35 research outputs found

    Analysis of the Use of a Wind Turbine as an Energy Recovery Device in Transport Systems

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    [EN] A wind turbine can act as an energy recovery device (ERS) in a comparable way to brakes (regenerative braking). When the velocity of a vehicle changes, the amount of energy related to it also changes. When its velocity decreases, the energy tends to dissipate. Over time, this dissipated energy has been ignored. For example, during the braking process, the kinetic energy of the vehicle was converted into heat. In recent years, society¿s greater awareness of climate change, pollution, and environmental issues has led to a great deal of interest in developing energy recovery systems. It allows the recovery of kinetic energy from braking (KERS), resulting in consumption reductions (efficiency gains) of up to 45%. The usefulness of installing a wind turbine as an energy recovery device is analysed, evaluating the savings that can be achieved with its two possible working modes: as an energy recovery device and as a system for utilizing aerodynamic force. The wind turbine has a horizontal axis and a diameter of 50 cm and is installed on the front of a vehicle. This vehicle will undergo three particular driving schemes, which will operate under different experimental conditions and operational parameters characterized by speeds, accelerations, stops, and driving time. The results clearly show the advantages of using the proposed technology.Rubio Montoya, FJ.; Llopis-Albert, C. (2021). Analysis of the Use of a Wind Turbine as an Energy Recovery Device in Transport Systems. Mathematics. 9(18):1-15. https://doi.org/10.3390/math9182265S11591

