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Developments in deep learning for time-series problems have shown promising results for data prediction. Particulate Matter equal or smaller than 10 μm (PM10) have increased importance in the research field due to the negative impact in the respiratory system. PM10 particles show non-linear behavior, hence it is not an easy task to implement techniques to predict subsequent concentration of the particles in the atmosphere. This paper presents a forecasting model using gated Recurrent unit (GRU) and Long-Short Term Memory (LSTM) networks, which are types of a deep recurrent neural network (RNN). The predicted results of PM10 are presented using data of Mexico City as a case study, showing that this type of deep network is feasible for predicting the non-linearities of this type of data. Several experiments were carried out for 12, 24, 48, and 120 h prediction, showing that this method may be applied to accurately forecast the behavior of PM10.

Three-dimensional vision cameras, such as RGB-D, use 3D point cloud to represent scenes. File formats as XYZ and PLY are commonly used to store 3D point information as raw data, this information does not contain further details, such as metadata or segmentation, for the different objects in the scene. Moreover, objects in the scene can be recognized in a posterior process and can be used for other purposes, such as camera calibration or scene segmentation. We are proposing a method to recognize a basketball in the scene using its known dimensions to fit a sphere formula. In the proposed cost function we search for three different points in the scene using RANSAC (Random Sample Consensus). Furthermore, taking into account the fixed basketball size, our method differentiates the sphere geometry from other objects in the scene, making our method robust in complex scenes. In a posterior step, the sphere center is fitted using z-score values eliminating outliers from the sphere. Results show our methodology converges in finding the basketball in the scene and the center precision improves using z-score, the proposed method obtains a significant improvement by reducing outliers in scenes with noise from 1.75 to 8.3 times when using RANSAC alone. Experiments show our method has advantages when comparing with novel deep learning method.

Glaucoma is an eye disease that gradually deteriorates vision. Much research focuses on extracting information from the optic disc and optic cup, the structure used for measuring the cup-to-disc ratio. These structures are commonly segmented with deeplearning techniques, primarily using Encoder–Decoder models, which are hard to train and time-consuming. Object detection models using convolutional neural networks can extract features from fundus retinal images with good precision. However, the superiority of one model over another for a specific task is still being determined. The main goal of our approach is to compare object detection model performance to automate segment cups and discs on fundus images. This study brings the novelty of seeing the behavior of different object detection models in the detection and segmentation of the disc and the optical cup (Mask R-CNN, MS R-CNN, CARAFE, Cascade Mask R-CNN, GCNet, SOLO, Point_Rend), evaluated on Retinal Fundus Images for Glaucoma Analysis (REFUGE), and G1020 datasets. Reported metrics were Average Precision (AP), F1-score, IoU, and AUCPR. Several models achieved the highest AP with a perfect 1.000 when the threshold for IoU was set up at 0.50 on REFUGE, and the lowest was Cascade Mask R-CNN with an AP of 0.997. On the G1020 dataset, the best model was Point_Rend with an AP of 0.956, and the worst was SOLO with 0.906. It was concluded that the methods reviewed achieved excellent performance with high precision and recall values, showing efficiency and effectiveness. The problem of how many images are needed was addressed with an initial value of 100, with excellent results. Data augmentation, multi-scale handling, and anchor box size brought improvements. The capability to translate knowledge from one database to another shows promising results too.

The lack of air quality affects population’s health exposed to it. This makes it a topic of current interest. There are different pollutants that contribute to this problem, such as particulate matter generated mainly by industrial development and traffic flow. The World Health Organization stipulates air quality guidelines globally based in their risk assessment which allows certain airborne pollution. This paper proposes a methodology to improve the prediction of exceedances of PM10 and PM2.5 made by a recurrent long-term/short term memory (LSTM) network using the Ant Colony Optimization (ACO) algorithm. Getting improvements of an averaged 2.57% in accuracy, 1.88% in precision, 3.58% in recall and 3.63% in F1-score using as reference the averaged results obtained with the LSTM network.

