This thesis presents a means for representing and computing beliefs in the form of arbitrary probability density functions with a guarantee for the ongoing validity of such beliefs over indefinte time frames. The foremost aspect of this proposal is the introduction of a general, theoretical, solution to the guaranteed state estimation problem from within the recursive Bayesian estimation framework. The solution presented here determines the minimum space required, at each stage of the estimation process, to represent the belief with limited, or no, loss of information. Beyond this purely theoretical aspect, a number of numerical techniques, capable of determining the required space and performing the appropriate spatial reconfiguration, whilst also computing and representing the belief functions, are developed. This includes a new, hybrid particle-element approach to recursive Bayesian estimation. The advantage of spatial reconfiguration as presented here is that it ensures that the belief functions consider all plausible states of the target system, without altering the recursive Bayesian estimation equations used to form those beliefs. Furthermore, spatial reconfiguration as proposed in this dissertation enhances the estimation process since it allows computational resources to be concentrated on only those states considered plausible. Autonomous maritime search and rescue is used as a focus application throughout this dissertation since the searching-and-tracking requirements of the problem involve uncertainty, the use of arbitrary belief functions and dynamic target systems. Nevertheless, the theoretical development in this dissertation has been kept general and independent of an application, and as such the theory and techniques presented here may be applied to any problem involving dynamic Bayesian beliefs. A number of numerical experiments and simulations show the efficacy of the proposed spatially reconfigurable representations, not only in ensuring the validity of the belief functions over indefinite time frames, but also in reducing computation time and improving the accuracy of function approximation. Improvements of an order of magnitude were achieved when compared with traditional, spatially static representations.

This thesis presents a means for representing and computing beliefs in the form of arbitrary probability density functions with a guarantee for the ongoing validity of such beliefs over indefinte time frames. The foremost aspect of this proposal is the introduction of a general, theoretical, solution to the guaranteed state estimation problem from within the recursive Bayesian estimation framework. The solution presented here determines the minimum space required, at each stage of the estimation process, to represent the belief with limited, or no, loss of information. Beyond this purely theoretical aspect, a number of numerical techniques, capable of determining the required space and performing the appropriate spatial reconfiguration, whilst also computing and representing the belief functions, are developed. This includes a new, hybrid particle-element approach to recursive Bayesian estimation. The advantage of spatial reconfiguration as presented here is that it ensures that the belief functions consider all plausible states of the target system, without altering the recursive Bayesian estimation equations used to form those beliefs. Furthermore, spatial reconfiguration as proposed in this dissertation enhances the estimation process since it allows computational resources to be concentrated on only those states considered plausible. Autonomous maritime search and rescue is used as a focus application throughout this dissertation since the searching-and-tracking requirements of the problem involve uncertainty, the use of arbitrary belief functions and dynamic target systems. Nevertheless, the theoretical development in this dissertation has been kept general and independent of an application, and as such the theory and techniques presented here may be applied to any problem involving dynamic Bayesian beliefs. A number of numerical experiments and simulations show the efficacy of the proposed spatially reconfigurable representations, not only in ensuring the validity of the belief functions over indefinite time frames, but also in reducing computation time and improving the accuracy of function approximation. Improvements of an order of magnitude were achieved when compared with traditional, spatially static representations.

Trotz der Entwicklungen der letzten Jahre kommt es in der Robotik immer noch vor, dass mobile Roboter scheinbar sinnlose Handlungen ausführen. Der Grund für dieses Verhalten ist oftmals, dass sich das interne Weltbild des Roboters stark von der tatsächlichen Situation, in der sich der Roboter befindet, unterscheidet. Die darauf basierende Robotersteuerung wählt infolge dieser Diskrepanz scheinbar sinnlose Handlungen aus. Eine wichtige Ursache von Lokalisierungsfehlern stellen Kollisionen des Roboters mit anderen Robotern oder seiner Umwelt dar. Mit Hilfe eines Hindernismodells wird der Roboter in die Lage versetzt, Hindernisse zu erkennen, sich ihre Position zu merken und Kollisionen zu vermeiden. Ferner wird in dieser Arbeit eine Erweiterung der Bewegungsmodellierung beschrieben, die die Bewegung in Mobilitätszustände untergliedert, die jeweils ein eigenes Bewegungsmodell besitzen und die mit Hilfe von Propriozeption unterschieden werden können. Mit Hilfe der Servo-Motoren des Roboters lässt sich eine Art Propriozeption erzielen: der momentan gewünschte, angesteuerte Gelenkwinkel wird mit dem tatsächlich erreichten, im Servo-Motor gemessenen Winkel verglichen. Dieser "Sinn" erlaubt eine bessere Beschreibung der Roboterbewegung. Verbesserung des Sensormodells wird das bisher wenig untersuchte Konzept der Negativinformation, d.h. das Ausbleiben einer erwarteten Messung, genutzt. Bestehende Lokalisierungsansätze nutzen diese Information nicht, da es viele Gründe für ein Ausbleiben einer erwarteten Messung gibt. Eine genaue Modellierung des Sensors ermöglicht es jedoch, Negativinformation nutzbar zu machen. Eine Weltmodellierung, die Negativinformation verarbeiten kann, ermöglicht eine Lokalisierung des Roboters in Situationen, in denen einzig auf Landmarken basierende Ansätze scheitern. / Despite the dramatic advancements in the field of robotics, robots still tend to exhibit erratic behavior when facing unexpected situations, causing them, for example, to run into walls. This is mainly the result of the robot''s internal world model no longer being an accurate description of the environment and the robot''s localization within the environment. The key challenge explored in this dissertation is the creation of an internal world model for mobile robots that is more robust and accurate in situations where existing approaches exhibit a tendency to fail. First, means to avoid a major source of localization error - collisions - are investigated. Efficient collision avoidance is achieved by creating a model of free space in the direct vicinity of the robot. The model is based on camera images and serves as a short term memory, enabling the robot to avoid obstacles that are out of sight. It allows the robot to efficiently circumnavigate obstacles. The motion model of the robot is enhanced by integrating proprioceptive information. Since the robot lacks sensors dedicated to proprioception, information about the current state and configuration of the robot''s body is generated by comparing control commands and actual motion of individual joints. This enables the robot to detect collisions with other robots or obstacles and is used as additional information for modeling locomotion. In the context of sensing, the notion of negative information is introduced. Negative information marks the ascertained absence of an expected observation in feature-based localization. This information is not used in previous work on localization because of the several reasons for a sensor to miss a feature, even if the object lies within its sensing range. This information can, however, be put to good use by carefully modeling the sensor. Integrating negative information allows the robot to localize in situations where it cannot do so based on landmark observation alone.