    Modelling an Industrial Robot and Its Impact on Productivity

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    [EN] This research aims to design an efficient algorithm leading to an improvement of productivity by posing a multi-objective optimization, in which both the time consumed to carry out scheduled tasks and the associated costs of the autonomous industrial system are minimized. The algorithm proposed models the kinematics and dynamics of the industrial robot, provides collision-free trajectories, allows to constrain the energy consumed and meets the physical characteristics of the robot (i.e., restriction on torque, jerks and power in all driving motors). Additionally, the trajectory tracking accuracy is improved using an adaptive fuzzy sliding mode control (AFSMC), which allows compensating for parametric uncertainties, bounded external disturbances and constraint uncertainties. Therefore, the system stability and robustness are enhanced; thus, overcoming some of the limitations of the traditional proportional-integral-derivative (PID) controllers. The trade-offs among the economic issues related to the assembly line and the optimal time trajectory of the desired motion are analyzed using Pareto fronts. The technique is tested in different examples for a six-degrees-of-freedom (DOF) robot system. Results have proved how the use of this methodology enhances the performance and reliability of assembly lines.Llopis-Albert, C.; Rubio Montoya, FJ.; Valero Chuliá, FJ. (2021). Modelling an Industrial Robot and Its Impact on Productivity. Mathematics. 9(7):1-13. https://doi.org/10.3390/math907076911397AOYAMA, T., NISHI, T., & ZHANG, G. (2017). Production planning problem with market impact under demand uncertainty. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 11(2), JAMDSM0019-JAMDSM0019. doi:10.1299/jamdsm.2017jamdsm0019Llopis-Albert, C., Rubio, F., & Valero, F. (2015). Improving productivity using a multi-objective optimization of robotic trajectory planning. Journal of Business Research, 68(7), 1429-1431. doi:10.1016/j.jbusres.2015.01.027Rubio, F., Valero, F., Sunyer, J., & Cuadrado, J. (2012). Optimal time trajectories for industrial robots with torque, power, jerk and energy consumed constraints. Industrial Robot: An International Journal, 39(1), 92-100. doi:10.1108/01439911211192538Llopis-Albert, C., Rubio, F., & Valero, F. (2018). Optimization approaches for robot trajectory planning. Multidisciplinary Journal for Education, Social and Technological Sciences, 5(1), 1. doi:10.4995/muse.2018.9867Yang, Y., Pan, J., & Wan, W. (2019). Survey of optimal motion planning. IET Cyber-Systems and Robotics, 1(1), 13-19. doi:10.1049/iet-csr.2018.0003Gasparetto, A., & Zanotto, V. (2008). A technique for time-jerk optimal planning of robot trajectories. Robotics and Computer-Integrated Manufacturing, 24(3), 415-426. doi:10.1016/j.rcim.2007.04.001Mohammed, A., Schmidt, B., Wang, L., & Gao, L. (2014). Minimizing Energy Consumption for Robot Arm Movement. Procedia CIRP, 25, 400-405. doi:10.1016/j.procir.2014.10.055Van den Berg, J., Abbeel, P., & Goldberg, K. (2011). LQG-MP: Optimized path planning for robots with motion uncertainty and imperfect state information. The International Journal of Robotics Research, 30(7), 895-913. doi:10.1177/0278364911406562Liu, S., Sun, D., & Zhu, C. (2011). Coordinated Motion Planning for Multiple Mobile Robots Along Designed Paths With Formation Requirement. IEEE/ASME Transactions on Mechatronics, 16(6), 1021-1031. doi:10.1109/tmech.2010.2070843Plaku, E., Kavraki, L. E., & Vardi, M. Y. (2010). Motion Planning With Dynamics by a Synergistic Combination of Layers of Planning. IEEE Transactions on Robotics, 26(3), 469-482. doi:10.1109/tro.2010.2047820Rubio, F., Llopis-Albert, C., Valero, F., & Suñer, J. L. (2015). Assembly Line Productivity Assessment by Comparing Optimization-Simulation Algorithms of Trajectory Planning for Industrial Robots. Mathematical Problems in Engineering, 2015, 1-10. doi:10.1155/2015/931048Rubio, F., Llopis-Albert, C., Valero, F., & Suñer, J. L. (2016). Industrial robot efficient trajectory generation without collision through the evolution of the optimal trajectory. Robotics and Autonomous Systems, 86, 106-112. doi:10.1016/j.robot.2016.09.008Llopis-Albert, C., Valero, F., Mata, V., Pulloquinga, J. L., Zamora-Ortiz, P., & Escarabajal, R. J. (2020). Optimal Reconfiguration of a Parallel Robot for Forward Singularities Avoidance in Rehabilitation Therapies. A Comparison via Different Optimization Methods. Sustainability, 12(14), 5803. doi:10.3390/su12145803Llopis-Albert, C., Valero, F., Mata, V., Escarabajal, R. J., Zamora-Ortiz, P., & Pulloquinga, J. L. (2020). Optimal Reconfiguration of a Limited Parallel Robot for Forward Singularities Avoidance. Multidisciplinary Journal for Education, Social and Technological Sciences, 7(1), 113. doi:10.4995/muse.2020.13352Yang, J., Su, H., Li, Z., Ao, D., & Song, R. (2016). Adaptive control with a fuzzy tuner for cable-based rehabilitation robot. International Journal of Control, Automation and Systems, 14(3), 865-875. doi:10.1007/s12555-015-0049-4Zhang, G., & Zhang, X. (2016). Concise adaptive fuzzy control of nonlinearly parameterized and periodically time-varying systems via small gain theory. International Journal of Control, Automation and Systems, 14(4), 893-905. doi:10.1007/s12555-015-0054-7SUTONO, S. B., ABDUL-RASHID, S. H., AOYAMA, H., & TAHA, Z. (2016). Fuzzy-based Taguchi method for multi-response optimization of product form design in Kansei engineering: a case study on car form design. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 10(9), JAMDSM0108-JAMDSM0108. doi:10.1299/jamdsm.2016jamdsm0108DUBEY, A. K. (2009). Performance Optimization Control of ECH using Fuzzy Inference Application. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 3(1), 22-34. doi:10.1299/jamdsm.3.22Zhang, H., Fang, H., Zhang, D., Luo, X., & Zou, Q. (2020). Adaptive Fuzzy Sliding Mode Control for a 3-DOF Parallel Manipulator with Parameters Uncertainties. Complexity, 2020, 1-16. doi:10.1155/2020/2565316Markazi, A. H. D., Maadani, M., Zabihifar, S. H., & Doost-Mohammadi, N. (2018). Adaptive Fuzzy Sliding Mode Control of Under-actuated Nonlinear Systems. International Journal of Automation and Computing, 15(3), 364-376. doi:10.1007/s11633-017-1108-5Truong, H. V. A., Tran, D. T., To, X. D., Ahn, K. K., & Jin, M. (2019). Adaptive Fuzzy Backstepping Sliding Mode Control for a 3-DOF Hydraulic Manipulator with Nonlinear Disturbance Observer for Large Payload Variation. Applied Sciences, 9(16), 3290. doi:10.3390/app9163290Li, T.-H. S., & Huang, Y.-C. (2010). MIMO adaptive fuzzy terminal sliding-mode controller for robotic manipulators. Information Sciences, 180(23), 4641-4660. doi:10.1016/j.ins.2010.08.00

