Reducing actuator switchings for motion control of autonomous underwater vehicles

A priority when designing control strategies for autonomous underwater vehicles is to emphasize their cost of implementation on a real vehicle and at the same time to minimize a prescribed criterion such as time, energy, payload or combination of those. Indeed, the major issue is that due to the vehicles' design and the actuation modes usually under consideration for underwater platforms the number of actuator switchings must be kept to a small value to ensure feasibility and precision. This constraint is typically not verified by optimal trajectories which might not even be piecewise constants. Our goal is to provide a feasible trajectory that minimizes the number of switchings while maintaining some qualities of the desired trajectory, such as optimality with respect to a given criterion. The one-sided Lipschitz constant is used to derive theoretical estimates. The theory is illustrated on two examples, one is a fully actuated underwater vehicle capable of motion in six degrees-of-freedom and one is minimally actuated with control motions constrained to the vertical plane.

Understanding the relationships between the calf muscle pump, ankle range of motion and healing for adults with venous leg ulcers: a review of the literature

Exercise offers the potential to improve circulation, wound healing outcomes, and functional and emotional wellbeing for adults experiencing venous leg ulceration. Individuals with chronic leg ulcers typically have multiple comorbidities such as arthritis, asthma, chronic obstructive airways disease, cardiac disease or neuromuscular disorders, which would also benefit from regular exercise. The aim of this review is to highlight the relationships between the calf muscle pump and venous return and range of ankle motion for adults with venous leg ulcers. The effect of exercise will also be considered in relation to the healing rates for adults experiencing venous leg ulceration. The findings suggest there is evidence that exercises which engage the calf muscle pump improve venous return. Ankle range of motion, which is crucial for complete activation of the calf muscle pump, can also be improved with simple, home-based exercise programs. However, observational studies still report that venous leg ulcer patients are less physically active than age-matched controls. Therefore, the behavioural reasons for not exercising must be considered. Only two studies, both underpowered, have assessed the effect of exercise on the healing rates of venous leg ulcers. In conclusion, exercise is feasible with this patient population. However, future studies with larger sample sizes are needed to provide stronger evidence to support the therapeutic benefit of exercise as an adjunct therapy in wound care.

Visual motion perception predicts driving hazard perception ability

PURPOSE: To examine the basis of previous findings of an association between indices of driving safety and visual motion sensitivity and to examine whether this association could be explained by low-level changes in visual function. METHODS: 36 visually normal participants (aged 19 – 80 years), completed a battery of standard vision tests including visual acuity, contrast sensitivity and automated visual fields. and two tests of motion perception including sensitivity for movement of a drifting Gabor stimulus, and sensitivity for displacement in a random-dot kinematogram (Dmin). Participants also completed a hazard perception test (HPT) which measured participants’ response times to hazards embedded in video recordings of real world driving which has been shown to be linked to crash risk. RESULTS: Dmin for the random-dot stimulus ranged from -0.88 to -0.12 log minutes of arc, and the minimum drift rate for the Gabor stimulus ranged from 0.01 to 0.35 cycles per second. Both measures of motion sensitivity significantly predicted response times on the HPT. In addition, while the relationship involving the HPT and motion sensitivity for the random-dot kinematogram was partially explained by the other visual function measures, the relationship with sensitivity for detection of the drifting Gabor stimulus remained significant even after controlling for these variables. CONCLUSION: These findings suggest that motion perception plays an important role in the visual perception of driving-relevant hazards independent of other areas of visual function and should be further explored as a predictive test of driving safety. Future research should explore the causes of reduced motion perception in order to develop better interventions to improve road safety.

The effect of warm-up intensity on range of motion and anaerobic performance

Although there is a paucity of scientific support for the benefits of warm-up, athletes commonly warm up prior to activity with the intention of improving performance and reducing the incidence of injuries. The purpose of this study was to examine the role of warm-up intensity on both range of motion (ROM) and anaerobic performance. Nine males (age = 21.7 +/- 1.6 years, height = 1.77 +/- 0.04 m, weight = 80.2 +/- 6.8 kg, and VO2max = 60.4 +/- 5.4 ml/kg/min) completed four trials. Each trial consisted of hip, knee, and ankle ROM evaluation using an electronic inclinometer and an anaerobic capacity test on the treadmill (time to fatigue at 13 km/hr and 20% grade). Subjects underwent no warm-up or a warm-up of 15 minutes running at 60, 70 or 80% VO2max followed by a series of lower limb stretches. Intensity of warm-up had little effect on ROM, since ankle dorsiflexion and hip extension significantly increased in all warm-up conditions, hip flexion significantly increased only after the 80% VO2max warm-up, and knee flexion did not change after any warm-up. Heart rate and body temperature were significantly increased (p < 0.05) prior to anaerobic performance for each of the warm-up conditions, but anaerobic performance improved significantly only after warm-up at 60% VO2max (10%) and 70% VO2max (13%). A 15-minute warm-up at an intensity of 60-70% VO2max is therefore recommended to improve ROM and enhance subsequent anaerobic performance.

