This article introduces two approximations that allow the evaluation of Fresnel integrals without the need for using numerical algorithms. These equations accomplish the characteristic of being continuous in the same interval as Fresnel. Both expressions have been determined applying the least squares method to suitable expressions. Accuracy of equations improves as x increases; as for small values of x, it is possible to achieve an absolute error less than 8×10-5. To probe the efficiency of the equations, two case studies are presented, both applied in the optics field. The first case is related to the semi-infinite opaque screen for Fresnel diffraction. In this case study Fresnel integrals are evaluated with the proposed equations to calculate the irradiance distribution and the Cornu spiral for diffraction computations of the Fresnel diffraction; obtained results show a good accuracy. The second case is related to the double aperture problem for Fresnel diffraction.

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.

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.

Feature extraction for speech emotion recognition (SER) has evolved from handcrafted techniques through deep learning methods to embeddings derived from pre-trained models (PTMs). This study presents the first comparative analysis focused on using PTMs for Spanish SER, evaluating six models—Whisper, Wav2Vec 2.0, WavLM, HuBERT, TRILLsson, and CLAP—across six emotional speech databases: EmoMatchSpanishDB, MESD, MEACorpus, EmoWisconsin, INTER1SP, and EmoFilm. We propose a robust framework combining layer-wise feature extraction with Leave-One-Speaker-Out validation to ensure interpretable model comparisons. Our method significantly outperforms existing state-of-the-art benchmarks, notably achieving scores on metrics such as F1 on EmoMatchSpanishDB (88.32%), INTER1SP (99.83%), and MEACorpus (92.53%). Layer-wise analyses reveal optimal emotional representation extraction at early layers in 24-layer models and middle layers in larger architectures. Additionally, TRILLsson exhibits remarkable generalization in speaker-independent evaluations, highlighting the necessity of strategic model selection, fine-tuning, and language-specific adaptations to maximize SER performance for Spanish.

In recent times, autonomous robots have become more relevant, aiming not only to be an extension of mobility and human performance but also allowing them to independently solve specific problems such as finding free-collision paths within some defined environments. In order to achieve this, several techniques have been developed, like action-reaction algorithms, sampling-based algorithms, and deterministic algorithms such as the Homotopy Path Planning Method (HPPM). This work presents, for the first time, a complete deterministic collision-free path planning scheme implemented in FPGA, which is mounted on a Scribbler 2 robot from Parallax. Then, an automatic algorithm of the repulsion parameter for the HPPM method is presented, using as a reference the minimum distance between the center of each obstacle with respect to the homotopic ideal path; furthermore, an algorithm is proposed for discriminating dead-end routes and collision risk trajectories, which allows us to obtain a feasible free-collision path that takes into account the robot dimensions. Besides, comparative performance tests have been carried out against other path-finding methods from the low degrees of freedom (low DoF) and sampling-based planners. Our proposal exhibits path calculation times which are 5 to 10 times faster on FPGA implementation, compared to the other methods and 10 to 100 times faster on PC implementation also compared to the rest. Similar results are obtained with regards to memory consumption, namely 20 to 200 times lower on FPGA implementation and 10 to 100 times lower on PC implementation.

In this paper, we propose a new scheme to find a free-collision path for complex environment maps. This scheme considers the obstacles in the configuration space as prohibited circular areas. Once the obstacles are modelled, the Non-Linear Algebraic Equation System (NAES) is formulated. Next, we apply a Homotopy Path Planning Method (HPPM) to find a set of points that conforms the solution path on the free-space. HPPM uses the Homotopy Continuation Method (HCM) and the Spherical Algorithm (SA) to obtain the solutions of the NAES emanating from the map. In the present work, we propose a scheme for partitioning complex maps into a set of local maps. This is useful for reducing the computation time. Several simulations of complex environment maps with thousands of obstacles are presented. Furthermore, a strategy to obtain the shortest path is applied. Finally, a simulation of the path tracking on Robot Operating System (ROS) for a differential mobile robot is shown.