    A review of mobile robots: Concepts, methods, theoretical framework, and applications

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    [EN] Humanoid robots, unmanned rovers, entertainment pets, drones, and so on are great examples of mobile robots. They can be distinguished from other robots by their ability to move autonomously, with enough intelligence to react and make decisions based on the perception they receive from the environment. Mobile robots must have some source of input data, some way of decoding that input, and a way of taking actions (including its own motion) to respond to a changing world. The need to sense and adapt to an unknown environment requires a powerful cognition system. Nowadays, there are mobile robots that can walk, run, jump, and so on like their biological counterparts. Several fields of robotics have arisen, such as wheeled mobile robots, legged robots, flying robots, robot vision, artificial intelligence, and so on, which involve different technological areas such as mechanics, electronics, and computer science. In this article, the world of mobile robots is explored including the new trends. These new trends are led by artificial intelligence, autonomous driving, network communication, cooperative work, nanorobotics, friendly human-robot interfaces, safe human-robot interaction, and emotion expression and perception. Furthermore, these news trends are applied to different fields such as medicine, health care, sports, ergonomics, industry, distribution of goods, and service robotics. These tendencies will keep going their evolution in the coming years.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Spanish Ministry of Economy and Competitiveness, which has funded the DPI2013-44227-R project.Rubio Montoya, FJ.; Valero Chuliá, FJ.; Llopis Albert, C. (2019). A review of mobile robots: Concepts, methods, theoretical framework, and applications. International Journal of Advanced Robotic Systems. 16(2):1-22. https://doi.org/10.1177/1729881419839596S122162Brunete, A., Ranganath, A., Segovia, S., de Frutos, J. P., Hernando, M., & Gambao, E. (2017). Current trends in reconfigurable modular robots design. International Journal of Advanced Robotic Systems, 14(3), 172988141771045. doi:10.1177/1729881417710457Bajracharya, M., Maimone, M. W., & Helmick, D. (2008). Autonomy for Mars Rovers: Past, Present, and Future. Computer, 41(12), 44-50. doi:10.1109/mc.2008.479Carsten, J., Rankin, A., Ferguson, D., & Stentz, A. (2007). Global Path Planning on Board the Mars Exploration Rovers. 2007 IEEE Aerospace Conference. doi:10.1109/aero.2007.352683Grotzinger, J. P., Crisp, J., Vasavada, A. R., Anderson, R. C., Baker, C. J., Barry, R., … Wiens, R. C. (2012). Mars Science Laboratory Mission and Science Investigation. 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Mobile Wheel-Legged Robot: Researching of Suspension Leveling System. Mechanisms and Machine Science, 3-12. doi:10.1007/978-94-007-5125-5_1Williams, R. L., Carter, B. E., Gallina, P., & Rosati, G. (2002). Dynamic model with slip for wheeled omnidirectional robots. IEEE Transactions on Robotics and Automation, 18(3), 285-293. doi:10.1109/tra.2002.1019459Chan, R. P. M., Stol, K. A., & Halkyard, C. R. (2013). Review of modelling and control of two-wheeled robots. Annual Reviews in Control, 37(1), 89-103. doi:10.1016/j.arcontrol.2013.03.004Kim, H., & Kim, B. K. (2014). Online Minimum-Energy Trajectory Planning and Control on a Straight-Line Path for Three-Wheeled Omnidirectional Mobile Robots. IEEE Transactions on Industrial Electronics, 61(9), 4771-4779. doi:10.1109/tie.2013.2293706Carbone, G., & Ceccarelli, M. (2005). Legged Robotic Systems. Cutting Edge Robotics. doi:10.5772/4669Chestnutt, J., Lau, M., Cheung, G., Kuffner, J., Hodgins, J., & Kanade, T. (s. f.). Footstep Planning for the Honda ASIMO Humanoid. Proceedings of the 2005 IEEE International Conference on Robotics and Automation. doi:10.1109/robot.2005.1570188Arikawa, K., & Hirose, S. (s. f.). Development of quadruped walking robot TITAN-VIII. Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. IROS ’96. doi:10.1109/iros.1996.570670Kurazume, R., Byong-won, A., Ohta, K., & Hasegawa, T. (s. f.). Experimental study on energy efficiency for quadruped walking vehicles. Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453). doi:10.1109/iros.2003.1250697Hirose, S., Fukuda, Y., Yoneda, K., Nagakubo, A., Tsukagoshi, H., Arikawa, K., … Hodoshima, R. (2009). Quadruped walking robots at Tokyo Institute of Technology. IEEE Robotics & Automation Magazine, 16(2), 104-114. doi:10.1109/mra.2009.932524Stoica, A., Carbone, G., Ceccarelli, M., & Pisla, D. (2010). 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    Improving productivity using a multi-objective optimization of robotic trajectory planning

