912 resultados para Robot manipulators
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Nowadays robots have made their way into real applications that were prohibitive and unthinkable thirty years ago. This is mainly due to the increase in power computations and the evolution in the theoretical field of robotics and control. Even though there is plenty of information in the current literature on this topics, it is not easy to find clear concepts of how to proceed in order to design and implement a controller for a robot. In general, the design of a controller requires of a complete understanding and knowledge of the system to be controlled. Therefore, for advanced control techniques the systems must be first identified. Once again this particular objective is cumbersome and is never straight forward requiring of great expertise and some criteria must be adopted. On the other hand, the particular problem of designing a controller is even more complex when dealing with Parallel Manipulators (PM), since their closed-loop structures give rise to a highly nonlinear system. Under this basis the current work is developed, which intends to resume and gather all the concepts and experiences involve for the control of an Hydraulic Parallel Manipulator. The main objective of this thesis is to provide a guide remarking all the steps involve in the designing of advanced control technique for PMs. The analysis of the PM under study is minced up to the core of the mechanism: the hydraulic actuators. The actuators are modeled and experimental identified. Additionally, some consideration regarding traditional PID controllers are presented and an adaptive controller is finally implemented. From a macro perspective the kinematic and dynamic model of the PM are presented. Based on the model of the system and extending the adaptive controller of the actuator, a control strategy for the PM is developed and its performance is analyzed with simulation.
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Esta tesis se centra en desarrollo de tecnologías para la interacción hombre-robot en entornos nucleares de fusión. La problemática principal del sector de fusión nuclear radica en las condiciones ambientales tan extremas que hay en el interior del reactor, y la necesidad de que los equipos cumplan requisitos muy restrictivos para poder aguantar esos niveles de radiación, magnetismo, ultravacío, temperatura... Como no es viable la ejecución de tareas directamente por parte de humanos, habrá que utilizar dispositivos de manipulación remota para llevar a cabo los procesos de operación y mantenimiento. En las instalaciones de ITER es obligatorio tener un entorno controlado de extrema seguridad, que necesita de estándares validados. La definición y uso de protocolos es indispensable para regir su buen funcionamiento. Si nos centramos en la telemanipulación con algo grado de escalado, surge la necesidad de definir protocolos para sistemas abiertos que permitan la interacción entre equipos y dispositivos de diversa índole. En este contexto se plantea la definición del Protocolo de Teleoperación que permita la interconexión entre dispositivos maestros y esclavos de distinta tipología, pudiéndose comunicar bilateralmente entre sí y utilizar distintos algoritmos de control según la tarea a desempeñar. Este protocolo y su interconectividad se han puesto a prueba en la Plataforma Abierta de Teleoperación (P.A.T.) que se ha desarrollado e integrado en la ETSII UPM como una herramienta que permita probar, validar y realizar experimentos de telerrobótica. Actualmente, este Protocolo de Teleoperación se ha propuesto a través de AENOR al grupo ISO de Telerobotics como una solución válida al problema existente y se encuentra bajo revisión. Con el diseño de dicho protocolo se ha conseguido enlazar maestro y esclavo, sin embargo con los niveles de radiación tan altos que hay en ITER la electrónica del controlador no puede entrar dentro del tokamak. Por ello se propone que a través de una mínima electrónica convenientemente protegida se puedan multiplexar las señales de control que van a través del cableado umbilical desde el controlador hasta la base del robot. En este ejercicio teórico se demuestra la utilidad y viabilidad de utilizar este tipo de solución para reducir el volumen y peso del cableado umbilical en cifras aproximadas de un 90%, para ello hay que desarrollar una electrónica específica y con certificación RadHard para soportar los enormes niveles de radiación de ITER. Para este manipulador de tipo genérico y con ayuda de la Plataforma Abierta de Teleoperación, se ha desarrollado un algoritmo que mediante un sensor de fuerza/par y una IMU colocados en la muñeca del robot, y convenientemente protegidos ante la radiación, permiten calcular las fuerzas e inercias que produce la carga, esto es necesario para poder transmitirle al operador unas fuerzas escaladas, y que pueda sentir la carga que manipula, y no otras fuerzas que puedan influir en el esclavo remoto, como ocurre con otras técnicas de estimación de fuerzas. Como el blindaje de los sensores no debe ser grande ni pesado, habrá que destinar este tipo de tecnología a las tareas de mantenimiento de las paradas programadas de ITER, que es cuando los niveles de radiación están en sus valores mínimos. Por otro lado para que el operador sienta lo más fielmente posible la fuerza de carga se ha desarrollado una electrónica que mediante el control en corriente de los motores permita realizar un control en fuerza a partir de la caracterización de los motores del maestro. Además para aumentar la percepción del operador se han realizado unos experimentos que