The manipulator robots have many applications, such as industrial process, objects translation, process automation, medicine process, etc. Therefore, these kind of robots are studied in many ways. However, most of the reported works use electrical or hydraulic actuators. These actuators have a linear behaviour and the control is easier than pneumatic actuators. The main disadvantages of electrical actuators are the low power-weight rate, the high current related with its load and its weight. The hydraulic actuators are not ecological, needs hydraulic oil which is feedback to the pump. On the other hand, the pneumatic actuators are lighter, faster, having a greater power-weight rate and air feedback is not needed. However, pneumatic actuators are not used into flexible manipulators developing, due to their highly non linear behaviour. In the case of robot dynamic analysis, other researchers have presented the following works. An equations and algorithms are presented in an easy way to understand for all practical robots (Featherstone, 1987), (Featherstone & Orin, 2000), (Khalil & Dombre, 2002). Also, a dynamic simulation is developed to investigate the effects of different profiles into the contact force and the joint torques of a rigid-flexible manipulator (Ata & Johar, 2004). A study of dynamic equations is developed for a robot system holding a rigid object without friction (Gudino-Lau & Arteaga, 2006). Furthermore, a dynamic modeling analysis is developed for parallel robots (Zhaocai & Yueqing, 2008). The link flexibility is considered for system performance and stability. Moreover, an innovative method for simulation is developed (Celentano, 2008) to allow students and researchers, to easily model planar and spatial robots with practical links. However, the reported works are developed using only electrical actuators, not pneumatic actuators. Therefore, this chapter presents how the pneumatic model is used with a two-link flexible robot and its dynamic analysis for the simplified system. Previous researches by the authors include: a simplified thermo-mechanical model for pneumatic actuator has been obtained (Ramos et al., 2006). For animation purposes, the 27

Image pre-processing is a critical stage in computer vision systems, with greater relevance when the input images are captured in outdoor environments because the pictures could contain low contrast and modified colors. A common condition present in outdoor images is haze. In this work, a new dehazing algorithm based on dark channel prior mathematical morphology operations (opening and dilation), and a Gaussian filter, is proposed. Moreover, the proposed algorithm performance is compared qualitatively and quantitatively against previously reported algorithms. Obtained results show that the proposed algorithm requires less processing time providing higher quality dehazing results than other state-of-the-art approaches.

Stable augmented reality applications consist of an accurate registration supported by a robust tracking module. In outdoor locations, the changing environmental and light conditions compromise this tracking. Reliable descriptors under unsettled conditions are essential for this process. The most used descriptors have this distinctive capacity, but computers and mobile devices process them in a long time frame. This paper investigates a new lightweight environment dedicated descriptor (EDD) trained with a machine-learning algorithm. The descriptor analyzes the scene characteristics with elements that can be computed fast and that have distinctive information about the selected area. The complete descriptor is used for semantic feature extraction with the aid of a trained random forest classifier. The descriptor is compared with the most popular descriptors—with respect to speed, accuracy, and invariance to illumination changes, scale, affine transformation, and rotation—and the results show that it is faster and in most cases equally reliable .

The present work presents an improved method to align the measurement scale mark in an immersion hydrometer calibration system of CENAM, the National Metrology Institute (NMI) of Mexico, The proposed method uses a vision system to align the scale mark of the hydrometer to the surface of the liquid where it is immersed by implementing image processing algorithms. This approach reduces the variability in the apparent mass determination during the hydrostatic weighing in the calibration process, therefore decreasing the relative uncertainty of calibration.

This paper describes a novel method for on-line real-time data reduction of radiofrequency (RF) ultrasound signals. The approach is based on a field programmable gate array (FPGA) system intended mainly for steel thickness measurements. Ultrasound data reduction is desirable when: (1) direct measurements performed by an operator are not accessible; (2) it is required to store a considerable amount of data; (3) the application requires measuring at very high speeds; and (4) the physical space for the embedded hardware is limited. All the aforementioned scenarios can be present in applications such as pipeline inspection where data reduction is traditionally performed on-line using pipeline inspection gauges (PIG). The method proposed in this work consists of identifying and storing in real-time only the time of occurrence (TOO) and the maximum amplitude of each echo present in a given RF ultrasound signal. The method is tested with a dedicated immersion system where a significant data reduction with an average of 96.5% is achieved.

The use of Recurrence plots have been extensively used in various fields. In this work, Recurrence Plots (RPs) investigates the changes in the non-linear behaviour of urban air pollution using large datasets of raw data (hourly). This analysis has not been used before to extract information from large datasets for this type non-linear problem. Two different approaches have been used to tackle this problem. The first approach is to show results according to monitoring network. The second approach is to show the results by particle type. This analysis shows the feasibility of using Recurrence Analysis for pollution monitoring and control.

