A Novel Collision-Free Homotopy Path Planning for Planar Robotic Arms.

Achieving the smart motion of any autonomous or semi-autonomous robot requires an efficient algorithm to determine a feasible collision-free path. In this paper, a novel collision-free path homotopy-based path-planning algorithm applied to planar robotic arms is presented. The algorithm utilizes homotopy continuation methods (HCMs) to solve the non-linear algebraic equations system (NAES) that models the robot's workspace. The method was validated with three case studies with robotic arms in different configurations. For the first case, a robot arm with three links must enter a narrow corridor with two obstacles. For the second case, a six-link robot arm with a gripper is required to take an object inside a narrow corridor with two obstacles. For the third case, a twenty-link arm must take an object inside a maze-like environment. These case studies validated, by simulation, the versatility and capacity of the proposed path-planning algorithm. The results show that the CPU time is dozens of milliseconds with a memory consumption less than 4.5 kB for the first two cases. For the third case, the CPU time is around 2.7 s and the memory consumption around 18 kB. Finally, the method's performance was further validated using the industrial robot arm CRS CataLyst-5 by Thermo Electron.

Exploring a Novel Multiple-Query Resistive Grid-Based Planning Method Applied to High-DOF Robotic Manipulators.

The applicability of the path planning strategy to robotic manipulators has been an exciting topic for researchers in the last few decades due to the large demand in the industrial sector and its enormous potential development for space, surgical, and pharmaceutical applications. The automation of high-degree-of-freedom (DOF) manipulator robots is a challenging task due to the high redundancy in the end-effector position. Additionally, in the presence of obstacles in the workspace, the task becomes even more complicated. Therefore, for decades, the most common method of integrating a manipulator in an industrial automated process has been the demonstration technique through human operator intervention. Although it is a simple strategy, some drawbacks must be considered: first, the path's success, length, and execution time depend on operator experience; second, for a structured environment with few objects, the planning task is easy. However, for most typical industrial applications, the environments contain many obstacles, which poses challenges for planning a collision-free trajectory. In this paper, a multiple-query method capable of obtaining collision-free paths for high DOF manipulators with multiple surrounding obstacles is presented. The proposed method is inspired by the resistive grid-based planner method (RGBPM). Furthermore, several improvements are implemented to solve complex planning problems that cannot be handled by the original formulation. The most important features of the proposed planner are as follows: (1) the easy implementation of robotic manipulators with multiple degrees of freedom, (2) the ability to handle dozens of obstacles in the environment, (3) compatibility with various obstacle representations using mathematical models, (4) a new recycling of a previous simulation strategy to convert the RGBPM into a multiple-query planner, and (5) the capacity to handle large sparse matrices representing the configuration space. A numerical simulation was carried out to validate the proposed planning method's effectiveness for manipulators with three, five, and six DOFs on environments with dozens of surrounding obstacles. The case study results show the applicability of the proposed novel strategy in quickly computing new collision-free paths using the first execution data. Each new query requires less than 0.2 s for a 3 DOF manipulator in a configuration space free-modeled by a 7291 × 7291 sparse matrix and less than 30 s for five and six DOF manipulators in a configuration space free-modeled by 313,958 × 313,958 and 204,087 × 204,087 sparse matrices, respectively. Finally, a simulation was conducted to validate the proposed multiple-query RGBPM planner's efficacy in finding feasible paths without collision using a six-DOF manipulator (KUKA LBR iiwa 14R820) in a complex environment with dozens of surrounding obstacles.

Statistical Assessment of Discrimination Capabilities of a Fractional Calculus Based Image Watermarking System for Gaussian Watermarks.

In this paper, we explore the advantages of a fractional calculus based watermarking system for detecting Gaussian watermarks. To reach this goal, we selected a typical watermarking scheme and replaced the detection equation set by another set of equations derived from fractional calculus principles; then, we carried out a statistical assessment of the performance of both schemes by analyzing the Receiver Operating Characteristic (ROC) curve and the False Positive Percentage (FPP) when they are used to detect Gaussian watermarks. The results show that the ROC of a fractional equation based scheme has 48.3% more Area Under the Curve (AUC) and a False Positives Percentage median of 0.2% whilst the selected typical watermarking scheme has 3%. In addition, the experimental results suggest that the target applications of fractional schemes for detecting Gaussian watermarks are as a semi-fragile image watermarking systems robust to Gaussian noise.

Multiple-Target Homotopic Quasi-Complete Path Planning Method for Mobile Robot Using a Piecewise Linear Approach.

