Functional range of movement of the hand : declination angles to reachable space

 The measurement of the range of hand joint movement is an essential part of clinical practice and rehabilitation. Current methods use three finger joint declination angles of the metacarpophalangeal, proximal interphalangeal and distal interphalangeal joints. In this paper we propose an alternate form of measurement for the finger movement. Using the notion of reachable space instead of declination angles has significant advantages. Firstly, it provides a visual and quantifiable method that therapists, insurance companies and patients can easily use to understand the functional capabilities of the hand. Secondly, it eliminates the redundant declination angle constraints. Finally, reachable space, defined by a set of reachable fingertip positions, can be measured and constructed by using a modern camera such as Creative Senz3D or built-in hand gesture sensors such as the Leap Motion Controller. Use of cameras or optical-type sensors for this purpose have considerable benefits such as eliminating and minimal involvement of therapist errors, non-contact measurement in addition to valuable time saving for the clinician. A comparison between using declination angles and reachable space were made based on Hume's experiment on functional range of movement to prove the efficiency of this new approach.

Deducing the reachable space from fingertip positions

The reachable space of the hand has received significant interests in the past from relevant medical researchers and health professionals. The reachable space was often computed from the joint angles acquired from a motion capture system such as gloves or markers attached to each bone of the finger. However, the contact between the hand and device can cause difficulties particularly for hand with injuries, burns or experiencing certain dermatological conditions. This paper introduces an approach to find the reachable space of the hand in a non-contact measurement form utilizing the Leap Motion Controller. The approach is based on the analysis of each position in the motion path of the fingertip acquired by the Leap Motion Controller. For each position of the fingertip, the inverse kinematic problem was solved under the physiological multiple constraints of the human hand to find a set of all possible configurations of three finger joints. Subsequently, all the sets are unified to form a set of all possible configurations specific for that motion. Finally, a reachable space is computed from the configuration corresponding to the complete extension and the complete flexion of the finger joint angles in this set.

Quantification of the finger functional range via explicit descriptions of reachable subspaces

In recent times, the finger flexibility assessment by means of reachable space is considered as an effective tool to describe the range of motion of the hand. Existing approaches numerically compute the reachable space using forward kinematics such as exhaustive scanning or Monte Carlo methods. In this paper, we provide explicit formulas mathematically determining the reachable space boundary. Green's theorem is used to deduce the corresponding capacity formula for the size of the reachable space as opposed to an implicit numerical solution. Using this new mechanism, we accurately quantify and compare the reachable space of different subjects in order to effectively compare the functionality of the fingers. We evaluate the performance of our proposed method against the kinematic feed-forward (KFF) approach in calculating the reachable space. The execution time to capture the reachable space is significantly less than that for the standard KFF method. The computational cost for quantifying the reachable space capacity is significantly improved due to explicit capacity formulas resulting from the abstract form of boundary descriptions of the reachable space, unique to the proposed approach.

Describing human finger flexibility via reachable subspaces

In recent years, the reachable space concept has attracted the attention of many researchers as a mean of describing finger flexibility. Existing approaches such as exhaustive scanning or Monte Carlo methods to obtain the reachable space are resource-hungry techniques. In this paper, we introduce a novel approach to determine and quantify the reachable space of the finger. The approach was developed around a set of formulae determining the boundary of the reachable space. The Monte Carlo simulation is proposed to estimate the capacity of the reachable space. Using the new technique, reachable spaces can be visualised and quantified in order to effectively compare the functionality of different subjects and their therapeutic status. The performance of the proposed method was evaluated against the kinematic feed-forward approach. The computational cost to obtain the reachable space is significantly less than the standard kinematic feed-forward approach due to exclusive description of the reachable space boundary, unique to the proposed approach.

Robot navigation in sensor space

This thesis investigates the problem of robot navigation using only landmark bearings. The proposed system allows a robot to move to a ground target location specified by the sensor values observed at this ground target posi- tion. The control actions are computed based on the difference between the current landmark bearings and the target landmark bearings. No Cartesian coordinates with respect to the ground are computed by the control system. The robot navigates using solely information from the bearing sensor space. Most existing robot navigation systems require a ground frame (2D Cartesian coordinate system) in order to navigate from a ground point A to a ground point B. The commonly used sensors such as laser range scanner, sonar, infrared, and vision do not directly provide the 2D ground coordi- nates of the robot. The existing systems use the sensor measurements to localise the robot with respect to a map, a set of 2D coordinates of the objects of interest. It is more natural to navigate between the points in the sensor space corresponding to A and B without requiring the Cartesian map and the localisation process. Research on animals has revealed how insects are able to exploit very limited computational and memory resources to successfully navigate to a desired destination without computing Cartesian positions. For example, a honeybee balances the left and right optical flows to navigate in a nar- row corridor. Unlike many other ants, Cataglyphis bicolor does not secrete pheromone trails in order to find its way home but instead uses the sun as a compass to keep track of its home direction vector. The home vector can be inaccurate, so the ant also uses landmark recognition. More precisely, it takes snapshots and compass headings of some landmarks. To return home, the ant tries to line up the landmarks exactly as they were before it started wandering. This thesis introduces a navigation method based on reflex actions in sensor space. The sensor vector is made of the bearings of some landmarks, and the reflex action is a gradient descent with respect to the distance in sensor space between the current sensor vector and the target sensor vec- tor. Our theoretical analysis shows that except for some fully characterized pathological cases, any point is reachable from any other point by reflex action in the bearing sensor space provided the environment contains three landmarks and is free of obstacles. The trajectories of a robot using reflex navigation, like other image- based visual control strategies, do not correspond necessarily to the shortest paths on the ground, because the sensor error is minimized, not the moving distance on the ground. However, we show that the use of a sequence of waypoints in sensor space can address this problem. In order to identify relevant waypoints, we train a Self Organising Map (SOM) from a set of observations uniformly distributed with respect to the ground. This SOM provides a sense of location to the robot, and allows a form of path planning in sensor space. The navigation proposed system is analysed theoretically, and evaluated both in simulation and with experiments on a real robot.

Constraints on neutrino mass fraction using Redshift Space Distortions

Redshift Space Distortions (RSD) are an apparent anisotropy in the distribution of galaxies due to their peculiar motion. These features are imprinted in the correlation function of galaxies, which describes how these structures distribute around each other. RSD can be represented by a distortions parameter $\beta$, which is strictly related to the growth of cosmic structures. For this reason, measurements of RSD can be exploited to give constraints on the cosmological parameters, such us for example the neutrino mass. Neutrinos are neutral subatomic particles that come with three flavours, the electron, the muon and the tau neutrino. Their mass differences can be measured in the oscillation experiments. Information on the absolute scale of neutrino mass can come from cosmology, since neutrinos leave a characteristic imprint on the large scale structure of the universe. The aim of this thesis is to provide constraints on the accuracy with which neutrino mass can be estimated when expoiting measurements of RSD. In particular we want to describe how the error on the neutrino mass estimate depends on three fundamental parameters of a galaxy redshift survey: the density of the catalogue, the bias of the sample considered and the volume observed. In doing this we make use of the BASICC Simulation from which we extract a series of dark matter halo catalogues, characterized by different value of bias, density and volume. This mock data are analysed via a Markov Chain Monte Carlo procedure, in order to estimate the neutrino mass fraction, using the software package CosmoMC, which has been conveniently modified. In this way we are able to extract a fitting formula describing our measurements, which can be used to forecast the precision reachable in future surveys like Euclid, using this kind of observations.

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.