Background A needle placement system using a serial robot arm for manipulation of biopsy and/or treatment needles is introduced. A method for fast calibration of the robot and the preliminary accuracy tests of the robotic system are presented. Methods The setup consists of a DLR/KUKA Light Weight Robot III especially designed for safe human/robot interaction mounted on a mobile platform, a robot-driven angiographic C-arm system and a navigation system. Results Calibration of the robot with the navigation system has a residual error of 0.23 mm (rms) with a standard deviation of ± 0.1 mm. Needle targeting accuracy with different trajectories was 1.2 mm (rms) with a standard deviation of ± 0.4 mm. Conclusions Robot absolute positioning accuracy was reduced to the navigation camera accuracy. The approach includes control strategies that may be very useful for interventional applications. Copyright © 2011 John Wiley & Sons, Ltd.

An improved method which considers the use of Fourier and wavelet transform based analysis to infer and extract 3D information from an object by fringe projection on it is presented. This method requires a single image which contains a sinusoidal white light fringe pattern projected on it, and this pattern has a known spatial frequency and its information is used to avoid any discontinuities in the fringes with high frequency. Several computer simulations and experiments have been carried out to verify the analysis. The comparison between numerical simulations and experiments has proved the validity of this proposed method.

This paper presents a simulation methodology proposal, applying a multilanguage technique to simulate a mechatronic system. Firstly, a way to interact between two programming languages is presented, by taking advantage of each language to facilitate the development of a complex simulation tool. Later, the mechanical structure is obtained in VRML format. Next, special software is used to compute the mathematical model for kinematics and dynamic behavior. The results are showed by graphical simulation with Graphic Libraries support. Finally, the methodology is applied to flexible manipulator with one degree of freedom as study case, and the graphical simulation is presented.

In various applications of computer vision, there is the need to calibrate the coordinate systems of different elements respect to one another in order to have a proper perspective of the objects in the scene. In the field of computer assisted surgery (CAS) we encounter this problem in many applications, like navigation of surgical tools, surgical robotics, etc. This paper proposes an estimate calibration by means of the extraction of points of a grid plane pattern and the pair point method getting a proper calibration of an optical stereo-tracker with a videometric system. As a result, we obtained a calibration that allows to track the pose of a webcam within the working space of a stereo-tracker. This procedure will allow us to use this method to calibrate different navigated tools that have a videometric system attached.

In this paper, a high-speed digital processed microscopic observational system for telemicrooperation is proposed with a dynamic focusing system and a high-speed digital-processing system using the "depth from focus" criterion. In our previous work [10], we proposed a system that could simultaneously obtain an "all-in-focus image" as well as the "depth" of an object. In reality, in a microoperation, it is not easy to obtain good visibility of objects with a microscope focused at a shallow depth, especially in microsurgery and DNA studies, among other procedures. In this sense, the all-in-focus image, which keeps an in-focus texture over the entire object, is useful for observing microenvironments with the microscope. However, one drawback of the all-in-focus image is that there is no information about the objects' depth. It is also important to obtain a depth map and show the 3D microenvironments at any view angle in real time to actuate the microobjects. Our earlier system with a dynamic focusing lens and a smart sensor could obtain the all-in-focus image and the depth in 2s. To realize real-time microoperation, a system that could process at least 30 frames per second (60 times faster than the previous system) would be required. This paper briefly reviews the depth from focus criterion to Simultaneously achieve the all-in-focus image and the reconstruction of 3D microenvironments. After discussing the problem inherent in our earlier system, a frame-rate system constructed with a high-speed video camera and FPGA (field programmable gate array) hardware is discussed. To adapt this system for use with the microscope, new criteria to solve the "ghost problem" in reconstructing the all-in-focus image are proposed, Finally, microobservation shows the validity of this system.

In this paper, an observational sensor system for tele-micro-operation is proposed with a dynamic focusing lens and a smart vision sensor using the 'depth from focus' criteria. Recently, micro-operations, such as for micro-surgery, DNA manipulations, etc., have gained in importance. However, the small depth of focus of the microscope produces poor observability. For example, if the focus is on the object, the actuator cannot be seen with the microscope. On the other hand, if the focus is on the actuator, the object cannot be observed. In this sense, the 'all-in-focus image', which holds the in-focused texture all over the image, is useful to observe the micro-environments with a microscope. One drawback of the all-in-focus image is that there is no information about the depth of objects. It is also important to obtain the depth map and show the three-dimensional (3D) micro virtual environments in real-time to actuate the micro objects intuitively. First, this paper reviews the criteria of 'depth from focu...