The ability to plan a multiple-target path that goes through places considered important is desirable for autonomous mobile robots that perform tasks in industrial environments. This characteristic is necessary for inspection robots that monitor the critical conditions of sectors in thermal, nuclear, and hydropower plants. This ability is also useful for applications such as service at home, victim rescue, museum guidance, land mine detection, and so forth. Multiple-target collision-free path planning is a topic that has not been very studied because of the complexity that it implies. Usually, this issue is left in second place because, commonly, it is solved by segmentation using the point-to-point strategy. Nevertheless, this approach exhibits a poor performance, in terms of path length, due to unnecessary turnings and redundant segments present in the found path. In this paper, a multiple-target method based on homotopy continuation capable to calculate a collision-free path in a single execution for complex environments is presented. This method exhibits a better performance, both in speed and efficiency, and robustness compared to the original Homotopic Path Planning Method (HPPM). Among the new schemes that improve their performance are the Double Spherical Tracking (DST), the dummy obstacle scheme, and a systematic criterion to a selection of repulsion parameter. The case studies show its effectiveness to find a solution path for office-like environments in just a few milliseconds, even if they have narrow corridors and hundreds of obstacles. Additionally, a comparison between the proposed method and sampling-based planning algorithms (SBP) with the best performance is presented. Furthermore, the results of case studies show that the proposed method exhibits a better performance than SBP algorithms for execution time, memory, and in some cases path length metrics. Finally, to validate the feasibility of the paths calculated by the proposed planner; two simulations using the pure-pursuit controlled and differential drive robot model contained in the Robotics System Toolbox of MATLAB are presented.

Recent Advances of MEMS Resonators for Lorentz Force Based Magnetic Field Sensors: Design, Applications and Challenges.

Microelectromechanical systems (MEMS) resonators have allowed the development of magnetic field sensors with potential applications such as biomedicine, automotive industry, navigation systems, space satellites, telecommunications and non-destructive testing. We present a review of recent magnetic field sensors based on MEMS resonators, which operate with Lorentz force. These sensors have a compact structure, wide measurement range, low energy consumption, high sensitivity and suitable performance. The design methodology, simulation tools, damping sources, sensing techniques and future applications of magnetic field sensors are discussed. The design process is fundamental in achieving correct selection of the operation principle, sensing technique, materials, fabrication process and readout systems of the sensors. In addition, the description of the main sensing systems and challenges of the MEMS sensors are discussed. To develop the best devices, researches of their mechanical reliability, vacuum packaging, design optimization and temperature compensation circuits are needed. Future applications will require multifunctional sensors for monitoring several physical parameters (e.g., magnetic field, acceleration, angular ratio, humidity, temperature and gases).

Digital signal processing by virtual instrumentation of a MEMS magnetic field sensor for biomedical applications.

We present a signal processing system with virtual instrumentation of a MEMS sensor to detect magnetic flux density for biomedical applications. This system consists of a magnetic field sensor, electronic components implemented on a printed circuit board (PCB), a data acquisition (DAQ) card, and a virtual instrument. It allows the development of a semi-portable prototype with the capacity to filter small electromagnetic interference signals through digital signal processing. The virtual instrument includes an algorithm to implement different configurations of infinite impulse response (IIR) filters. The PCB contains a precision instrumentation amplifier, a demodulator, a low-pass filter (LPF) and a buffer with operational amplifier. The proposed prototype is used for real-time non-invasive monitoring of magnetic flux density in the thoracic cage of rats. The response of the rat respiratory magnetogram displays a similar behavior as the rat electromyogram (EMG).

Recent Progress of Nanogenerators for Green Energy Harvesting: Performance, Applications, and Challenges.

Natural sources of green energy include sunshine, water, biomass, geothermal heat, and wind. These energies are alternate forms of electrical energy that do not rely on fossil fuels. Green energy is environmentally benign, as it avoids the generation of greenhouse gases and pollutants. Various systems and equipment have been utilized to gather natural energy. However, most technologies need a huge amount of infrastructure and expensive equipment in order to power electronic gadgets, smart sensors, and wearable devices. Nanogenerators have recently emerged as an alternative technique for collecting energy from both natural and artificial sources, with significant benefits such as light weight, low-cost production, simple operation, easy signal processing, and low-cost materials. These nanogenerators might power electronic components and wearable devices used in a variety of applications such as telecommunications, the medical sector, the military and automotive industries, and internet of things (IoT) devices. We describe new research on the performance of nanogenerators employing several green energy acquisition processes such as piezoelectric, electromagnetic, thermoelectric, and triboelectric. Furthermore, the materials, applications, challenges, and future prospects of several nanogenerators are discussed.

Comparative Study on the Quality of Microcrystalline and Epitaxial Silicon Films Produced by PECVD Using Identical SiF4 Based Process Conditions.

