Journal articles: 'Robots Mathematical models'

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Korendiy, Vitaliy. "Generalized design diagram and mathematical model of suspension system of vibration-driven robot." Ukrainian Journal of Mechanical Engineering and Materials Science 7, no. 3-4 (2021): 1–10. http://dx.doi.org/10.23939/ujmems2021.03-04.001.

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Problem statement. Mobile robotic systems are widely used in various fields of industry and social life: from small household appliances to large-size road-building machinery. Specific attention of scientists and designers is paid to the vibration-driven locomotion systems able to move in the environments where the use of classical wheeled and caterpillar robots is impossible or inefficient. Purpose. The main objective of this paper consists in generalizing the actual research results dedicated to various design diagrams and mathematical models of suspension systems of mobile vibration-driven robots. Methodology. The differential equations describing the robot motion are derived using the Lagrange-d'Alembert principle. The numerical modeling is carried out in the Mathematica software by solving the derived system of differential equations with the help of the Runge-Kutta methods. The verification of the obtained results is performed by computer simulation of the robot motion in the SolidWorks and MapleSim software. Findings (results). The time dependencies of the basic kinematic parameters (displacement, velocity, acceleration) of the robot’s vibratory system are analyzed. The possibilities of maximizing the robot translational velocity are considered. Originality (novelty). The paper generalizes the existent designs and mathematical models of the mobile vibration-driven robots’ suspensions and studies the combined four-spring locomotion system moving along a rough horizontal surface. Practical value. The obtained results can be effectively used by researchers and designers of vibration-driven locomotion systems while improving the existent designs and developing the new ones. Scopes of further investigations. While carrying out further investigations on the subject of the paper, it is necessary to solve the problem of optimizing the robot’s oscillatory system parameters in order to maximize its translational velocity.

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Matuliauskas, Arvydas, and Bronislovas Spruogis. "PIPELINE ROBOTS WITH ELASTIC ELEMENTS." TRANSPORT 17, no. 5 (October 31, 2002): 177–81. http://dx.doi.org/10.3846/16483840.2002.10414039.

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In the article constructions of the pipeline robots with elastic elements are reviewed and the scheme of new original construction is presented. The mathematical models of a robot with one-dimensional vibration exciter with two degrees of freedom were developed and the equations of movement were formed and written. The mathematical model of the pipeline robot with circular elements is formed and its motion equations are presented.

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Moshayedi, Ata Jahangir, Atanu Shuvam Roy, Sithembiso Khaya Sambo, Yangwan Zhong, and Liefa Liao. "Review On: The Service Robot Mathematical Model." EAI Endorsed Transactions on AI and Robotics 1 (February 23, 2022): 1–19. http://dx.doi.org/10.4108/airo.v1i.20.

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After nearly 30 years of development, service robot technology has made important achievements in the interdisciplinary aspects of machinery, information, materials, control, medicine, etc. These robot types have different shapes, and mainly in some are shaped based on application. Till today various structure are proposed which for the better analysis’s need to have the mathematical equation that can model the structure and later the behaviour of them after implementing the controlling strategy. The current paper discusses the various shape and applications of all available service robots and briefly summarizes the research progress of key points such as robot dynamics, robot types, and different dynamic models of the differential types of service robots. The current review study can be helpful as an initial node for all researchers in this topic and help them to have the better simulation and analyses. Besides the current research shows some application that can specify the service robot model over the application.

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Krakhmalev, O. N., D. I. Petreshin, and O. N. Fedonin. "Mathematical models for base calibration in industrial robots." Russian Engineering Research 37, no. 11 (November 2017): 995–1000. http://dx.doi.org/10.3103/s1068798x17110089.

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Migdalovici, Marcel, L. Vladareanu, Hongnian Yu, N. Pop, M. Iliescu, V. Vladareanu, D. Baran, and G. Vladeanu. "The walking robots critical position of the kinematics or dynamic systems applied on the environment model." International Journal of Engineering & Technology 7, no. 2.28 (May 16, 2018): 134. http://dx.doi.org/10.14419/ijet.v7i2.28.12896.

