Autonomous and semiautonomous mobile robots play an important role in making tasks in environments considered hostile or dangerous for a human being. In order to execute many of the required tasks, robots need, in its architecture, a module of navigation with an appropriate path planning algorithm. This paper presents the development and implementation of a methodology for path planning of a mobile robot using a spherical algorithm and homotopy continuation methods (HCMs). The first section is a brief introduction about HCMs. Subsequently, the homotopy path planning method and spherical path tracking algorithm are explained, as well as the upgraded version and its main features. Then, the main contributions of this paper are presented and the effectiveness of the proposed method is proved. Besides, numerical examples, implementation results in multiple platforms including a 32b microcontroller and robot operating system, are displayed. Finally, some favorable results from a comparative between the proposed methodology against sampling-based planners using the open motion planning library are presented.

This work presents the application of the differential transform method (DTM) to the model of pollution for a system of three lakes interconnected by channels. Three input models (periodic, exponentially decaying, and linear) are solved to show that DTM can provide analytical solutions of pollution model in convergent series form. In addition, we present the posttreatment of the power series solutions with the Laplace-Padé resummation method as a useful strategy to extend the domain of convergence of the approximate solutions. The Fehlberg fourth-fifth order Runge-Kutta method with degree four interpolant (RKF45) numerical solution of the lakes system problem is used as a reference to compare with the analytical approximations showing the high accuracy of the results. The main advantage of the proposed technique is that it is based on a few straightforward steps and does not generate secular terms or depend of a perturbation parameter.

Nonlinear differential equations have applications in the modelling area for a broad variety of phenomena and physical processes; having applications for all areas in science and engineering. At the present time, the homotopy perturbation method (HPM) is amply used to solve in an approximate or exact manner such nonlinear differential equations. This method has found wide acceptance for its versatility and ease of use. The origin of the HPM is found in the coupling of homotopy methods with perturbation methods. Homotopy methods are a well established research area with applications, in particular, an applied branch of such methods are the homotopy continuation methods, which are employed on the numerical solution of nonlinear algebraic equation systems. Therefore, this paper presents two modified versions of standard HPM method inspired in homotopy continuation methods. Both modified HPMs deal with nonlinearities distribution of the nonlinear differential equation. Besides, we will use a calcium‐induced calcium released mechanism model as study case to test the proposed techniques. Finally, results will be discussed and possible research lines will be proposed using this work as a starting point.

The assessment of photovoltaic devices, which convert light energy into electricity, has become significantly more relevant due to the aspiration to reduce pollution on a global scale. In this context, the pursuit of optimizing the efficiency of converting light energy into electrical energy involves exhaustive studies and structural analyses of solar cells, all directed toward achieving this goal. This study introduces a research proposal aimed at analyzing the losses associated with series resistance (Rs). The analysis takes into account each component comprising this resistance, proposing a network of resistances that precisely models each of these elements. The aforementioned research focused on simple-structured crystalline silicon cells. During this investigation, the junction depth (xj) of the n-p materials was varied, with the aim of achieving efficiencies in the range of 12%. However, in the pursuit of this desired efficiency, a significant impact on series resistance was observed when analyzing the I-V curves of the cells obtained in each manufacturing process.