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    This study presents a methodology to tackle robot tasks in a cost-efficientway. It poses amulti-objective optimization problemfor trajectory planning of robotic arms that an efficient algorithmwill solve. Themethod finds the minimum time to perform robot tasks while considering the physical constraints of the real working problem and the economic issues participating in the process. This process also considers robotic system dynamics and the presence of obstacles to avoid collisions. It generates an entire set of equally optimal solutions for each process, the Pareto-optimal frontiers. They provide information about the trade-offs between the different decision variables of the multi-objective optimization problem. This procedure can help managers in decision-making processes regarding performing tasks, items to be manufactured or robotic services performed to meet with the current demand, and also, to define an efficient scheduling. It improves productivity and allows firms to stay competitive in rapid changing markets.The authors thank the funding of Science and Innovation Ministry of the Spain Government by means of the Researching and Technologic Development Project DPI2010-20814-C02-01 (IDEMOV).Llopis Albert, C.; Rubio Montoya, FJ.; Valero Chuliá, FJ. (2015). Improving productivity using a multi-objective optimization of robotic trajectory planning. Journal of Business Research. 68(7):1429-1431. https://doi.org/10.1016/j.jbusres.2015.01.027S1429143168

    Assessment of the Effect of Energy Consumption on Trajectory Improvement for a Car-like Robot

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    [EN] Reducing the energy consumed by a car-like mobile robot makes it possible to move at a lower cost, yet it takes more working time. This paper proposes an optimization algorithm for trajectories with optimal times and analyzes the consequences of restricting the energy consumed on the trajectory obtained for a car-like robot. When modeling the dynamic behavior of the vehicle, it is necessary to consider its inertial parameters, the behavior of the motor, and the basic properties of the tire in its interaction with the ground. To obtain collision-free, minimum-time trajectories quadratic sequential optimization techniques are used, where the objective function is the time taken by the robot to move between two given configurations. This is subject to constraints relating to the vehicle and tires as well as the energy consumed, which is the basis for this paper. We work with a real random distribution of consumed energy values following a normal Gaussian distribution in order to analyze its influence on the trajectories obtained by the vehicle. The energy consumed, the time taken, the maximum velocity reached, and the distance traveled are analyzed in order to characterize the properties of the trajectories obtained. The proposed algorithm has been applied to 101 examples, showing that the computational times needed to obtain the solutions are always lower than those required to realize the trajectories. The results obtained allow us to reach conclusions about the energy efficiency of the trajectories.Valero Chuliá, FJ.; Rubio Montoya, FJ.; Llopis Albert, C. (2019). Assessment of the Effect of Energy Consumption on Trajectory Improvement for a Car-like Robot. Robotica. 37(11):1998-2009. https://doi.org/10.1017/S0263574719000407S199820093711Rubio, F., Valero, F., Lluís Sunyer, J., & Garrido, A. (2010). The simultaneous algorithm and the best interpolation function for trajectory planning. Industrial Robot: An International Journal, 37(5), 441-451. doi:10.1108/01439911011063263Liu, S., & Sun, D. (2014). Minimizing Energy Consumption of Wheeled Mobile Robots via Optimal Motion Planning. IEEE/ASME Transactions on Mechatronics, 19(2), 401-411. doi:10.1109/tmech.2013.2241777Renny Simba, K., Uchiyama, N., & Sano, S. (2016). Real-time smooth trajectory generation for nonholonomic mobile robots using Bézier curves. Robotics and Computer-Integrated Manufacturing, 41, 31-42. doi:10.1016/j.rcim.2016.02.00

