Geometric Control Theory and its Application to Underwater Vehicles

This dissertation is based on theoretical study and experiments which extend geometric control theory to practical applications within the field of ocean engineering. We present a method for path planning and control design for underwater vehicles by use of the architecture of differential geometry. In addition to the theoretical design of the trajectory and control strategy, we demonstrate the effectiveness of the method via the implementation onto a test-bed autonomous underwater vehicle. Bridging the gap between theory and application is the ultimate goal of control theory. Major developments have occurred recently in the field of geometric control which narrow this gap and which promote research linking theory and application. In particular, Riemannian and affine differential geometry have proven to be a very effective approach to the modeling of mechanical systems such as underwater vehicles. In this framework, the application of a kinematic reduction allows us to calculate control strategies for fully and under-actuated vehicles via kinematic decoupled motion planning. However, this method has not yet been extended to account for external forces such as dissipative viscous drag and buoyancy induced potentials acting on a submerged vehicle. To fully bridge the gap between theory and application, this dissertation addresses the extension of this geometric control design method to include such forces. We incorporate the hydrodynamic drag experienced by the vehicle by modifying the Levi-Civita affine connection and demonstrate a method for the compensation of potential forces experienced during a prescribed motion. We present the design method for multiple different missions and include experimental results which validate both the extension of the theory and the ability to implement control strategies designed through the use of geometric techniques. By use of the extension presented in this dissertation, the underwater vehicle application successfully demonstrates the applicability of geometric methods to design implementable motion planning solutions for complex mechanical systems having equal or fewer input forces than available degrees of freedom. Thus, we provide another tool with which to further increase the autonomy of underwater vehicles.

Controlling a submerged rigid body : a geometric analysis

In this paper we analyze the equations of motion of a submerged rigid body. Our motivation is based on recent developments done in trajectory design for this problem. Our goal is to relate some properties of singular extremals to the existence of decoupling vector fields. The ideas displayed in this paper can be viewed as a starting point to a geometric formulation of the trajectory design problem for mechanical systems with potential and external forces.

Geometric and force relationships for the development of a scaled model hydraulic excavator

Hydraulic excavators in the mining industry are widely used owing to the large payload capabilities these machines can achieve. However, there are very few optimisation studies for producing efficient hydraulic excavator backets. An efficient bucket can avoid unnecessary weight; greatly influence the payload and optimise the efficiency of hydraulic mining excavators. This paper presents a framework for the development of a scaled hydraulic excavator by examining the geometry and force relationships. A small hydraulic excavator was purchased and fitted with a broom scaled to a factor. Geometric and force relationships of the model were derived to assist computer instrumentation to retrieve necessary variable input for bucket design.

Can the contra-lateral limb be used as a control with respect to analyses of bone remodelling?

Bone loss may result from remodelling initiated by implant stress protection. Quantifying remodelling requires bone density distributions which can be obtained from computed tomography scans. Pre-operative scans of large animals however are rarely possible. This study aimed to determine if the contra-lateral bone is a suitable control for the purpose of quantifying bone remodelling. CT scans of 8 pairs of ovine tibia were used to determine the likeness of left and right bones. The deviation between the outer surfaces of the bone pairs was used to quantify geometric similarity. The density differences were determined by dividing the bones into discrete volumes along the shaft of the tibia. Density differences were also determined for fractured and contra-lateral bone pairs to determine the magnitude of implant related remodelling. Left and right ovine tibiae were found to have a high degree of similarity with differences of less than 1.0 mm in the outer surface deviation and density difference of less than 5% in over 90% of the shaft region. The density differences (10–40%) as a result of implant related bone remodelling were greater than left-right differences. Therefore, for the purpose of quantifying bone remodelling in sheep, the contra-lateral tibia may be considered an alternative to a pre-operative control.

A Stochastic View of Optimal Regret through Minimax Duality

We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary's action sequence, of the difference between a sum of minimal expected losses and the minimal empirical loss. We show that the optimal regret has a natural geometric interpretation, since it can be viewed as the gap in Jensen's inequality for a concave functional--the minimizer over the player's actions of expected loss--defined on a set of probability distributions. We use this expression to obtain upper and lower bounds on the regret of an optimal strategy for a variety of online learning problems. Our method provides upper bounds without the need to construct a learning algorithm; the lower bounds provide explicit optimal strategies for the adversary. Peter L. Bartlett, Alexander Rakhlin