Hydrogenated microcrystalline silicon (µc-Si:H) and epitaxial silicon (epi-Si) films have been produced from SiF4, H2 and Ar mixtures by plasma enhanced chemical vapor deposition (PECVD) at 200 °C. Here, both films were produced using identical deposition conditions, to determine if the conditions for producing µc-Si with the largest crystalline fraction (XC), will also result in epi-Si films that encompass the best quality and largest crystalline silicon (c-Si) fraction. Both characteristics are of importance for the development of thin film transistors (TFTs), thin film solar cells and novel 3D devices since epi-Si films can be grown or etched in a selective manner. Therefore, we have distinguished that the H2/SiF4 ratio affects the XC of µc-Si, the c-Si fraction in epi-Si films, and the structure of the epi-Si/c-Si interface. Raman and UV-Vis ellipsometry were used to evaluate the crystalline volume fraction (Xc) and composition of the deposited layers, while the structure of the films were inspected by high resolution transmission electron microscopy (HRTEM). Notably, the conditions for producing µc-Si with the largest XC are different in comparison to the fabrication conditions of epi-Si films with the best quality and largest c-Si fraction.

The novel family of transcendental Leal-functions with applications to science and engineering.

During the phenomena modelling process in the different areas of science and engineering is common to face nonlinear equations without exact solutions; thus, the need of employing numerical methods to obtain such solutions. Therefore, in order to provide new possibilities for the isolation of variables, we propose a novel family of transcendental functions with new algebraic properties including their integration and differentiation rules. Likewise, in order facilitate the numerical evaluation for every new family set of functions, a highly accurate series of approximations is proposed by employing analytical expressions in terms of known transcendental functions and polynomials combinations. By the use of known functions for the proposed approximations, makes possible the use of any programming language for their respective implementation. In this article, three interesting case studies are presented with applications on: coastal engineering, transmission lines span on electrical engineering, and the planar one-dimensional Bratu equation. Finally, based on the results from study cases, it can be concluded that Leal-functions will have relevant impact in all areas of physics and mathematics, by providing new tools to scientists and engineers for the proposal of new mathematical models and numerical/analytical analysis, design and implementation of new theories and technological innovations.

The novel Leal-polynomials for the multi-expansive approximation of nonlinear differential equations.

This work presents the novel Leal-polynomials (LP) for the approximation of nonlinear differential equations of different kind. The main characteristic of LPs is that they satisfy multiple expansion points and its derivatives as a mechanism to replicate behaviour of the nonlinear problem, giving more accuracy within the region of interest. Therefore, the main contribution of this work is that LP satisfies the successive derivatives in some specific points, resulting more accurate polynomials than Taylor expansion does for the same degree of their respective polynomials. Such characteristic makes of LPs a handy and powerful tool to approximate different kind of differential equations including: singular problems, initial condition and boundary-valued problems, equations with discontinuities, coupled differential equations, high-order equations, among others. Additionally, we show how the process to obtain the polynomials is straightforward and simple to implement; generating a compact, and easy to compute, expression. Even more, we present the process to approximate Gelfand's equation, an equation of an isothermal reaction, a model for chronic myelogenous leukemia, Thomas-Fermi equation, and a high order nonlinear differential equations with discontinuities getting, as result, accurate, fast and compact approximate solutions. In addition, we present the computational convergence and error studies for LPs resulting convergent polynomials and error tendency to zero as the order of LPs increases for all study cases. Finally, a study of CPU time shows that LPs require a few nano-seconds to be evaluated, which makes them suitable for intensive computing applications.

A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations.

This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.

Transforming the canonical piecewise-linear model into a smooth-piecewise representation.

A smoothed representation (based on natural exponential and logarithmic functions) for the canonical piecewise-linear model, is presented. The result is a completely differentiable formulation that exhibits interesting properties, like preserving the parameters of the original piecewise-linear model in such a way that they can be directly inherited to the smooth model in order to determine their parameters, the capability of controlling not only the smoothness grade, but also the approximation accuracy at specific breakpoint locations, a lower or equal overshooting for high order derivatives in comparison with other approaches, and the additional advantage of being expressed in a reduced mathematical form with only two types of inverse functions (logarithmic and exponential). By numerical simulation examples, this proposal is verified and well-illustrated.

GHM method for obtaining rationalsolutions of nonlinear differential equations.

In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.

Analytical solutions for systems of partial differential-algebraic equations.

This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.