    On near-redundancy and identifiability of parametric hazard regression models under censoring

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    We study parametric inference on a rich class of hazard regression models in the presence of right-censoring. Previous literature has reported some inferential challenges, such as multimodal or flat likelihood surfaces, in this class of models for some particular data sets. We formalize the study of these inferential problems by linking them to the concepts of near-redundancy and practical nonidentifiability of parameters. We show that the maximum likelihood estimators of the parameters in this class of models are consistent and asymptotically normal. Thus, the inferential problems in this class of models are related to the finite-sample scenario, where it is difficult to distinguish between the fitted model and a nested nonidentifiable (i.e., parameter-redundant) model. We propose a method for detecting near-redundancy, based on distances between probability distributions. We also employ methods used in other areas for detecting practical nonidentifiability and near-redundancy, including the inspection of the profile likelihood function and the Hessian method. For cases where inferential problems are detected, we discuss alternatives such as using model selection tools to identify simpler models that do not exhibit these inferential problems, increasing the sample size, or extending the follow-up time. We illustrate the performance of the proposed methods through a simulation study. Our simulation study reveals a link between the presence of near-redundancy and practical nonidentifiability. Two illustrative applications using real data, with and without inferential problems, are presented

    Optimal allocation of energy sources in hydrogen production for sustainable deployment of electric vehicles

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    [EN] We analyze the use of hydrogen as a fuel for the automotive industry with the aim of decarbonizing the economy. Hydrogen is a suitable option for avoiding pollutant gas emissions, developing environmentally friendly tech-nologies, replacing fossil fuels with clean, renewable energies, and complying with the Paris Agreement and Glasgow resolutions. In this sense, renewable energies such as wind, solar, photovoltaic, geothermal, biomass, etc. can be used to produce the necessary hydrogen to power vehicles. In this way, the entire process from hydrogen production to its consumption as fuel will be 100% clean. If we are to meet future energy demands, it is necessary to forecast the amount of hydrogen needed, taking into account the facilities currently available and new ones that will be required for its generation, storage, and distribution.This paper presents a process for optimizing hydrogen production for the automotive industry that considers the amount of hydrogen needed, the type of facilities from which it will be produced, how the different sources of production are to be combined to achieve a competitive product, and the potential environmental impacts of each energy source. It can serve as a frame of reference for the various actors in the hydropower and automotive industries so that more efficient designs can be planned for the gradual introduction of hydrogen fuel cell ve-hicles (HFCVs).The methodology implemented in this paper sets an optimization problem for minimizing energy production costs and reducing environmental impacts according to the source of energy production. The EU framework with respect to the decarbonization of the economy, the percentages of the different types of energy sources used, and the non-polluting vehicle fleet in the automotive sector will be considered.Rubio Montoya, FJ.; Llopis-Albert, C.; Besa Gonzálvez, AJ. (2023). Optimal allocation of energy sources in hydrogen production for sustainable deployment of electric vehicles. Technological Forecasting and Social Change. 188:1-9. https://doi.org/10.1016/j.techfore.2022.1222901918

    A new approach to the kinematic modeling of a three-dimensional car-like robot with differential drive using computational mechanics