Evaluation of texture and geometry for dimensional facial expression recognition

Facial expression recognition (FER) algorithms mainly focus on classification into a small discrete set of emotions or representation of emotions using facial action units (AUs). Dimensional representation of emotions as continuous values in an arousal-valence space is relatively less investigated. It is not fully known whether fusion of geometric and texture features will result in better dimensional representation of spontaneous emotions. Moreover, the performance of many previously proposed approaches to dimensional representation has not been evaluated thoroughly on publicly available databases. To address these limitations, this paper presents an evaluation framework for dimensional representation of spontaneous facial expressions using texture and geometric features. SIFT, Gabor and LBP features are extracted around facial fiducial points and fused with FAP distance features. The CFS algorithm is adopted for discriminative texture feature selection. Experimental results evaluated on the publicly accessible NVIE database demonstrate that fusion of texture and geometry does not lead to a much better performance than using texture alone, but does result in a significant performance improvement over geometry alone. LBP features perform the best when fused with geometric features. Distributions of arousal and valence for different emotions obtained via the feature extraction process are compared with those obtained from subjective ground truth values assigned by viewers. Predicted valence is found to have a more similar distribution to ground truth than arousal in terms of covariance or Bhattacharya distance, but it shows a greater distance between the means.

Inexact uniformization method for computing transient distributions of Markov chains

The uniformization method (also known as randomization) is a numerically stable algorithm for computing transient distributions of a continuous time Markov chain. When the solution is needed after a long run or when the convergence is slow, the uniformization method involves a large number of matrix-vector products. Despite this, the method remains very popular due to its ease of implementation and its reliability in many practical circumstances. Because calculating the matrix-vector product is the most time-consuming part of the method, overall efficiency in solving large-scale problems can be significantly enhanced if the matrix-vector product is made more economical. In this paper, we incorporate a new relaxation strategy into the uniformization method to compute the matrix-vector products only approximately. We analyze the error introduced by these inexact matrix-vector products and discuss strategies for refining the accuracy of the relaxation while reducing the execution cost. Numerical experiments drawn from computer systems and biological systems are given to show that significant computational savings are achieved in practical applications.

The geometric modelling of social frames and contexts

How do humans respond to their social context? This question is becoming increasingly urgent in a society where democracy requires that the citizens of a country help to decide upon its policy directions, and yet those citizens frequently have very little knowledge of the complex issues that these policies seek to address. Frequently, we find that humans make their decisions more with reference to their social setting, than to the arguments of scientists, academics, and policy makers. It is broadly anticipated that the agent based modelling (ABM) of human behaviour will make it possible to treat such social effects, but we take the position here that a more sophisticated treatment of context will be required in many such models. While notions such as historical context (where the past history of an agent might affect its later actions) and situational context (where the agent will choose a different action in a different situation) abound in ABM scenarios, we will discuss a case of a potentially changing context, where social effects can have a strong influence upon the perceptions of a group of subjects. In particular, we shall discuss a recently reported case where a biased worm in an election debate led to significant distortions in the reports given by participants as to who won the debate (Davis et al 2011). Thus, participants in a different social context drew different conclusions about the perceived winner of the same debate, with associated significant differences among the two groups as to who they would vote for in the coming election. We extend this example to the problem of modelling the likely electoral responses of agents in the context of the climate change debate, and discuss the notion of interference between related questions that might be asked of an agent in a social simulation that was intended to simulate their likely responses. A modelling technology which could account for such strong social contextual effects would benefit regulatory bodies which need to navigate between multiple interests and concerns, and we shall present one viable avenue for constructing such a technology. A geometric approach will be presented, where the internal state of an agent is represented in a vector space, and their social context is naturally modelled as a set of basis states that are chosen with reference to the problem space.

Insect distributions and sampling protocols for stored commodities

Purpose of review: This review provides an overview on the importance of characterising and considering insect distribution infor- mation for designing stored commodity sampling protocols. Findings: Sampling protocols are influenced by a number of factors including government regulations, management practices, new technology and current perceptions of the status of insect pest damage. The spatial distribution of insects in stored commodities influ- ences the efficiency of sampling protocols; these can vary in response to season, treatment and other factors. It is important to use sam- pling designs based on robust statistics suitable for the purpose. Future research: The development of sampling protocols based on flexible, robust statistics allows for accuracy across a range of spatial distributions. Additionally, power can be added to sampling protocols through the integration of external information such as treatment history and climate. Bayesian analysis provides a coherent and well understood means to achieve this.

