Planning rigid body motions using elastic curves

This paper tackles the problem of computing smooth, optimal trajectories on the Euclidean group of motions SE(3). The problem is formulated as an optimal control problem where the cost function to be minimized is equal to the integral of the classical curvature squared. This problem is analogous to the elastic problem from differential geometry and thus the resulting rigid body motions will trace elastic curves. An application of the Maximum Principle to this optimal control problem shifts the emphasis to the language of symplectic geometry and to the associated Hamiltonian formalism. This results in a system of first order differential equations that yield coordinate free necessary conditions for optimality for these curves. From these necessary conditions we identify an integrable case and these particular set of curves are solved analytically. These analytic solutions provide interpolating curves between an initial given position and orientation and a desired position and orientation that would be useful in motion planning for systems such as robotic manipulators and autonomous-oriented vehicles.

Rigid body trajectories in different 6D spaces

The objective of this paper is to show that the group SE(3) with an imposed Lie-Poisson structure can be used to determine the trajectory in a spatial frame of a rigid body in Euclidean space. Identical results for the trajectory are obtained in spherical and hyperbolic space by scaling the linear displacements appropriately since the influence of the moments of inertia on the trajectories tends to zero as the scaling factor increases. The semidirect product of the linear and rotational motions gives the trajectory from a body frame perspective. It is shown that this cannot be used to determine the trajectory in the spatial frame. The body frame trajectory is thus independent of the velocity coupling. In addition, it is shown that the analysis can be greatly simplified by aligning the axes of the spatial frame with the axis of symmetry which is unchanging for a natural system with no forces and rotation about an axis of symmetry.

Storm track sensitivity to sea surface temperature resolution in a regional atmosphere model

A high resolution regional atmosphere model is used to investigate the sensitivity of the North Atlantic storm track to the spatial and temporal resolution of the sea surface temperature (SST) data used as a lower boundary condition. The model is run over an unusually large domain covering all of the North Atlantic and Europe, and is shown to produce a very good simulation of the observed storm track structure. The model is forced at the lateral boundaries with 15–20 years of data from the ERA-40 reanalysis, and at the lower boundary by SST data of differing resolution. The impacts of increasing spatial and temporal resolution are assessed separately, and in both cases increasing the resolution leads to subtle, but significant changes in the storm track. In some, but not all cases these changes act to reduce the small storm track biases seen in the model when it is forced with low-resolution SSTs. In addition there are several clear mesoscale responses to increased spatial SST resolution, with surface heat fluxes and convective precipitation increasing by 10–20% along the Gulf Stream SST gradient.

Many-body effect in electrorheological responses

The many-body effect in the kinetic responses of ER fluids is studied by a molecular-dynamic simulation method. The mutual polarization effects of the particles are considered by self-consistently calculating the dipole strength on each particle according to the external field and the dipole field due to all the other particles in the fluids. The many-body effect is found to increase with the enhancement of the particle concentration and the permittivity ratio between the solvent and the particles. The calculated response times are shorter than that predicted with the 'point-dipole' model and agree very well with experimental results. The many-body effect enhances the shear stresses of the fluids by several times. But they are not proportional to the many-body correction factor lambda as expected. This is due to the fact that larger interaction forces between the particles lead to coarsening of the fibers formed in the suspensions. The results show that the many-body and multipolar interaction between the particles must be treated comprehensively in the simulations in order to get more reliable results.

Modelling the rheology of sea ice as a collection of diamond-shaped floes

In polar oceans, seawater freezes to form a layer of sea ice of several metres thickness that can cover up to 8% of the Earth’s surface. The modelled sea ice cover state is described by thickness and orientational distribution of interlocking, anisotropic diamond-shaped ice floes delineated by slip lines, as supported by observation. The purpose of this study is to develop a set of equations describing the mean-field sea ice stresses that result from interactions between the ice floes and the evolution of the ice floe orientation, which are simple enough to be incorporated into a climate model. The sea ice stress caused by a deformation of the ice cover is determined by employing an existing kinematic model of ice floe motion, which enables us to calculate the forces acting on the ice floes due to crushing into and sliding past each other, and then by averaging over all possible floe orientations. We describe the orientational floe distribution with a structure tensor and propose an evolution equation for this tensor that accounts for rigid body rotation of the floes, their apparent re-orientation due to new slip line formation, and change of shape of the floes due to freezing and melting. The form of the evolution equation proposed is motivated by laboratory observations of sea ice failure under controlled conditions. Finally, we present simulations of the evolution of sea ice stress and floe orientation for several imposed flow types. Although evidence to test the simulations against is lacking, the simulations seem physically reasonable.