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    [EN] This article presents a kinematic analysis of a four-wheeled mobile robot in three-dimensions, introducing computational mechanics. The novelty lies in (1) the type of robot that is analyzed, which has been scarcely dealt with in the literature, and (2) the methodology used which enables the systematic implementation of kinematic algorithms using the computer. The mobile robot has four wheels, four rockers (like an All-Terrain Mobile Robot), and a main body. It also has two actuators and uses a drive mechanism known as differential drive (like those of a slip/skid mobile robot). We characterize the mobile robot as a set of kinematic closed chains with rotational pairs between links and a higher contact pair between the wheels and the terrain. Then, a set of generalized coordinates are chosen and the constraint equations are established. A new concept named ¿driving modes¿ has been introduced because some of the constraint equations are derived from these. The kinematics is the first step in solving the dynamics of this robot in order to set a control algorithm for an autonomous car-like robot. This methodology has been successfully applied to a real mobile robot, ¿Robotnik,¿ and the results are analyzed.Rubio Montoya, FJ.; Llopis Albert, C.; Valero Chuliá, FJ.; Besa Gonzálvez, AJ. (2019). A new approach to the kinematic modeling of a three-dimensional car-like robot with differential drive using computational mechanics. Advances in Mechanical Engineering. 11(3):1-14. https://doi.org/10.1177/1687814019825907S114113Campion, G., Bastin, G., & Dandrea-Novel, B. (1996). Structural properties and classification of kinematic and dynamic models of wheeled mobile robots. IEEE Transactions on Robotics and Automation, 12(1), 47-62. doi:10.1109/70.481750Bajracharya, M., Maimone, M. W., & Helmick, D. (2008). Autonomy for Mars Rovers: Past, Present, and Future. Computer, 41(12), 44-50. doi:10.1109/mc.2008.479Poczter, S. L., & Jankovic, L. M. (2013). The Google Car: Driving Toward A Better Future? Journal of Business Case Studies (JBCS), 10(1), 7. doi:10.19030/jbcs.v10i1.8324Wang, T., Wu, Y., Liang, J., Han, C., Chen, J., & Zhao, Q. (2015). Analysis and Experimental Kinematics of a Skid-Steering Wheeled Robot Based on a Laser Scanner Sensor. Sensors, 15(5), 9681-9702. doi:10.3390/s150509681Alexander, J. C., & Maddocks, J. H. (1989). On the Kinematics of Wheeled Mobile Robots. The International Journal of Robotics Research, 8(5), 15-27. doi:10.1177/027836498900800502Muir, P. F., & Neuman, C. P. (1987). Kinematic modeling of wheeled mobile robots. Journal of Robotic Systems, 4(2), 281-340. doi:10.1002/rob.4620040209Tarokh, M., & McDermott, G. J. (2005). Kinematics modeling and analyses of articulated rovers. IEEE Transactions on Robotics, 21(4), 539-553. doi:10.1109/tro.2005.847602Zhang, N., Zhao, Y., Wei, H., & Chen, G. (2016). Experimental study on the influence of air injection on unsteady cloud cavitating flow dynamics. Advances in Mechanical Engineering, 8(11), 168781401667667. doi:10.1177/168781401667667

    Inverse Modelling and Medical Imaging Applied to Biomechanical Research

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    [EN] The prediction of heterogeneous material properties in biomedical applications is becoming a major problem in cases with complex microstructures and multiphase materials. Several branches in medicine require accurate measurements, which can be achieved by means of medical imaging. They are non-destructive techniques to visualize the inside features of solid objects and for obtaining digital information on their three-dimensional geometries and properties. Therefore, for relating the observed measurements to unknown physical parameters, through medical imaging reconstruction, inverse modelling approaches are advisable.Llopis Albert, C.; Rubio Montoya, FJ.; Merigó-Lindahl, JM.; Valero Chuliá, FJ. (2018). Inverse Modelling and Medical Imaging Applied to Biomechanical Research. Biomedical Journal of Scientific & Technical Research. 4(3):1-2. https://doi.org/10.26717/BJSTR.2018.04.001065S124