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The exposure is dedicated in the first to mathematical modeling of the environment where the aspects on the walking robots evolution models are described. The environment’s mathematical model is defined through the models of kinematics or dynamic systems in the general case of systems that depend on parameters. The important property of the dynamic system evolution models that approach the phenomenon from the environment is property of separation between stable and unstable regions from the free parameters domain of the system. Some mathematical conditions that imply the separation of stable regions from the free parameters domain of the system are formulated. In the second part is described our idea on walking robot kinematics and dynamic models with aspects exemplified on walking robot leg. An inverse method for identification of possible critical positions of the walking robot leg is established.

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Cerrillo, Diego, Antonio Barrientos, and Jaime Del Cerro. "Kinematic Modelling for Hyper-Redundant Robots—A Structured Guide." Mathematics 10, no. 16 (August 12, 2022): 2891. http://dx.doi.org/10.3390/math10162891.

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Obtaining mathematical equations to model the kinematics of a hyper-redundant robot is not intuitive and of greater difficulty than for traditional robots. Depending on the characteristics of the robot, the most appropriate methodology to approach the modelling may be one or another. This article provides a general overview of the different approaches there are when modelling a hyper-redundant cable-driven robot, while proposing a guide to help the novel researcher that approaches this field decide which methodology to apply when modelling a robot. After providing some definitions, a simple framework to understand all the underlying models is presented. Afterwards, the mathematical equations for the most important methods of modelling are developed. Finally, the proposal for a step-by-step tutorial is included, and it is exemplified by applying it to three real robots.

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Negrean, Iuliu, Claudiu Schonstein, Kalman Kacso, Calin Negrean, and Adina Duca. "Formulations about Dynamics of Mobile Robots." Solid State Phenomena 166-167 (September 2010): 309–14. http://dx.doi.org/10.4028/www.scientific.net/ssp.166-167.309.

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In this paper the dynamics equations for a mobile robot, named PatrolBot, will be developed, using new concepts in advanced mechanics, based on important scientific researches of the main author, concerning the kinetic energy. In keeping the fact that the mathematical models of the mobile platforms are different besides the other robots types, due to nonholonomic constraints, these dynamic control functions, will be computed, according to these restrictions for robot motion.

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Qiu, Ning Jia, Ming Zhe Li, Zhen Sui, Cheng Xiang Zheng, Ren Jun Li, and Wei Yao. "Analysis and Synthesis of 6-DOF Robot Measurement Errors." Advanced Materials Research 718-720 (July 2013): 455–59. http://dx.doi.org/10.4028/www.scientific.net/amr.718-720.455.

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Robot motion accuracy plays a vital role in the production which makes use of industrial robots. This paper takes advantage of iterative algorithm to calibrate the robot joint parameters on the basis of setting up mathematical models of 6-DOF robot crossed technology on the mathematical model. It puts forward the method obtained by measuring the pose compared with the theoretical and the robot absolute posing deviation. It provides the basis of surface sheet metal precise scribing work on the next stage.

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Lin, Deng, Giovanni Mottola, Marco Carricato, and Xiaoling Jiang. "Modeling and Control of a Cable-Suspended Sling-Like Parallel Robot for Throwing Operations." Applied Sciences 10, no. 24 (December 18, 2020): 9067. http://dx.doi.org/10.3390/app10249067.

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Cable-driven parallel robots can provide interesting advantages over conventional robots with rigid links; in particular, robots with a cable-suspended architecture can have very large workspaces. Recent research has shown that dynamic trajectories allow the robot to further increase its workspace by taking advantage of inertial effects. In our work, we consider a three-degrees-of-freedom parallel robot suspended by three cables, with a point-mass end-effector. This model was considered in previous works to analyze the conditions for dynamical feasibility of a trajectory. Here, we enhance the robot’s capabilities by using it as a sling, that is, by throwing a mass at a suitable time. The mass is carried at the end-effector by a gripper, which releases the mass so that it can reach a given target point. Mathematical models are presented that provide guidelines for planning the trajectory. Moreover, results are shown from simulations that include the effect of cable elasticity. Finally, suggestions are offered regarding how such a trajectory can be optimized.

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Wang, Chuanwei, Saisai Wang, Hongwei Ma, Heng Zhang, Xusheng Xue, Haibo Tian, and Lei Zhang. "Research on the Obstacle-Avoidance Steering Control Strategy of Tracked Inspection Robots." Applied Sciences 12, no. 20 (October 18, 2022): 10526. http://dx.doi.org/10.3390/app122010526.