demuestran que al aplicar estímulos multimodales (visuales, auditivos y hápticos) aumenta su inmersión y el rendimiento en la consecución de la tarea puesto que influyen directamente en su capacidad de respuesta. Finalmente, y en referencia a la realimentación visual del operador, en ITER se trabaja con cámaras situadas en localizaciones estratégicas, si bien el humano cuando manipula objetos hace uso de su visión binocular cambiando constantemente el punto de vista adecuándose a las necesidades visuales de cada momento durante el desarrollo de la tarea. Por ello, se ha realizado una reconstrucción tridimensional del espacio de la tarea a partir de una cámara-sensor RGB-D, lo cual nos permite obtener un punto de vista binocular virtual móvil a partir de una cámara situada en un punto fijo que se puede proyectar en un dispositivo de visualización 3D para que el operador pueda variar el punto de vista estereoscópico según sus preferencias. La correcta integración de estas tecnologías para la interacción hombre-robot en la P.A.T. ha permitido validar mediante pruebas y experimentos para verificar su utilidad en la aplicación práctica de la telemanipulación con alto grado de escalado en entornos nucleares de fusión. Abstract This thesis focuses on developing technologies for human-robot interaction in nuclear fusion environments. The main problem of nuclear fusion sector resides in such extreme environmental conditions existing in the hot-cell, leading to very restrictive requirements for equipment in order to deal with these high levels of radiation, magnetism, ultravacuum, temperature... Since it is not feasible to carry out tasks directly by humans, we must use remote handling devices for accomplishing operation and maintenance processes. In ITER facilities it is mandatory to have a controlled environment of extreme safety and security with validated standards. The definition and use of protocols is essential to govern its operation. Focusing on Remote Handling with some degree of escalation, protocols must be defined for open systems to allow interaction among different kind of equipment and several multifunctional devices. In this context, a Teleoperation Protocol definition enables interconnection between master and slave devices from different typologies, being able to communicate bilaterally one each other and using different control algorithms depending on the task to perform. This protocol and its interconnectivity have been tested in the Teleoperation Open Platform (T.O.P.) that has been developed and integrated in the ETSII UPM as a tool to test, validate and conduct experiments in Telerobotics. Currently, this protocol has been proposed for Teleoperation through AENOR to the ISO Telerobotics group as a valid solution to the existing problem, and it is under review. Master and slave connection has been achieved with this protocol design, however with such high radiation levels in ITER, the controller electronics cannot enter inside the tokamak. Therefore it is proposed a multiplexed electronic board, that through suitable and RadHard protection processes, to transmit control signals through an umbilical cable from the controller to the robot base. In this theoretical exercise the utility and feasibility of using this type of solution reduce the volume and weight of the umbilical wiring approximate 90% less, although it is necessary to develop specific electronic hardware and validate in RadHard qualifications in order to handle huge levels of ITER radiation. Using generic manipulators does not allow to implement regular sensors for force feedback in ITER conditions. In this line of research, an algorithm to calculate the forces and inertia produced by the load has been developed using a force/torque sensor and IMU, both conveniently protected against radiation and placed on the robot wrist. Scaled forces should be transmitted to the operator, feeling load forces but not other undesirable forces in slave system as those resulting from other force estimation techniques. Since shielding of the sensors should not be large and heavy, it will be necessary to allocate this type of technology for programmed maintenance periods of ITER, when radiation levels are at their lowest levels. Moreover, the operator perception needs to feel load forces as accurate as possible, so some current control electronics were developed to perform a force control of master joint motors going through a correct motor characterization. In addition to increase the perception of the operator, some experiments were conducted to demonstrate applying multimodal stimuli (visual, auditory and haptic) increases immersion and performance in achieving the task since it is directly correlated with response time. Finally, referring to the visual feedback to the operator in ITER, it is usual to work with 2D cameras in strategic locations, while humans use binocular vision in direct object manipulation, constantly changing the point of view adapting it to the visual needs for performing manipulation during task procedures. In this line a three-dimensional reconstruction of non-structured scenarios has been developed using RGB-D sensor instead of cameras in the remote environment. Thus a mobile virtual binocular point of view could be generated from a camera at a fixed point, projecting stereoscopic images in 3D display device according to operator preferences. The successful integration of these technologies for human-robot interaction in the T.O.P., and validating them through tests and experiments, verify its usefulness in practical application of high scaling remote handling at nuclear fusion environments.