In this paper, a real time virtual reality camera system for the micro environments has been developed with a dynamic focusing lens and a smart vision sensor using the "depth from focus" criteria.In the operation with a microscope, such as the micro-surgery, DNA operation and etc., the small depth of a focus makes bad controllability to actuate 3D micro objects with actuators. For example, if the focus is on the object, the actuator could not be seen in the microscope. On the other hand, if the focus is on the actuator, the object could not be observed. In this sense, the "all-in-focus image" is useful for the actuation in micro environments. However, one drawback on the all-in-focus image is that there is no information about the depth of objects. It is also important to reconstruct the micro 3D environments in real time to actuate the object with the micro virtual environments.This paper discusses the criteria of "depth from focus" to achieve the all-in-focus image and micro 3D reconstruction, simultaneously. Then, a micro VR camera system has been developed to achieve the micro VR environments with the "depth from focus" criteria, i.e. the combination of the all-in-focus image and the micro 3D reconstruction. This system is constructed by a dynamic focusing lens, which can change the focus in high frequency, and a smart vision system, which is capable in capturing and processing the image data in high speed with SIMD architecuture.

In this paper, we propose a modified face authentication method based on the image preprocessing (histogram equalization, HE) and with SURF algorithm (Speeded Up Robust Features) in the feature extraction step. In particular, our methodology aims at determining a person’s authenticity when he/she has a few facial expressions, different backgrounds or a variance in lighting. We evaluated the performance of this method using public face databases like The Extended Cohn-Kanade Dataset (CK+) and Caltech Faces. We made some test using sixty images (thirty per database), Equal (E) or Different (D) and according to the match between images (for example Image 1 and Image 2) and a defined threshold, our method determines if a person is authenticated or not. The results showed that with the database CK+ was obtained 93% and with Caltech Faces 86% of accuracy in the authentication process, these results were compared with those obtained by some algorithms like LDA, PCA, SIFT and SURF (without preprocessing) and we can conclude that the authentication rate was improved.

In this research, an improved method for three-dimensional shape measurement by fringe projection is presented. The use of Fourier and Wavelet transform based analysis to extract the 3D information from the objects is proposed. The method requires a single image which contains a sinusoidal white light fringe pattern projected on it. This fringe pattern has a known spatial frequency and this information is used to avoid the discontinuities in the fringes with high frequency. Several computer simulations and experiments have been carried out to verify the analysis. The comparison between numerical simulations and experiments has proved the validity of this proposed method.

The flexible manipulators have many industrial applications; but most of the reported works are using electrical or hydraulic actuators. These actuators have a linear behaviour and the control is easier than pneumatic actuators; but the pneumatic position control is a highly non linear problem, due to the air compressibility behaviour and internal friction (Moore & Pu, 1993). Because of these conditions, there are certain difficulties in pneumatics cylinder control design. The main disadvantage of electrical actuators is the low powerweight rate, the high current related with its load and it is heavy. The hydraulic actuators are not ecological, needs hydraulic oil and return lines to the pump is needed. By the other hand, the pneumatic actuators are clean, economy, light, faster, have a great power-weight rate and return lines are not needed. However, pneumatic actuators are not used into flexible manipulators developed due to their highly non linear behaviour. It is important to note that research lines; such as pneumatic control, embedded systems and flexible manipulators, are used in separate way. As a matter of fact, most of manipulators robots use electric or hydraulic actuators; however, the pneumatic actuators are being used in recent years (Ramos at al, 2006a; Ramos et al, 2006b) to control a flexible manipulator arm. This is the beginning of a project which involves the use of a pneumatic cylinder to control a flexible manipulator robot. Our first approach is to use one degree of freedom, but the main goal is to have a two degree of freedom flexible manipulator. Several pneumatic controllers had been developed; for example, the Model Reference Adaptive Control, MRAC (Suarez & Luis, 2005); however, the pneumatic model used for the control design, have the next considerations; a lineal actuator, a lineal valve, without damping systems at the sides, ideal gas, adiabatic changes and constant viscous friction. Other works have been focused in friction parameter identification techniques of cylinder pneumatic (Wang & Wang, 2004), dynamic modelling and simulation (Jozsef & Claude