    Efficient trajectory of a car-like mobile robot

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    This article is (c) Emerald Group Publishing and permission has been granted for this version to appear here https://riunet.upv.es/. Emerald does not grant permission for this article to be further copied/distributed or hosted elsewhere without the express permission from Emerald Group Publishing Limited.[EN] Purpose The purpose is to create an algorithm that optimizes the trajectories that an autonomous vehicle must follow to reduce its energy consumption and reduce the emission of greenhouse gases. Design/methodology/approach An algorithm is presented that respects the dynamic constraints of the robot, including the characteristics of power delivery by the motor, the behaviour of the tires and the basic inertial parameters. Using quadratic sequential programming with distributed and non-monotonous search direction (Quadratic Programming Algorithm with Distributed and Non-Monotone Line Search), an optimization algorithm proposed and developed by Professor K. Schittkowski is implemented. Findings Relations between important operating variables have been obtained, such as the evolution of the autonomous vehicle's velocity, the driving torque supplied by the engine and the forces acting on the tires. In a subsequent analysis, the aim is to analyse the relationship between trajectory made and energy consumed and calculate the reduction of greenhouse gas emissions. Also this method has been checked against another different methodology commented on in the references. Research limitations/implications The main limitation comes from the modelling that has been done. As greater is the mechanical systems analysed, more simplifying hypotheses should be introduced to solve the corresponding equations with the current computers. However, the solutions are obtained and they can be used qualitatively to draw conclusions. Practical implications One main objective is to obtain guidelines to reduce greenhouse gas emissions by reducing energy consumption in the realization of autonomous vehicles' trajectories. The first step to achieve that is to obtain a good model of the autonomous vehicle that takes into account not only its kinematics but also its dynamic properties, and to propose an optimization process that allows to minimize the energy consumed. In this paper, important relationships between work variables have been obtained. Social implications The idea is to be friendly with nature and the environment. This algorithm can help by reducing an instance of greenhouse gases. Originality/value Originality comes from the fact that we not only look for the autonomous vehicle's modelling, the simulation of its motion and the analysis of its working parameters, but also try to obtain from its working those guidelines that are useful to reduce the energy consumed and the contamination capability of these autonomous vehicles or car-like robots.Valero Chuliá, FJ.; Rubio Montoya, FJ.; Besa Gonzálvez, AJ.; Llopis Albert, C. (2019). Efficient trajectory of a car-like mobile robot. Industrial Robot An International Journal. 46(2):211-222. https://doi.org/10.1108/IR-10-2018-0214S211222462Ghita, N., & Kloetzer, M. (2012). Trajectory planning for a car-like robot by environment abstraction. Robotics and Autonomous Systems, 60(4), 609-619. doi:10.1016/j.robot.2011.12.004Katrakazas, C., Quddus, M., Chen, W.-H., & Deka, L. (2015). Real-time motion planning methods for autonomous on-road driving: State-of-the-art and future research directions. Transportation Research Part C: Emerging Technologies, 60, 416-442. doi:10.1016/j.trc.2015.09.011Li, B., & Shao, Z. (2015). Simultaneous dynamic optimization: A trajectory planning method for nonholonomic car-like robots. Advances in Engineering Software, 87, 30-42. doi:10.1016/j.advengsoft.2015.04.011Rubio, F., Llopis-Albert, C., Valero, F., & Suñer, J. L. (2016). Industrial robot efficient trajectory generation without collision through the evolution of the optimal trajectory. Robotics and Autonomous Systems, 86, 106-112. doi:10.1016/j.robot.2016.09.008Rubio, F., Valero, F., Lluís Sunyer, J., & Garrido, A. (2010). The simultaneous algorithm and the best interpolation function for trajectory planning. Industrial Robot: An International Journal, 37(5), 441-451. doi:10.1108/01439911011063263Sariff, N., & Buniyamin, N. (2006). An Overview of Autonomous Mobile Robot Path Planning Algorithms. 2006 4th Student Conference on Research and Development. doi:10.1109/scored.2006.4339335Renny Simba, K., Uchiyama, N., & Sano, S. (2016). Real-time smooth trajectory generation for nonholonomic mobile robots using Bézier curves. Robotics and Computer-Integrated Manufacturing, 41, 31-42. doi:10.1016/j.rcim.2016.02.002Tokekar, P., Karnad, N., & Isler, V. (2014). Energy-optimal trajectory planning for car-like robots. Autonomous Robots, 37(3), 279-300. doi:10.1007/s10514-014-9390-
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