A first extension of geometric control theory to underwater vehicles

This paper serves as a first study on the implementation of control strategies developed using a kinematic reduction onto test bed autonomous underwater vehicles (AUVs). The equations of motion are presented in the framework of differential geometry, including external dissipative forces, as a forced affine connection control system. We show that the hydrodynamic drag forces can be included in the affine connection, resulting in an affine connection control system. The definitions of kinematic reduction and decoupling vector field are thus extended from the ideal fluid scenario. Control strategies are computed using this new extension and are reformulated for implementation onto a test-bed AUV. We compare these geometrically computed controls to time and energy optimal controls for the same trajectory which are computed using a previously developed algorithm. Through this comparison we are able to validate our theoretical results based on the experiments conducted using the time and energy efficient strategies.

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.

Quantifying axial deformation of columns using vibration characteristics

Column elements at a certain level in building are subjected to loads from different tributary areas. Consequently, differential axial deformation among these elements occurs. Adverse effects of differential axial deformation increase with building height and geometric complexity. Vibrating wire, electronic strain and external mechanical strain gauges are used to measure the axial deformations to take adequate provisions to mitigate the adverse effects. These gauges require deploying in or on the elements during their construction in order to acquire necessary measurements continuously. The use of these gauges is therefore inconvenient and uneconomical. This highlights the need for a method to quantify the axial deformation using ambient measurements. This paper proposes a comprehensive vibration based method. The unique capabilities of the proposed method present through an illustrative example.

Quantifying axial deformations of core shear walls using modal parameters

Differential axial deformation between column elements and shear wall elements of cores increase with building height and geometric complexity. Adverse effects due to the differential axial deformation reduce building performance and life time serviceability. Quantifying axial deformations using ambient measurements from vibrating wire, external mechanical and electronic strain gauges in order to acquire adequate provisions to mitigate the adverse effects is well established method. However, these gauges require installing in or on elements to acquire continuous measurements and hence use of these gauges is uneconomical and inconvenient. This motivates to develop a method to quantify the axial deformations. This paper proposes an innovative method based on modal parameters to quantify axial deformations of shear wall elements in cores of buildings. Capabilities of the method are presented though an illustrative example.

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.

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.

Error and uncertainty of adult age estimation of the pubic symphysis in an Australian sub-population using computed tomography

After attending this presentation, attendees will gain awareness of: (1) the error and uncertainty associated with the application of the Suchey-Brooks (S-B) method of age estimation of the pubic symphysis to a contemporary Australian population; (2) the implications of sexual dimorphism and bilateral asymmetry of the pubic symphysis through preliminary geometric morphometric assessment; and (3) the value of three-dimensional (3D) autopsy data acquisition for creating forensic anthropological standards. This presentation will impact the forensic science community by demonstrating that, in the absence of demographically sound skeletal collections, post-mortem autopsy data provides an exciting platform for the construction of large contemporary ‘virtual osteological libraries’ for which forensic anthropological research can be conducted on Australian individuals. More specifically, this study assesses the applicability and accuracy of the S-B method to a contemporary adult population in Queensland, Australia, and using a geometric morphometric approach, provides an insight to the age-related degeneration of the pubic symphysis. Despite the prominent use of the Suchey-Brooks (1990) method of age estimation in forensic anthropological practice, it is subject to intrinsic limitations, with reports of differential inter-population error rates between geographical locations1-4. Australian forensic anthropology is constrained by a paucity of population specific standards due to a lack of repositories of documented skeletons. Consequently, in Australian casework proceedings, standards constructed from predominately American reference samples are applied to establish a biological profile. In the global era of terrorism and natural disasters, more specific population standards are required to improve the efficiency of medico-legal death investigation in Queensland. The sample comprises multi-slice computed tomography (MSCT) scans of the pubic symphysis (slice thickness: 0.5mm, overlap: 0.1mm) on 195 individuals of caucasian ethnicity aged 15-70 years. Volume rendering reconstruction of the symphyseal surface was conducted in Amira® (v.4.1) and quantitative analyses in Rapidform® XOS. The sample was divided into ten-year age sub-sets (eg. 15-24) with a final sub-set of 65-70 years. Error with respect to the method’s assigned means were analysed on the basis of bias (directionality of error), inaccuracy (magnitude of error) and percentage correct classification of left and right symphyseal surfaces. Morphometric variables including surface area, circumference, maximum height and width of the symphyseal surface and micro-architectural assessment of cortical and trabecular bone composition were quantified using novel automated engineering software capabilities. The results of this study demonstrated correct age classification utilizing the mean and standard deviations of each phase of the S-B method of 80.02% and 86.18% in Australian males and females, respectively. Application of the S-B method resulted in positive biases and mean inaccuracies of 7.24 (±6.56) years for individuals less than 55 years of age, compared to negative biases and mean inaccuracies of 5.89 (±3.90) years for individuals greater than 55 years of age. Statistically significant differences between chronological and S-B mean age were demonstrated in 83.33% and 50% of the six age subsets in males and females, respectively. Asymmetry of the pubic symphysis was a frequent phenomenon with 53.33% of the Queensland population exhibiting statistically significant (χ2 - p<0.01) differential phase classification of left and right surfaces of the same individual. Directionality was found in bilateral asymmetry, with the right symphyseal faces being slightly older on average and providing more accurate estimates using the S-B method5. Morphometric analysis verified these findings, with the left surface exhibiting significantly greater circumference and surface area than the right (p<0.05). Morphometric analysis demonstrated an increase in maximum height and width of the surface with age, with most significant changes (p<0.05) occurring between the 25-34 and 55-64 year age subsets. These differences may be attributed to hormonal components linked to menopause in females and a reduction in testosterone in males. Micro-architectural analysis demonstrated degradation of cortical composition with age, with differential bone resorption between the medial, ventral and dorsal surfaces of the pubic symphysis. This study recommends that the S-B method be applied with caution in medico-legal death investigations of unknown skeletal remains in Queensland. Age estimation will always be accompanied by error; therefore this study demonstrates the potential for quantitative morphometric modelling of age related changes of the pubic symphysis as a tool for methodological refinement, providing a rigor and robust assessment to remove the subjectivity associated with current pelvic aging methods.