Método de perturbación con transformada de Laplace para resolver problemas no lineales de múltiples soluciones, con condiciones a la frontera mixtas y Neumann / Laplace transform-perturbation method to solve nonlinear perturbative multiple solutions problems with mixed and Neumann boundary conditions

RESUMEN El campo de las ecuaciones diferenciales ha cobrado auge en la actualidad por el desarrollo científico y tecnológico. Por esta situación, el estudio de nuevas metodologías para solucionarlas se ha vuelto importante. A partir de la combinación del método de Laplace Transform (LT) y el método de perturbación (PM) este trabajo presenta el método LT-PM, y su motivación se encuentra en la aplicación conocida de la LT a ecuaciones diferenciales ordinarias lineales. El objetivo de este trabajo fue presentar una modificación del método de perturbación (PM), el método de perturbación con transformada de Laplace (LT-PM), con el fin de resolver problemas perturbativos no lineales, con condiciones a la frontera definidas en intervalos finitos. La metodología consistió en aplicar LT a la ecuación diferencial por resolver y después de asumir que la solución de la misma se puede expresar como una serie de potencias de un parámetro perturbativo, se obtiene la solución del problema aplicando sistemáticamente la transformada inversa de Laplace. Los principales resultados de este trabajo se muestran a partir de dos casos de estudio presentados, donde se observa que LT-PM es potencialmente útil para encontrar soluciones múltiples de problemas no lineales. Además, LT-PM mejora la aplicabilidad del método de perturbación en algunos casos de condiciones a la frontera mixtas y de Neumann, donde PM simplemente no funciona. Con el fin de verificar la exactitud de los resultados obtenidos, se calculó su error residual cuadrático (SRE), el cual resultó muy bajo, de donde se dedujo su precisión y la potencialidad de LT-PM. Se concluye que si bien el método propuesto resulta eficiente en los casos particulares presentados, se espera que sea una herramienta potencialmente eficiente y útil para otros casos de estudio, particularmente, en aquellos relacionados con aplicaciones prácticas en ciencias e ingeniería.

ABSTRACT The field of differential equations has recently gained attention due to recent developments in science and technology. For this reason, the analysis for the use of new methodologies to solve them has become important. Based on the combination of Laplace Transform method (LT) and Perturbation Method (PM) this article pro- poses the Laplace transform-Perturbation Method (LT-PM) which finds its motivation on the application of LT to linear ordinary differential equations. The goal of this work is to propose a modification of PM - the LT-PM), in order to solve nonlinear perturbative problems with boundary conditions defined on finite intervals. The proposed methodology consisted on the application of LT to the differential equation to solve and then, assuming that its solutions can be expressed as a series of perturbative parameter powers. Thus, the solution of the problem is obtained by systematically applying the transformed inverse LT. The main results of this paper were shown through two case studies, where LT-PM is identified as potentially useful for finding multiple solutions to nonlinear problems. Additionally, the LT-PM enhances the applicability of PM, in some cases of mixed and Neumann boundary conditions, where PM is unsuitable to provide the results. With the purpose of verifying the accuracy of the obtained results, the Square Residual Error (SRE) was calculated. The resulting value was extremely low, which showed the precision and potential of LT-PM. We conclude that, although the proposed method resulted efficient for the case studies presented in this article, it is expected that LT-PM can be a potentially useful tool for other case studies. Particularly those related to the practical applications of science and engineering.

Direct application of Padé approximant for solving nonlinear differential equations.

UNLABELLED: This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. AMS SUBJECT CLASSIFICATION: 34L30.

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

ABSTRACT: In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. AMS SUBJECT CLASSIFICATION: 34L30.

Nonlinearities distribution Laplace transform-homotopy perturbation method.

This article proposes non-linearities distribution Laplace transform-homotopy perturbation method (NDLT-HPM) to find approximate solutions for linear and nonlinear differential equations with finite boundary conditions. We will see that the method is particularly relevant in case of equations with nonhomogeneous non-polynomial terms. Comparing figures between approximate and exact solutions we show the effectiveness of the proposed method.

A handy approximate solution for a squeezing flow between two infinite plates by using of Laplace transform-homotopy perturbation method.

This article proposes Laplace Transform Homotopy Perturbation Method (LT-HPM) to find an approximate solution for the problem of an axisymmetric Newtonian fluid squeezed between two large parallel plates. After comparing figures between approximate and exact solutions, we will see that the proposed solutions besides of handy, are highly accurate and therefore LT-HPM is extremely efficient.

A handy approximation for a mediated bioelectrocatalysis process, related to Michaelis-Menten equation.

In this article, Perturbation Method (PM) is employed to obtain a handy approximate solution to the steady state nonlinear reaction diffusion equation containing a nonlinear term related to Michaelis-Menten of the enzymatic reaction. Comparing graphics between the approximate and exact solutions, it will be shown that the PM method is quite efficient.