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Image Based Visual Servoing (IBVS) is a robotic control scheme based on vision. This scheme uses only the visual information obtained from a camera to guide a robot from any robot pose to a desired one. However, IBVS requires the estimation of different parameters that cannot be obtained directly from the image. These parameters range from the intrinsic camera parameters (which can be obtained from a previous camera calibration), to the measured distance on the optical axis between the camera and visual features, it is the depth. This paper presents a comparative study of the performance of D-IBVS estimating the depth from three different ways using a low cost RGB-D sensor like Kinect. The visual servoing system has been developed over ROS (Robot Operating System), which is a meta-operating system for robots. The experiments prove that the computation of the depth value for each visual feature improves the system performance.
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Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40
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Safe collaboration between a robot and human operator forms a critical requirement for deploying a robotic system into a manufacturing and testing environment. In this dissertation, the safety requirement for is developed and implemented for the navigation system of the mobile manipulators. A methodology for human-robot co-existence through a 3d scene analysis is also investigated. The proposed approach exploits the advance in computing capability by relying on graphic processing units (GPU’s) for volumetric predictive human-robot contact checking. Apart from guaranteeing safety of operators, human-robot collaboration is also fundamental when cooperative activities are required, as in appliance test automation floor. To achieve this, a generalized hierarchical task controller scheme for collision avoidance is developed. This allows the robotic arm to safely approach and inspect the interior of the appliance without collision during the testing procedure. The unpredictable presence of the operators also forms dynamic obstacle that changes very fast, thereby requiring a quick reaction from the robot side. In this aspect, a GPU-accelarated distance field is computed to speed up reaction time to avoid collision between human operator and the robot. An automated appliance testing also involves robotized laundry loading and unloading during life cycle testing. This task involves Laundry detection, grasp pose estimation and manipulation in a container, inside the drum and during recovery grasping. A wrinkle and blob detection algorithms for grasp pose estimation are developed and grasp poses are calculated along the wrinkle and blobs to efficiently perform grasping task. By ranking the estimated laundry grasp poses according to a predefined cost function, the robotic arm attempt to grasp poses that are more comfortable from the robot kinematic side as well as collision free on the appliance side. This is achieved through appliance detection and full-model registration and collision free trajectory execution using online collision avoidance.
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The industrial context is changing rapidly due to advancements in technology fueled by the Internet and Information Technology. The fourth industrial revolution counts integration, flexibility, and optimization as its fundamental pillars, and, in this context, Human-Robot Collaboration has become a crucial factor for manufacturing sustainability in Europe. Collaborative robots are appealing to many companies due to their low installation and running costs and high degree of flexibility, making them ideal for reshoring production facilities with a short return on investment. The ROSSINI European project aims to implement a true Human-Robot Collaboration by designing, developing, and demonstrating a modular and scalable platform for integrating human-centred robotic technologies in industrial production environments. The project focuses on safety concerns related to introducing a cobot in a shared working area and aims to lay the groundwork for a new working paradigm at the industrial level. The need for a software architecture suitable to the robotic platform employed in one of three use cases selected to deploy and test the new technology was the main trigger of this Thesis. The chosen application consists of the automatic loading and unloading of raw-material reels to an automatic packaging machine through an Autonomous Mobile Robot composed of an Autonomous Guided Vehicle, two collaborative manipulators, and an eye-on-hand vision system for performing tasks in a partially unstructured environment. The results obtained during the ROSSINI use case development were later used in the SENECA project, which addresses the need for robot-driven automatic cleaning of pharmaceutical bins in a very specific industrial context. The inherent versatility of mobile collaborative robots is evident from their deployment in the two projects with few hardware and software adjustments. The positive impact of Human-Robot Collaboration on diverse production lines is a motivation for future investments in research on this increasingly popular field by the industry.