In this paper, a new application system with high speed photography, i.e. an observational system for the tele-micro-operation, has been proposed with a dynamic focusing system and a high-speed image processing system using the "Depth From Focus (DFF)" criteria. In micro operation, such as for the microsurgery, DNA operation and etc., the small depth of a focus on the microscope makes bad observation. For example, if the focus is on the object, the actuator cannot be seen with the microscope. On the other hand, if the focus is on the actuator, the object cannot be observed. In this sense, the "all-in-focus image," which holds the in-focused texture all over the image, is useful to observe the microenvironments on the microscope. It is also important to obtain the "depth map" which could show the 3D micro virtual environments in real-time to actuate the micro objects, intuitively. To realize the real-time micro operation with DFF criteria, which has to integrate several images to obtain "all-in-focus image" and "depth map," at least, the 240 frames par second based image capture and processing system should be required. At first, this paper briefly reviews the criteria of "depth from focus" to achieve the all-in-focus image and the 3D microenvironments' reconstruction, simultaneously. After discussing the problem in our past system, a new frame-rate system is constructed with the high-speed video camera and FPGA hardware with 240 frames par second. To apply this system in the real microscope, a new criterion "ghost filtering" technique to reconstruct the all-in-focus image is proposed. Finally, the micro observation shows the validity of this system.

2001, 【要旨】

"One of the most efficient ways to avoid hazards is to do it in the design phase; for that, a risk analysis should be made in order to evaluate the risks exposure to hazards. The EN ISO 12100 is a standard that pecifies basic terminology, principles and methodology to achieve safety in the design of machinery. It specifies the principles of risks assessment and risk reduction to help designer to identify risk during the design stage of machine production to complete a safe design. The correct use of this guidelines will lead to a machine which fulfil all the safety requirements that are demanded in their application area. Once a machine is ready to hit the market, the manufacturer must declare that all directives that apply to the product have been considered, affirming in that way that their product is safe. The CE Marking on a product is a manufacture’s declaration that the product complies with the essential requirements of the relevant European health, safety and environmental protection legislation. The “CE” stands for “Communauté Européenne” which literally means “European Conformity”. In the European Union only safe system are implemented in the market, this is why all the products have the CE Marking also referred to as the “Passport to Europe”. All the previous concepts and standards are well known by the big companies however for small companies and educational environments these safety concepts are not o clear, thus the aim of this master’s thesis is to introduce basic safety concepts into the educational environment, these concept will be introduced gradually by following the design’s guideline of the EN ISO 12100. The work carried out in this Thesis acts a base to understand the basic concepts of risk assessment in the design process of a machine and must be developed and improved further to incorporate additional safety sensors and additional features to make the demonstrator more user friendly and functional. "

Este trabajo propone una técnica para reconstruir imágenes en 3D, utilizando transformada Wavelet unideimensional, tres de ellas principalmente, la Morlet, la Shannon y la B-Spline, se mostrarán resultados gráficos de cada una de ellas con dos tipos de objetos, virtuales y reales.

"Este trabajo describe una técnica novedosa para la reducción de señales de radiofrecuencia de ultrasonido en tiempo real. La técnica se implementa en hardware, específicamente en un arreglo de compuertas programables en campo (FPGA), aprovechando sus propiedades de paralelización. La reducción de las señales de ultrasonido es deseable cuando: las instalaciones no son accesible para que una persona realice la inspección; se necesite almacenar una cantidad considerable de información; la aplicación requiera que se realice la inspección a velocidades muy altas; y el espacio físico para el hardware embebido es limitado. Todos estos escenarios están presentes en la inspección automática de ductos, donde se utilizan dispositivos de inspección los cuales tradicionalmente reducen la información en línea. La técnica de reducción propuesta consiste en identificar y almacenar en tiempo real sólo el tiempo de ocurrencia y la amplitud máxima correspondiente de cada eco presente en una señal de radiofrecuencia de ultrasonido dada. La técnica se probó con un sistema de inmersión dedicado, donde se logró una reducción significativa de la información, en promedio del 96,5%."

"En el lenguaje utilizado en el mantenimiento e inspección de ductos de hidrocarburos, un diablo o pig es un artefacto empleado para limpiar o inspeccionar un ducto. Es insertado en la tubería y es arrastrado por el flujo del petróleo o gas. De acuerdo con la información que generan los diablos instrumentados durante la inspección de una tubería en la cual se transportan hidrocarburos principalmente, es necesario la extracción, organización, análisis y tratamiento de ésta, así como de la presentación gráfica de los resultados obtenidos. En este trabajo se desarrolla un software que permite el tratamiento de la información en un diablo geómetra, desarrollado por CIDESI, así como la reconstrucción virtual de una tubería a partir de la información analizada. El desarrollo de la tubería virtual se realiza utilizando las librerías de OpenGL, bajo una plataforma del lenguaje C++ de Builder. En el software se crea una escena donde el usuario puede ir recorriendo la tubería como si estuviera recorriendo (dentro o fuera), una cámara de video a través o sobre la tubería en cuestión. La creación e identificación de los defectos que durante la inspección fueron detectados son representados a través de un código de colores o incluso agregando una marca a la tubería virtual, para que al usuario le sea más sencillo la ubicación de las mismas. Aquí se presenta cómo se crea el mallado de la tubería, así también, cómo se identifica el grado de defecto encontrado. Por otro lado se plantea cómo permite interactuar con el usuario por medio de selección de zonas de la tubería para poder realizar un mallado más fino de pequeñas zonas que se requiere examinar con mayor detalle. 3 Para realizar un detalle mayor de la tubería se prueban algunos métodos para el suavizado de las curvas, como son la duplicación de puntos de vértices, la parametrización de las líneas y la utilización de curvas de Bezier."