This thesis presents a technique used to stochastically estimate the location of hidden discontinuities in carbon fiber composite materials. Composites pose a challenge to signal processing because speckle noise, as a result of reflections from impregnated laminas, masks useful information and impedes detection of hidden discontinuities. Although digital signal processing techniques have been exploited to lessen speckle noise and help to localize discontinuities, uncertainty in ultrasonic wave propagation and broadband frequency based inspections of composites still make it a difficult task. The technique proposed in this thesis estimates the location of hidden discontinuities stochastically in one- and two-dimensions based on statistical data of A-Scans and C-Scans. Multiple experiments have been performed on carbon fiber reinforced plastics including artificial delaminations and porosity at different depths in the thickness of material. A probabilistic approach, which precisely localizes discontinuities in high and low amplitude signals, has been used to present this method. Compared to conventional techniques the proposed technique offers a more reliable package, with the ability to detect discontinuities in signals with lower intensities by utilizing the repetitive amplitudes in multiple sensor observations obtained from one-dimensional A-Scans or two-dimensional C-Scan data sets. The thesis presents the methodology encompassing the proposed technique and the implementation of a system to process real ultrasonic signals and images for effective discontinuity detection and localization.

[pt] Robôs móveis têm uma grande gama de aplicações, incluindo veículos autônomos, robôs industriais e veículos aéreos não tripulados. Navegação móvel autônoma é um assunto desafiador devido à alta incerteza e nãolinearidade inerente a ambientes não estruturados, locomoção e medições de sensores. Para executar navegação autônoma, um robô precisa de um mapa do ambiente e de uma estimativa de sua própria localização e orientação em relação ao sistema de referência global. No entando, geralmente o robô não possui informações prévias sobre o ambiente e deve criar o mapa usando informações de sensores e se localizar ao mesmo tempo, um problema chamado Mapeamento e Localização Simultâneos (SLAM). As formulações de SLAM usam algoritmos probabilísticos para lidar com as incertezas do problema, e a abordagem baseada em grafos é uma das soluções estado-da-arte para SLAM. Por muitos anos os sensores LRF (laser range finders) eram as escolhas mais populares de sensores para SLAM. No entanto, sensores RGB-D são uma alternativa interessante, devido ao baixo custo. Este trabalho apresenta uma implementação de RGB-D SLAM com uma abordagem baseada em grafos. A metodologia proposta usa o Sistema Operacional de Robôs (ROS) como middleware do sistema. A implementação é testada num robô de baixo custo e com um conjunto de dados reais obtidos na literatura. Também é apresentada a implementação de uma ferramenta de otimização de grafos para MATLAB. / [en] Mobile robots have a wide range of applications, including autonomous vehicles, industrial robots and unmanned aerial vehicles. Autonomous mobile navigation is a challenging subject due to the high uncertainty and nonlinearity inherent to unstructured environments, robot motion and sensor measurements. To perform autonomous navigation, a robot need a map of the environment and an estimation of its own pose with respect to the global coordinate system. However, usually the robot has no prior knowledge about the environment, and has to create a map using sensor information and localize itself at the same time, a problem called Simultaneous Localization and Mapping (SLAM). The SLAM formulations use probabilistic algorithms to handle the uncertainties of the problem, and the graph-based approach is one of the state-of-the-art solutions for SLAM. For many years, the LRF (laser range finders) were the most popular sensor choice for SLAM. However, RGB-D sensors are an interesting alternative, due to their low cost. This work presents an RGB-D SLAM implementation with a graph-based probabilistic approach. The proposed methodology uses the Robot Operating System (ROS) as middleware. The implementation is tested in a low cost robot and with real-world datasets from literature. Also, it is presented the implementation of a pose-graph optimization tool for MATLAB.