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In this paper, nonlinear dynamic equations of a wheeled mobile robot are described in the state-space form where the parameters are part of the state (angular velocities of the wheels). This representation, known as quasi-linear parameter varying, is useful for control designs based on nonlinear H(infinity) approaches. Two nonlinear H(infinity) controllers that guarantee induced L(2)-norm, between input (disturbances) and output signals, bounded by an attenuation level gamma, are used to control a wheeled mobile robot. These controllers are solved via linear matrix inequalities and algebraic Riccati equation. Experimental results are presented, with a comparative study among these robust control strategies and the standard computed torque, plus proportional-derivative, controller.
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This work presents an automated system for the measurement of form errors of mechanical components using an industrial robot. A three-probe error separation technique was employed to allow decoupling between the measured form error and errors introduced by the robotic system. A mathematical model of the measuring system was developed to provide inspection results by means of the solution of a system of linear equations. A new self-calibration procedure, which employs redundant data from several runs, minimizes the influence of probes zero-adjustment on the final result. Experimental tests applied to the measurement of straightness errors of mechanical components were accomplished and demonstrated the effectiveness of the employed methodology. (C) 2007 Elsevier Ltd. All rights reserved.
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Simulated annealing (SA) is an optimization technique that can process cost functions with degrees of nonlinearities, discontinuities and stochasticity. It can process arbitrary boundary conditions and constraints imposed on these cost functions. The SA technique is applied to the problem of robot path planning. Three situations are considered here: the path is represented as a polyline; as a Bezier curve; and as a spline interpolated curve. In the proposed SA algorithm, the sensitivity of each continuous parameter is evaluated at each iteration increasing the number of accepted solutions. The sensitivity of each parameter is associated to its probability distribution in the definition of the next candidate. (C) 2010 Elsevier Ltd. All rights reserved.
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Background: Posterior reconstruction (PR) of the rhabdosphincter has been previously described during retropubic radical prostatectomy, and shorter times to return of urinary continence were reported using this technical modification. This technique has also been applied during robot-assisted radical prostatectomy (RARP); however, contradictory results have been reported. Objective: We describe here a modified technique for PR of the rhabdosphincter during RARP and report its impact on early recovery of urinary continence and on cystographic leakage rates. Design, setting, and participants: We analyzed 803 consecutive patients who underwent RARP by a single surgeon over a 12-mo period: 330 without performing PR and 473 with PR. Surgical procedure: The reconstruction was performed using two 6-in 3-0 Poliglecaprone sutures tied together. The free edge of the remaining Denonvillier`s fascia was identified after prostatectomy and approximated to the posterior aspect of the rhabdosphincter and the posterior median raphe using one arm of the continuous suture. The second layer of the reconstruction was then performed with the other arm of the suture, approximating the posterior lip of the bladder neck and vesicoprostatic muscle to the posterior urethral edge. Measurements: Continence rates were assessed with a self-administrated, validated questionnaire (Expanded Prostate Cancer Index Composite) at 1, 4, 12, and 24 wk after catheter removal. Continence was defined as the use of ""no absorbent pads."" Cystogram was performed in all patients on postoperative day 4 or 5 before catheter removal. Results and limitations: There was no significant difference between the groups with respect to patient age, body mass index, prostate-specific antigen levels, prostate weight, American Urological Association symptom score, estimated blood loss, operative time, number of nerve-sparing procedures, and days with catheter. In the PR group, the continence rates at 1, 4, 12, and 24 wk postoperatively were 22.7%, 42.7%, 91.8%, and 96.3%, respectively; in the non-PR group, the continence rates were 28.7%, 51.6%, 91.1%, and 97%, respectively. The modified PR technique resulted in significantly higher continence rates at 1 and 4 wk after catheter removal (p = 0.048 and 0.016, respectively), although the continence rates at 12 and 24 wk were not significantly affected (p = 0.908 and p = 0.741, respectively). The median interval to recovery of continence was also statistically significantly shorter in the PR group (median: 4 wk; 95% confidence interval [CI]: 3.39-4.61) when compared to the non-PR group (median: 6 wk; 95% CI: 5.18-6.82; log-rank test, p = 0.037). Finally, the incidence of cystographic leaks was lower in the PR group (0.4% vs 2.1%; p = 0.036). Although the patients` baseline characteristics were similar between the groups, the patients were not preoperatively randomized and unknown confounding factors may have influenced the results. Conclusions: Our modified PR combines the benefits of early recovery of continence reported with the original PR technique with a reinforced watertight closure of the posterior anastomotic wall. Shorter interval to recovery of continence and lower incidence of cystographic leaks were demonstrated with our PR technique when compared to RARP with no reconstruction. (C) 2010 European Association of Urology. Published by Elsevier B.V. All rights reserved.