Quantitative morphometric examination of the human pubic symphyseal surface of Australian individuals with age using computed tomography

Current forensic practice in age estimation relies on the application of morphological standards as a means to characterize complex threedimensional skeletal surfaces. Research in our laboratory has demonstrated that the application of the morphologically based Suchey-Brooks method to a contemporary Queensland, Australian population demonstrated significant inaccuracy in age-estimation. Consequently, this study presents preliminary results to quantify age-related skeletal changes of the pubic symphysis in Queensland individuals using novel geometric and micro-architectural protocols that have the potential of improving age estimation in the forensic context. Computed tomography scans of the right and left pubis were obtained from Caucasian individuals aged 15–70 years (n=195) from the Queensland Health Forensic and Scientific Services. Morphometric variables including surface area, circumference, maximum height and width of the symphyseal surface, and micro-architectural assessment of cortical and trabecular bone structure were conducted in Rapidform XOS and Osteomeasure, respectively. Morphometric analysis demonstrated increases in maximum height and width of the surface with age independent of gender, with most significant (P<0.05) changes between the 25–34 and 55–64 year subsets. Sexual dimorphism and bilateral asymmetry were prominent features in the Queensland population. Micro-architectural analysis demonstrated degradation of cortical composition with age, with differential bone resorption between the medial, ventral and dorsal aspects of the symphysis. The ability to quantitatively model age-related changes to the pubic symphysis provides potential for future methodological refinement, where rigor and robust geometric assessment of the surface may remove the subjectivity associated with aging the pubic symphysis.

A geometric construction of travelling wave solutions to the Keller–Segel model

We study a version of the Keller–Segel model for bacterial chemotaxis, for which exact travelling wave solutions are explicitly known in the zero attractant diffusion limit. Using geometric singular perturbation theory, we construct travelling wave solutions in the small diffusion case that converge to these exact solutions in the singular limit.

Validity of maternal-reported weight and height of children 2-5 year olds

To the Editor: In affluent-urban areas of India, overweight (6 %) and obesity (8 %) are prevalent in children as young as 2–5 y [1]. A potential risk factor for childhood obesity could be parent’s under-reporting their child’s anthropometry. In Indian culture, a larger body size is typically acceptable, and mothers may consider a chubby baby as healthy [2]. Therefore, it was proposed that Indian mothers may under-report their child’s weight status. The present study examined the validity of maternal reported height and weight of young, urban-affluent Indian children aged 2–5 y. After receiving approval from the QUT Human Research Ethics Committee, Australia 111 mothers with children aged 2–5 y attending private medical clinics (n = 5) in the affluent areas of Mumbai were recruited. Child’s height and weight were measured by the researcher using standard equipment/protocols. Mothers also reported their child’s height and weight.