Body-centric modelling, identification, and acceleration tracking control of a quadrotor UAV

This paper presents the mathematical development of a body-centric nonlinear dynamic model of a quadrotor UAV that is suitable for the development of biologically inspired navigation strategies. Analytical approximations are used to find an initial guess of the parameters of the nonlinear model, then parameter estimation methods are used to refine the model parameters using the data obtained from onboard sensors during flight. Due to the unstable nature of the quadrotor model, the identification process is performed with the system in closed-loop control of attitude angles. The obtained model parameters are validated using real unseen experimental data. Based on the identified model, a Linear-Quadratic (LQ) optimal tracker is designed to stabilize the quadrotor and facilitate its translational control by tracking body accelerations. The LQ tracker is tested on an experimental quadrotor UAV and the obtained results are a further means to validate the quality of the estimated model. The unique formulation of the control problem in the body frame makes the controller better suited for bio-inspired navigation and guidance strategies than conventional attitude or position based control systems that can be found in the existing literature.

Multi-finger grasps in a dynamic environment

Most current state-of-the-art haptic devices render only a single force, however almost all human grasps are characterised by multiple forces and torques applied by the fingers and palms of the hand to the object. In this chapter we will begin by considering the different types of grasp and then consider the physics of rigid objects that will be needed for correct haptic rendering. We then describe an algorithm to represent the forces associated with grasp in a natural manner. The power of the algorithm is that it considers only the capabilities of the haptic device and requires no model of the hand, thus applies to most practical grasp types. The technique is sufficiently general that it would also apply to multi-hand interactions, and hence to collaborative interactions where several people interact with the same rigid object. Key concepts in friction and rigid body dynamics are discussed and applied to the problem of rendering multiple forces to allow the person to choose their grasp on a virtual object and perceive the resulting movement via the forces in a natural way. The algorithm also generalises well to support computation of multi-body physics

Beneath a learning management system: understanding the human information interaction in information systems

Studies on learning management systems have largely been technical in nature with an emphasis on the evaluation of the human computer interaction (HCI) processes in using the LMS. This paper reports a study that evaluates the information interaction processes on an eLearning course used in teaching an applied Statistics course. The eLearning course is used as a synonym for information systems. The study explores issues of missing context in stored information in information systems. Using the semiotic framework as a guide, the researchers evaluated an existing eLearning course with the view to proposing a model for designing improved eLearning courses for future eLearning programmes. In this exploratory study, a survey questionnaire is used to collect data from 160 participants on an eLearning course in Statistics in Applied Climatology. The views of the participants are analysed with a focus on only the human information interaction issues. Using the semiotic framework as a guide, syntactic, semantic, pragmatic and social context gaps or problems were identified. The information interactions problems identified include ambiguous instructions, inadequate information, lack of sound, interface design problems among others. These problems affected the quality of new knowledge created by the participants. The researchers thus highlighted the challenges of missing information context when data is stored in an information system. The study concludes by proposing a human information interaction model for improving the information interaction quality issues in the design of eLearning course on learning management platforms and those other information systems.

Rensch's rule in large herbivorous mammals derived from metabolic scaling

Rensch’s rule, which states that the magnitude of sexual size dimorphism tends to increase with increasing body size, has evolved independently in three lineages of large herbivorous mammals: bovids (antelopes), cervids (deer), and macropodids (kangaroos). This pattern can be explained by a model that combines allometry,life-history theory, and energetics. The key features are thatfemale group size increases with increasing body size and that males have evolved under sexual selection to grow large enough to control these groups of females. The model predicts relationships among body size and female group size, male and female age at first breeding,death and growth rates, and energy allocation of males to produce body mass and weapons. Model predictions are well supported by data for these megaherbivores. The model suggests hypotheses for why some other sexually dimorphic taxa, such as primates and pinnipeds(seals and sea lions), do or do not conform to Rensh’s rule.