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Background: Positive surgical margin (PSM) after radical prostatectomy (RP) has been shown to be an independent predictive factor for cancer recurrence. Several investigations have correlated clinical and histopathologic findings with surgical margin status after open RP. However, few studies have addressed the predictive factors for PSM after robot-assisted laparoscopic RP (RARP). Objective: We sought to identify predictive factors for PSMs and their locations after RARP. Design, setting, and participants: We prospectively analyzed 876 consecutive patients who underwent RARP from January 2008 to May 2009. Intervention: All patients underwent RARP performed by a single surgeon with previous experience of > 1500 cases. Measurements: Stepwise logistic regression was used to identify potential predictive factors for PSM. Three logistic regression models were built: (1) one using preoperative variables only, (2) another using all variables (preoperative, intraoperative, and postoperative) combined, and (3) one created to identify potential predictive factors for PSM location. Preoperative variables entered into the models included age, body mass index (BMI), prostate-specific antigen, clinical stage, number of positive cores, percentage of positive cores, and American Urological Association symptom score. Intra-and postoperative variables analyzed were type of nerve sparing, presence of median lobe, percentage of tumor in the surgical specimen, gland size, histopathologic findings, pathologic stage, and pathologic Gleason grade. Results and limitations: In the multivariable analysis including preoperative variables, clinical stage was the only independent predictive factor for PSM, with a higher PSM rate for T3 versus T1c (odds ratio [OR]: 10.7; 95% confidence interval [CI], 2.6-43.8) and for T2 versus T1c (OR: 2.9; 95% CI, 1.9-4.6). Considering pre-, intra-, and postoperative variables combined, percentage of tumor, pathologic stage, and pathologic Gleason score were associated with increased risk of PSM in the univariable analysis (p < 0.001 for all variables). However, in the multivariable analysis, pathologic stage (pT2 vs pT1; OR: 2.9; 95% CI, 1.9-4.6) and percentage of tumor in the surgical specimen (OR: 8.7; 95% CI, 2.2-34.5; p = 0.0022) were the only independent predictive factors for PSM. Finally, BMI was shown to be an independent predictive factor(OR: 1.1; 95% CI, 1.0-1.3; p = 0.0119) for apical PSMs, with increasing BMI predicting higher incidence of apex location. Because most of our patients were referred from other centers, the biopsy technique and the number of cores were not standardized in our series. Conclusions: Clinical stage was the only preoperative variable independently associated with PSM after RARP. Pathologic stage and percentage of tumor in the surgical specimen were identified as independent predictive factors for PSMs when analyzing pre-, intra-, and postoperative variables combined. BMI was shown to be an independent predictive factor for apical PSMs. (C) 2010 European Association of Urology. Published by Elsevier B. V. All rights reserved.