"This thesis presents a human/robot interaction in pick & place operations with optical tracking. The optical tracking consisted of in a complete vision system. It was developed using OpenCV Library integrated in Qt creator. A graphical user interface was designed, which contains the necessary requirements in order to achieve an optical tracking. The whole project is based on three main algorithms: Camera Calibration Algorithm, Object Detection Algorithm and Tracking algorithm. A webcam is used for capturing video. Hence the camera calibration has to be carried out. The parameters from the calibration are applied for solving the radial distortion. Handling of objects is the main goal. An object detection method is realized, which is based on geometry of the objects. The geometry is analyzed through a contour processing. Therefore the Canny Edge Detection algorithm is applied. The detection for the mark is the same method used for the objects. Optical tracking is achieved using the CamShift algorithm. CamShift permits to track the mark through camera view, and it is always possible to know the actual position of the mark. The main functions are provided from OpenCV Library, tests and comparisons between them were realized in order to obtain a better response. The robot system consists of an industrial robot with 6 degrees of freedom. This robot is mounted to a gantry robot. A gripper for the pick & place operation has been mounted onto the robot. The communication within the system robots and user interface was based on network technology. The final results obtained from each algorithm were completely successfully. The camera calibration algorithm was able to solve the radial distortion. Therefore the response of the object detection algorithm was a linear response. Due to undistortion the system presented high accuracy. The tracking based on CamShift algorithm is one of the functions that OpenCV Library provides. The definition of the color as feature to tracking is a powerful option for this application."

"En este trabajo se presenta una propuesta para generar automáticamente trayectorias para un robot manipulador, específicamente el robot manipulador Melfa RV-2AJ de Mitsubishi, a partir del procesamiento digital de imágenes y el uso de herramientas matemáticas. El proyecto consiste en adquirir una imagen de un objeto (o figura) del cual se desea conocer su contorno asociado. El cual representa la trayectoria que debe reproducir el robot manipulador. Como primer punto se adquiere la imagen y se le aplica el tratamiento correspondiente, para obtener una imagen binaria y finalmente el contorno asociado al objeto de la imagen. El contorno se guarda en dos vectores x e y, correspondientes a la posición en el plano del contorno, de este par de vectores se discriminan algunos puntos, en función a la geometría del contorno del objeto, ya a que el número inicial de puntos de estos vectores en algunos casos los hace inmanejables para el robot manipulador. A los puntos seleccionados de la discriminación de puntos de los vectores x e y, se les aplica un par de interpolaciones paramétricas, una interpolación circular segmentaría y otra interpolación polinómica segmentaría (splines). De acuerdo a una evaluación y a sus ventajas la interpolación por splines es mejor que la interpolación circular y por consiguiente es la más utilizada, sobre todo para realizar las interpolaciones en robótica. Sin embargo, el robot RV2- AJ sólo cuenta con la interpolación circular, lo que hace que sea necesario utilizarla, para poder validar todo el procedimiento. Así la interpolación por splines sólo puede ser evaluada hasta una etapa de simulación y la interpolación circular hasta la etapa experimental. De la interpolación por splines (que son polinomios cúbicos y por consiguiente fácilmente diferenciables), se obtienen los vectores tangentes y normales al contorno. Vectores que representan la orientación en el espacio de dicho contorno. Para los cálculos de la cinemática inversa y la generación de la trayectoria del robot manipulador, es necesario conocer la posición y orientación en el espacio de la trayectoria que se desea seguir. La posición se conoce procesando la imagen, obteniendo el contorno y la orientación determinando los vectores tangentes y normales de la interpolación, la cinemática se resuelve y se genera la trayectoria del robot manipulador. Los resultados de los cálculos de la cinemática inversa son escalados a las dimensiones reales y se utilizan pa