Singularity avoidance for manipulators with spherical wrists using the approximate damped reciprocal algorithm

Due to the loss of freedom, the stability and tracking ability of the manipulator around the singularity become worse. This article aims at improving the accuracy of the manipulator and ensuring the stability of the system with the damped reciprocal method. Firstly, the singularities are separated into forearm and wrist singularities to obtain the singular factors of the manipulator respectively. Secondly, a new mathematical function of the approximate damped reciprocal of the singular factor is proposed. Thirdly, the singularities are avoided by modifying the Jacobian matrixes of the manipulator with the approximate damped reciprocal algorithm. Finally, the effectiveness and the stability of the system are proved by the simulations on a manipulator with the spherical wrist. The simulation results prove that this method can largely improve the accuracy of the end-effector and can ensure the stability of the system around the singular region.

Research on Optimization Method of Tool Path in Five-Axis Process Singular Region

For the five-axis machine into the singular region in the process of parts processing, resulting in a discontinuous and rapid rotation of the axis of rotation of large angles. Based on the analysis of the cause of the obvious ripple on the machined surface and the influence on the machining precision, a mathematical model of the singular region is established, and an optimization method of the tool path in the singular region is proposed. The simulation and practical machining results show that the method can effectively overcome the problem of excessive movement of the rotating shaft in the Song singular region of 5-axis machine tool, and solve the surface corrugated defects caused by the problem, while improving the processing efficiency.

Dynamics of Learning in MLP: Natural Gradient and Singularity Revisited

The dynamics of supervised learning play a main role in deep learning, which takes place in the parameter space of a multilayer perceptron (MLP). We review the history of supervised stochastic gradient learning, focusing on its singular structure and natural gradient. The parameter space includes singular regions in which parameters are not identifiable. One of our results is a full exploration of the dynamical behaviors of stochastic gradient learning in an elementary singular network. The bad news is its pathological nature, in which part of the singular region becomes an attractor and another part a repulser at the same time, forming a Milnor attractor. A learning trajectory is attracted by the attractor region, staying in it for a long time, before it escapes the singular region through the repulser region. This is typical of plateau phenomena in learning. We demonstrate the strange topology of a singular region by introducing blow-down coordinates, which are useful for analyzing the natural gradient dynamics. We confirm that the natural gradient dynamics are free of critical slowdown. The second main result is the good news: the interactions of elementary singular networks eliminate the attractor part and the Milnor-type attractors disappear. This explains why large-scale networks do not suffer from serious critical slowdowns due to singularities. We finally show that the unit-wise natural gradient is effective for learning in spite of its low computational cost.

Competitividade de destinos turísticos: o caso das ilhas de Cabo Verde

The main goal of this research focuses on studying the performance and competitiveness of tourism destinations of the Cape Verde islands by main outbond markets. It was used the data of monthly overnight stays in hotels for the period 2005 to 2011. For that it was used the instrument Analysis of Market Share proposed by Faulkner (1997), as well as the Gini Index and the Dissimilarity among tourist destinations in major outbound markets, to better complement the study analysis. The results showed that the islands have changed in the tourism competitiveness, presented levels of tourism competitiveness different for the various origins. Concerning the Gini Index, nationally there was a decrease in concentration of overnights. As the dissimilarity, the island of Boavista was the most singular region and São Nicolau and Brava were the most similar

Computations of SIFs for Non-Symmetric V-Notched Plates by the FFEM

The present paper further develops The Fractal-like Finite Element Method (FFEM) to compute the stress intensity factors (SIFs) for non-symmetrical configurations of sharp V-notched plates. The use of global interpolation functions (GIFs) in the FFEM significantly reduces the number of unknown variables (nodal displacements) in a singular region surrounding a singular point to a small set of generalised coordinates. The same exact analytical solutions of the notch tip asymptotic field derived for a symmetrical notch case can be used as GIFs when the notch is non-symmetrical. However, appropriate local coordinate transformation in the singular region is required to obtain the correct global stiffness matrix. Neither post-processing technique to extract SIFs nor special singular elements to model the singular region are required. Any conventional finite elements can be used to model the singular region. The SIFs are directly computed because of the use of exact analytical solutions as GIFs whose coefficients (generalised coordinates) are the unknowns in the singular region. To demonstrate the accuracy and efficiency of the FFEM to compute the SIFs and model the singularity at a notch tip of non-symmetrical configurations of notched plates, various numerical examples are presented and results are validated via available published data.

Applications of the Fractal-Like Finite Element Method to Sharp Notched Plates

The fractal-like finite element method (FFEM) has been proved to be an accurate and efficient method to analyse the stress singularity of crack tips. The FFEM is a semi-analytical method. It divides the cracked body into singular and regular regions. Conventional finite elements are used to model both near field and far field regions. However, a very fine mesh of conventional finite elements is used within the singular regions. This mesh is generated layer by layer in a self-similar fractal process. The corresponding large number of degrees of freedom in the singular region is reduced extremely to a small set of global variables, called generalised co-ordinates, after performing a global transformation. The global transformation is performed using global interpolation functions. The Concept of these functions is similar to that of local interpolation functions (i.e. element shape functions.) The stress intensity factors are directly related to the generalised co-ordinates, and therefore no post-processing is necessary to extract them. In this paper, we apply this method to analyse the singularity problems of sharp notched plates. Following the work of Williams, the exact stress and displacement fields of a plate with a notch of general angle are derived for plane stress and plane strain conditions. These exact solutions which are eigenfunction expansion series are used as the global interpolation functions to perform the global transformation of the large number of local variables in the singular region around the notch tip to a few set of global co-ordinates and in the determination of the stress intensity factors. The numerical examples demonstrate the accuracy and efficiency of the FFEM for sharp notched problems.

A procedure to correct the effects of a relative delay between the quadrature components of radar signals at base band

The real and imaginary parts of baseband signals are obtained from a real narrow-band signal by quadrature mixing, i.e. by mixing with cosine and sine signals at the narrow band's selected center frequency. We address the consequences of a delay between the outputs of the quadrature mixer, which arise when digital samples of the quadrature baseband signals are not synchronised, i.e. when the real and imaginary components have been shifted by one or more samples with respect to each other. Through analytical considerations and simulations of such an error on different synthetic signals, we show how this error can be expected to afflict different measurements. In addition, we show the effect of the error on actual incoherent scatter radar data obtained by two different digital receiver systems used in parallel at the EISCAT Svalbard Radar (ESR). The analytical considerations indicate a procedure to correct the error, albeit with some limitations due to a small singular region. We demonstrate the correction procedure on actually afflicted data and compare the results to simultaneously acquired unafflicted data. We also discuss the possible data analysis strategies, including some that avoid dealing directly with the singular region mentioned above.