Visual sea-floor mapping from low overlap imagery using bi-objective bundle adjustment and constrained motion

In most visual mapping applications suited to Autonomous Underwater Vehicles (AUVs), stereo visual odometry (VO) is rarely utilised as a pose estimator as imagery is typically of very low framerate due to energy conservation and data storage requirements. This adversely affects the robustness of a vision-based pose estimator and its ability to generate a smooth trajectory. This paper presents a novel VO pipeline for low-overlap imagery from an AUV that utilises constrained motion and integrates magnetometer data in a bi-objective bundle adjustment stage to achieve low-drift pose estimates over large trajectories. We analyse the performance of a standard stereo VO algorithm and compare the results to the modified vo algorithm. Results are demonstrated in a virtual environment in addition to low-overlap imagery gathered from an AUV. The modified VO algorithm shows significantly improved pose accuracy and performance over trajectories of more than 300m. In addition, dense 3D meshes generated from the visual odometry pipeline are presented as a qualitative output of the solution.

Stability and convergence of a finite volume method for the space fractional advection-dispersion equation

We consider the space fractional advection–dispersion equation, which is obtained from the classical advection–diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis.

Numerical simulation of red blood cells’ motion : a review

The micro-circulation of blood plays an important role in human body by providing oxygen and nutrients to the cells and removing carbon dioxide and wastes from the cells. This process is greatly affected by the rheological properties of the Red Blood Cells (RBCs). Changes in the rheological properties of the RBCs are caused by certain human diseases such as malaria and sickle cell diseases. Therefore it is important to understand the motion and deformation mechanism of RBCs in order to diagnose and treat this kind of diseases. Although, many methods have been developed to explore the behavior of the RBCs in micro-channels, they could not explain the deformation mechanism of the RBCs properly. Recently developed Particle Methods are employed to explain the RBCs’ behavior in micro-channels more comprehensively. The main objective of this study is to critically analyze the present methods, used to model the RBC behavior in micro-channels, in order to develop a computationally efficient particle based model to describe the complete behavior of the RBCs in micro-channels accurately and comprehensively

Learning hierarchical prototypes of motion time series for interactive systems

Abstract. For interactive systems, recognition, reproduction, and generalization of observed motion data are crucial for successful interaction. In this paper, we present a novel method for analysis of motion data that we refer to as K-OMM-trees. K-OMM-trees combine Ordered Means Models (OMMs) a model-based machine learning approach for time series with an hierarchical analysis technique for very large data sets, the K-tree algorithm. The proposed K-OMM-trees enable unsupervised prototype extraction of motion time series data with hierarchical data representation. After introducing the algorithmic details, we apply the proposed method to a gesture data set that includes substantial inter-class variations. Results from our studies show that K-OMM-trees are able to substantially increase the recognition performance and to learn an inherent data hierarchy with meaningful gesture abstractions.

Re-targeting choreographic enquiry through motion capture

This creative work is the outcome of preliminary experiments through practice aiming to explore the collaboration of a Dancer/choreographer with an Animator, along with enquiry into the intergeneration of motion capture technologies within the work-flow. The animated visuals derived from the motion capture data is not aimed at just re-targeting of movement from one source to another but looks at describing the thought and emotions of the choreographed dance through visual aesthetics.

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

A preconditioned Lanczos method for space-fractional reaction-diffusion equations on two-dimensional unstructured meshes

We consider a two-dimensional space-fractional reaction diffusion equation with a fractional Laplacian operator and homogeneous Neumann boundary conditions. The finite volume method is used with the matrix transfer technique of Ilić et al. (2006) to discretise in space, yielding a system of equations that requires the action of a matrix function to solve at each timestep. Rather than form this matrix function explicitly, we use Krylov subspace techniques to approximate the action of this matrix function. Specifically, we apply the Lanczos method, after a suitable transformation of the problem to recover symmetry. To improve the convergence of this method, we utilise a preconditioner that deflates the smallest eigenvalues from the spectrum. We demonstrate the efficiency of our approach for a fractional Fisher’s equation on the unit disk.

Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

A novel numerical approximation for the space fractional advection-dispersion equation

In this paper, we consider a space fractional advection–dispersion equation. The equation is obtained from the standard advection–diffusion equation by replacing the first- and second-order space derivatives by the Riesz fractional derivatives of order β1 ∈ (0, 1) and β2 ∈ (1, 2], respectively. The fractional advection and dispersion terms are approximated by using two fractional centred difference schemes. A new weighted Riesz fractional finite-difference approximation scheme is proposed. When the weighting factor θ equals 12, a second-order accuracy scheme is obtained. The stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

Two novel numerical methods for solving the two-dimensional fractional Fitzhugh-Nagumo-monodomain model

Fractional mathematical models represent a new approach to modelling complex spatial problems in which there is heterogeneity at many spatial and temporal scales. In this paper, a two-dimensional fractional Fitzhugh-Nagumo-monodomain model with zero Dirichlet boundary conditions is considered. The model consists of a coupled space fractional diffusion equation (SFDE) and an ordinary differential equation. For the SFDE, we first consider the numerical solution of the Riesz fractional nonlinear reaction-diffusion model and compare it to the solution of a fractional in space nonlinear reaction-diffusion model. We present two novel numerical methods for the two-dimensional fractional Fitzhugh-Nagumo-monodomain model using the shifted Grunwald-Letnikov method and the matrix transform method, respectively. Finally, some numerical examples are given to exhibit the consistency of our computational solution methodologies. The numerical results demonstrate the effectiveness of the methods.