classes of solutions useful for resonance computations. Following these preliminaries, a detailed description of 2D-GLMT is presented. The emphasis is placed on the derivation of beam-shape coefficients for scattering computations, as well as the computation of resonant modes using a combination of 2D-GLMT and SALT. The final section contains several numerical examples illustrating the full potential of 2D-GLMT for scattering and resonance computations. These examples, drawn from the literature, include the design of integrated polarization filters and the computation of optical modes of photonic crystal cavities and random lasers.Comment: This is an author-created, un-copyedited version of an article published in Journal of Optics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

Mathematical Modelling of Mosquito Dispersal in a Heterogeneous Environment.

Mosquito dispersal is a key behavioural factor that affects the persistence and resurgence of several vector-borne diseases. Spatial heterogeneity of mosquito resources, such as hosts and breeding sites, affects mosquito dispersal behaviour and consequently affects mosquito population structures, human exposure to vectors, and the ability to control disease transmission. In this paper, we develop and simulate a discrete-space continuous-time mathematical model to investigate the impact of dispersal and heterogeneous distribution of resources on the distribution and dynamics of mosquito populations. We build an ordinary differential equation model of the mosquito life cycle and replicate it across a hexagonal grid (multi-patch system) that represents two-dimensional space. We use the model to estimate mosquito dispersal distances and to evaluate the effect of spatial repellents as a vector control strategy. We find evidence of association between heterogeneity, dispersal, spatial distribution of resources, and mosquito population dynamics. Random distribution of repellents reduces the distance moved by mosquitoes, offering a promising strategy for disease control

A two-dimensional hexagonal network model of alveolar mechanics

Pulmonary micromechanics (at the scale of alveoli) involves a delicate balance among tissue material properties, geometry, surface tension, pressure and stress distribution. To date, there is not a consensus among alveolar mechanics researchers about how these factors interact, in part because alveoli are so difficult to image and study in vivo. Here, we propose a basic mathematical model of a two-dimensional hexagonal network of mechanically coupled alveoli. We investigate equilibrium configurations of both dry and wet, internally pressurized elastic networks. Specifically, we compute pressure-area curves to quantify the differences among networks with different spring constants, internal pressures, network size and surface tensions. We conclude that a two-dimensional hexagonal network in force equilibrium is an appropriate first step in modeling the mechanics of the dynamic lung

Computer Generation of Integral Images using Interpolative Shading Techniques

Research to produce artificial 3D images that duplicates the human stereovision has been ongoing for hundreds of years. What has taken millions of years to evolve in humans is proving elusive even for present day technological advancements. The difficulties are compounded when real-time generation is contemplated. The problem is one of depth. When perceiving the world around us it has been shown that the sense of depth is the result of many different factors. These can be described as monocular and binocular. Monocular depth cues include overlapping or occlusion, shading and shadows, texture etc. Another monocular cue is accommodation (and binocular to some extent) where the focal length of the crystalline lens is adjusted to view an image. The important binocular cues are convergence and parallax. Convergence allows the observer to judge distance by the difference in angle between the viewing axes of left and right eyes when both are focussing on a point. Parallax relates to the fact that each eye sees a slightly shifted view of the image. If a system can be produced that requires the observer to use all of these cues, as when viewing the real world, then the transition to and from viewing a 3D display will be seamless. However, for many 3D imaging techniques, which current work is primarily directed towards, this is not the case and raises a serious issue of viewer comfort. Researchers worldwide, in university and industry, are pursuing their approaches in the development of 3D systems, and physiological disturbances that can cause nausea in some observers will not be acceptable. The ideal 3D system would require, as minimum, accurate depth reproduction, multiviewer capability, and all-round seamless viewing. The necessity not to wear stereoscopic or polarising glasses would be ideal and lack of viewer fatigue essential. Finally, for whatever the use of the system, be it CAD, medical, scientific visualisation, remote inspection etc on the one hand, or consumer markets such as 3D video games and 3DTV on the other, the system has to be relatively inexpensive. Integral photography is a ‘real camera’ system that attempts to comply with this ideal; it was invented in 1908 but due to technological reasons was not capable of being a useful autostereoscopic system. However, more recently, along with advances in technology, it is becoming a more attractive proposition for those interested in developing a suitable system for 3DTV. The fast computer generation of integral images is the subject of this thesis; the adjective ‘fast’ being used to distinguish it from the much slower technique of ray tracing integral images. These two techniques are the standard in monoscopic computer graphics whereby ray tracing generates photo-realistic images and the fast forward geometric approach that uses interpolative shading techniques is the method used for real-time generation. Before this present work began it was not known if it was possible to create volumetric integral images using a similar fast approach as that employed by standard computer graphics, but it soon became apparent that it would be successful and hence a valuable contribution in this area. Presented herein is a full description of the development of two derived methods for producing rendered integral image animations using interpolative shading. The main body of the work is the development of code to put these methods into practice along with many observations and discoveries that the author came across during this task.The Defence and Research Agency (DERA), a contract (LAIRD) under the European Link/EPSRC photonics initiative, and DTI/EPSRC sponsorship within the PROMETHEUS project