Measuring motion with kinematically redundant accelerometer arrays: theory, simulation and implementation

This work presents two schemes of measuring the linear and angular kinematics of a rigid body using a kinematically redundant array of triple-axis accelerometers with potential applications in biomechanics. A novel angular velocity estimation algorithm is proposed and evaluated that can compensate for angular velocity errors using measurements of the direction of gravity. Analysis and discussion of optimal sensor array characteristics are provided. A damped 2 axis pendulum was used to excite all 6 DoF of the a suspended accelerometer array through determined complex motion and is the basis of both simulation and experimental studies. The relationship between accuracy and sensor redundancy is investigated for arrays of up to 100 triple axis (300 accelerometer axes) accelerometers in simulation and 10 equivalent sensors (30 accelerometer axes) in the laboratory test rig. The paper also reports on the sensor calibration techniques and hardware implementation.

Exploring farmer preferences for contagious bovine pleuropneumonia vaccination: a case study of Narok District, Kenya

Contagious bovine pleuropneumonia (CBPP) is an economically important disease in most of sub-Saharan Africa. A conjoint analysis and ordered probit regression models were used to measure the preferences of farmers for CBPP vaccine and vaccination attributes. This was with regard to inclusion or not of an indicator in the vaccine, vaccine safety, vaccine stability as well as frequency of vaccination, vaccine administration and the nature of vaccination. The analysis was carried out in 190 households in Narok District of Kenya between October and December 2006 using structured questionnaires, 16 attribute profiles and a five-point Likert scale. The factors affecting attribute valuation were shown through a two-way location interaction model. The study also demonstrated the relative importance (RI) of attributes and the compensation value of attribute levels. The attribute coefficient estimates showed that farmers prefer a vaccine that has an indicator, is 100% safe and is administered by the government (p<0.0001). The preferences for the vaccine attributes were consistent with expectations. Preferences for stability, frequency of vaccination and nature of vaccination differed amongst farmers (p>0.05). While inclusion of an indicator in the vaccine was the most important attribute (RI=43.6%), price was the least important (RI=0.5%). Of the 22 household factors considered, 15 affected attribute valuation. The compensation values for a change from non inclusion to inclusion of an indicator, 95-100% safety, 2h to greater than 2h stability and from compulsory to elective vaccination were positive while those for a change from annual to biannual vaccination and from government to private administration were negative. The study concluded that the farmers in Narok District had preferences for specific vaccine and vaccination attributes. These preferences were conditioned by various household characteristics and disease risk factors. On average the farmers would need to be compensated or persuaded to accept biannual and private vaccination against CBPP. There is need for consideration of farmer preferences for vaccine attribute levels during vaccine formulations and farmer preferences for vaccination attribute levels when designing delivery of vaccines.

Model-based vehicle detection and classification using orthographic approximations

This paper reports the current state of work to simplify our previous model-based methods for visual tracking of vehicles for use in a real-time system intended to provide continuous monitoring and classification of traffic from a fixed camera on a busy multi-lane motorway. The main constraints of the system design were: (i) all low level processing to be carried out by low-cost auxiliary hardware, (ii) all 3-D reasoning to be carried out automatically off-line, at set-up time. The system developed uses three main stages: (i) pose and model hypothesis using 1-D templates, (ii) hypothesis tracking, and (iii) hypothesis verification, using 2-D templates. Stages (i) & (iii) have radically different computing performance and computational costs, and need to be carefully balanced for efficiency. Together, they provide an effective way to locate, track and classify vehicles.

A Generic Deformable Model for Vehicle Recognition

This paper reports the development of a highly parameterised 3-D model able to adopt the shapes of a wide variety of different classes of vehicles (cars, vans, buses, etc), and its subsequent specialisation to a generic car class which accounts for most commonly encountered types of car (includng saloon, hatchback and estate cars). An interactive tool has been developed to obtain sample data for vehicles from video images. A PCA description of the manually sampled data provides a deformable model in which a single instance is described as a 6 parameter vector. Both the pose and the structure of a car can be recovered by fitting the PCA model to an image. The recovered description is sufficiently accurate to discriminate between vehicle sub-classes.