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Background: Several studies have shown that robot-assisted laparoscopic radical prostatectomy (RALP) is feasible, with favorable complication rates and short hospital times. However, the early recovery of urinary continence remains a challenge to be overcome. Objective: We describe our technique of periurethral retropubic suspension stitch during RALP and report its impact on early recovery of urinary continence. Design, setting, and participants: We analyze prospectively 331 consecutive patients who underwent RALP, 94 without the placement of suspension stitch (group 1) and 237 with the application of the suspension stitch (group 2). Surgical procedure: The only difference between the groups was the placement of the puboperiurethral stitch after the ligation of the dorsal venous complex (DVC). The periurethral retropubic stitch was placed using a 12-in monofilament polyglytone suture on a CTI needle. The stitch was passed from right to left between the urethra and DVC, and then through the periostium on the pubic bone. The stitch was passed again through the DVC, and then through the pubic bone in a figure eight, and then tied. Measurements: Continence rates were assessed with a self-administered validated questionnaire (Expanded Prostate Cancer Index Composite [EPIC] at 1, 3, 6, and 12 mo after the procedure. Continence was defined as the use of no absorbent pads or no leakage of urine. Results and limitations: In group 1, the continence rate at 1, 3, 6, and 12 mo postoperatively was 33%, 83%, 94.7%, and 95.7%, respectively; in group 2, the continence rate was 40%, 92.8%, 97.9%, and 97.9%, respectively. The suspension technique resulted in significantly greater continence rates at 3 mo after RALP (p = 0.013). The median/mean interval to recovery of continence was also statistically significantly shorter in the suspension group (median: 6 wk; mean: 7.338 wk: 95% confidence interval [CI]: 6.387-8.288) compared to the non-suspension group (median: 7 wk; mean: 9.585 wk: 95% CI: 7.558-11.612; log rank test, p = 0.02). Conclusions: The suspension stitch during RALP resulted in a statistically significantly shorter interval to recovery of continence and higher continence rates at 3 mo after the procedure. (C) 2009 European Association of Urology. Published by Elsevier B.V. All rights reserved.
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Background: Widespread use of prostate-specific antigen screening has resulted in younger and healthier men being diagnosed with prostate cancer. Their demands and expectations of surgical intervention are much higher and cannot be adequately addressed with the classic trifecta outcome measures. Objective: A new and more comprehensive method for reporting outcomes after radical prostatectomy, the pentafecta, is proposed. Design, setting, and participants: From January 2008 through September 2009, details of 1111 consecutive patients who underwent robot-assisted radical prostatectomy performed by a single surgeon were retrospectively analyzed. Of 626 potent men, 332 who underwent bilateral nerve sparing and who had 1 yr of follow-up were included in the study group. Measurements: In addition to the traditional trifecta outcomes, two perioperative variables were included in the pentafecta: no postoperative complications and negative surgical margins. Patients who attained the trifecta and concurrently the two additional outcomes were considered as having achieved the pentafecta. A logistic regression model was created to evaluate independent factors for achieving the pentafecta. Results and limitations: Continence, potency, biochemical recurrence-free survival, and trifecta rates at 12 mo were 96.4%, 89.8%, 96.4%, and 83.1%, respectively. With regard to the perioperative outcomes, 93.4% had no postoperative complication and 90.7% had negative surgical margins. The pentafecta rate at 12 mo was 70.8%. On multivariable analysis, patient age (p = 0.001) was confirmed as the only factor independently associated with the pentafecta. Conclusions: A more comprehensive approach for reporting prostate surgery outcomes, the pentafecta, is being proposed. We believe that pentafecta outcomes more accurately represent patients` expectations after minimally invasive surgery for prostate cancer. This approach may be beneficial and may be used when counseling patients with clinically localized disease. (C) 2011 European Association of Urology. Published by Elsevier B. V. All rights reserved.
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This work discusses the use of optical flow to generate the sensorial information a mobile robot needs to react to the presence of obstacles when navigating in a non-structured environment. A sensing system based on optical flow and time-to-collision calculation is here proposed and experimented, which accomplishes two important paradigms. The first one is that all computations are performed onboard the robot, in spite of the limited computational capability available. The second one is that the algorithms for optical flow and time-to-collision calculations are fast enough to give the mobile robot the capability of reacting to any environmental change in real-time. Results of real experiments in which the sensing system here proposed is used as the only source of sensorial data to guide a mobile robot to avoid obstacles while wandering around are presented, and the analysis of such results allows validating the proposed sensing system.
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In the last decade, local image features have been widely used in robot visual localization. To assess image similarity, a strategy exploiting these features compares raw descriptors extracted from the current image to those in the models of places. This paper addresses the ensuing step in this process, where a combining function must be used to aggregate results and assign each place a score. Casting the problem in the multiple classifier systems framework, we compare several candidate combiners with respect to their performance in the visual localization task. A deeper insight into the potential of the sum and product combiners is provided by testing two extensions of these algebraic rules: threshold and weighted modifications. In addition, a voting method, previously used in robot visual localization, is assessed. All combiners are tested on a visual localization task, carried out on a public dataset. It is experimentally demonstrated that the sum rule extensions globally achieve the best performance. The voting method, whilst competitive to the algebraic rules in their standard form, is shown to be outperformed by both their modified versions.