A mask-based approach for the geometric calibration of thermal-infrared cameras

Accurate and efficient thermal-infrared (IR) camera calibration is important for advancing computer vision research within the thermal modality. This paper presents an approach for geometrically calibrating individual and multiple cameras in both the thermal and visible modalities. The proposed technique can be used to correct for lens distortion and to simultaneously reference both visible and thermal-IR cameras to a single coordinate frame. The most popular existing approach for the geometric calibration of thermal cameras uses a printed chessboard heated by a flood lamp and is comparatively inaccurate and difficult to execute. Additionally, software toolkits provided for calibration either are unsuitable for this task or require substantial manual intervention. A new geometric mask with high thermal contrast and not requiring a flood lamp is presented as an alternative calibration pattern. Calibration points on the pattern are then accurately located using a clustering-based algorithm which utilizes the maximally stable extremal region detector. This algorithm is integrated into an automatic end-to-end system for calibrating single or multiple cameras. The evaluation shows that using the proposed mask achieves a mean reprojection error up to 78% lower than that using a heated chessboard. The effectiveness of the approach is further demonstrated by using it to calibrate two multiple-camera multiple-modality setups. Source code and binaries for the developed software are provided on the project Web site.

The development of ground impact models for the analysis of the risks associated with Unmanned Aircraft Operations over inhabited areas

With the emergence of Unmanned Aircraft Systems (UAS) there is a growing need for safety standards and regulatory frameworks to manage the risks associated with their operations. The primary driver for airworthiness regulations (i.e., those governing the design, manufacture, maintenance and operation of UAS) are the risks presented to people in the regions overflown by the aircraft. Models characterising the nature of these risks are needed to inform the development of airworthiness regulations. The output from these models should include measures of the collective, individual and societal risk. A brief review of these measures is provided. Based on the review, it was determined that the model of the operation of an UAS over inhabited areas must be capable of describing the distribution of possible impact locations, given a failure at a particular point in the flight plan. Existing models either do not take the impact distribution into consideration, or propose complex and computationally expensive methods for its calculation. A computationally efficient approach for estimating the boundary (and in turn area) of the impact distribution for fixed wing unmanned aircraft is proposed. A series of geometric templates that approximate the impact distributions are derived using an empirical analysis of the results obtained from a 6-Degree of Freedom (6DoF) simulation. The impact distributions can be aggregated to provide impact footprint distributions for a range of generic phases of flight and missions. The maximum impact footprint areas obtained from the geometric template are shown to have a relative error of typically less than 1% compared to the areas calculated using the computationally more expensive 6DoF simulation. Computation times for the geometric models are on the order of one second or less, using a standard desktop computer. Future work includes characterising the distribution of impact locations within the footprint boundaries.

Restructuring of carbonaceous particles upon exposure to organic vapours

Recent research has described the restructuring of particles upon exposure to organic vapours; however, as yet hypotheses able to explain this phenomenon are limited. In this study, a range of experiments were performed to explore different hypotheses related to carbonaceous particle restructuring upon exposure to organic and water vapours, such as: the effect of surface tension, the role of organics in flocculating primary particles, as well as the ability of vapours to “wet” the particle surface. The change in mobility diameter (dm) was investigated for a range carbonaceous particle types (diesel exhaust, petrol exhaust, cigarette smoke, candle smoke, particles generated in a heptane/toluene flame, and wood smoke particles) exposed to different organic (heptane, ethanol, and dimethyl sulfoxide/water (1:1 vol%) mixture) and water vapours. Particles were first size-selected and then bubbled through an impinger (bubbler) containing either an organic solvent or water, where particles trapped inside rising bubbles were exposed to saturated vapours of the solvent in the impinger. The size distribution of particles was simultaneously measured upstream and downstream from the impinger. A size-dependent reduction in dm was observed when bubbling diesel exhaust, particles generated in a heptane/toluene flame, and candle smoke particles through heptane, ethanol and a dimethyl sulfoxide/water (1:1 vol %) mixture. In addition, the size distributions of particles bubbled through an impinger were broader. Moreover, an increase of the geometric standard deviation (σ) of the size distributions of particles bubbled through an impinger was also found to be size-dependent. Size-dependent reduction in dm and an increase of σ indicate that particles undergo restructuring to a more compact form, which was confirmed by TEM analysis. However, bubbling of these particles through water did not result in a size-dependent reduction in dm, nor in an increase of σ. Cigarette smoke, petrol exhaust, and wood smoke particles did not result in any substantial change in dm, or σ, when bubbled through organic solvents or water. Therefore, size-dependent reduction in the dm upon bubbling through organic solvents was observed only for particles that had a fractal-like structure, whilst particles that were liquid or were assumed to be spherical did not exhibit any reduction in dm. Compaction of fractal-like particles was attributed to the ability of condensing vapours to efficiently wet the particles. Our results also show that the presence of an organic layer on the surface of fractal-like particles, or the surface tension of the condensed liquid do not influence the extent of compaction.