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Tracked inspection robots possess prominent advantages in dealing with severe environment rescue, safety inspection, and other important tasks, and have been used widely. However, tracked robots are affected by skidding and slipping, so it is difficult to achieve accurate control. For example, the control parameters of a tracked robot are the same during driving, but the pressure, shear force and steering resistance of the robot on the road surface are different, which affects the steering characteristics of the robot on complex terrain. Based on analysis of the structural parameters and steering radius of the robot, the traction force and resistance torque models of the tracked robot were established, and the plane dynamics of the robot’s steering were analyzed and solved. The corresponding relationships between the road parameters, relative steering radius, and lateral relative offset of the robot on three typical roads were obtained. Mathematical models of the robot’s track speed and relative steering radius with and without skid and slip were established. Through simulation analysis of Matlab software, the corresponding relationship between the relative steering radius of the robot and the velocity difference of the two tracks were obtained. Taking angular obstacles as an example, three obstacle-avoidance steering control strategies, once turning in situ center, twice turning in situ center, and large-radius steering were developed. The tracked robot and obstacle multi-body dynamic simulation models were constructed using ADAMS simulation software. The simulation results show that all three methods can complete the steering tasks according to the requirements; however, under the influence of skid and slip, the trajectory of the robot deviates from the ideal trajectory, which has a great impact on large-radius steering, even though the large-radius obstacle-avoidance steering control strategy has the advantages of a smooth trajectory, fast steering speed, and high efficiency. The obstacle-avoidance steering experiments were completed by the robot prototype, which verifies the rationality of robot steering theory, which could provide the corresponding theoretical basis for autonomous obstacle-avoidance navigation control of a tracked robot.

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Góra, Krystian, Mateusz Kujawinski, Damian Wroński, and Grzegorz Granosik. "Comparison of Energy Prediction Algorithms for Differential and Skid-Steer Drive Mobile Robots on Different Ground Surfaces." Energies 14, no. 20 (October 15, 2021): 6722. http://dx.doi.org/10.3390/en14206722.

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A detailed literature analysis depicts that artificial neural networks are rarely used for the power consumption estimation in the mobile robotics field. Instead, researchers prefer to develop analytical models of investigated robots. This manuscript presents a comparison of mathematical models and non-complex artificial neural networks in energy prediction tasks for differential and skid-steer drive robots which move over various types of surfaces. The results show that both methods could be used interchangeably but AI methods are more universal, do not depend on the kinematic structure of a robot and are tolerant for designers not having a complex knowledge about the system.

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Pengfei, Zhou, Oleksiy Kozlov, Oleksandr Gerasin, and Galyna Kondratenko. "Development of computerized monitoring and control system of the mobile robot’s positioning on large ferromagnetic surfaces based on intelligent techniques. Thesis and study of the mathematical model of a caterpillar mobile robot for vertical movement." Science Journal Innovation Technologies Transfer, no. 2019-2 (May 5, 2019): 36–45. http://dx.doi.org/10.36381/iamsti.2.2019.36-45.

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The article considers the synthesis and study of a mathematical model of a caterpillar mobile robot (MR) with separate main clamping magnets for moving and performing specified technological operations along inclined and vertical ferromagnetic surfaces. The authors have developed the mathematical models of MR's individual elements and the robot as a whole, taking into account the basic features of its structural design. The resulting mathematical model allows studying the MR’s behavior in different production conditions under spatial motion on an inclined surface and can be applied for further synthesis of the automatic control system for positioning such robots.

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Savin, S. I., and L. Yu Vorochaeva. "SIMULATION OF ANTHROPOMORPHIC ROBOTS WITH ELASTIC DRIVES BY INTRODUCING VIRTUAL LINKS." Proceedings of the Southwest State University 22, no. 3 (June 28, 2018): 59–66. http://dx.doi.org/10.21869/2223-1560-2018-22-3-59-66.

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Anthropomorphic walking robots are among the most promising robot types, due to the possibility to introduce them into the urbane environment through the use of the existing infrastructure. Control systems developed for such robots require access to the exact mathematical models of these robots, taking into account the properties of actuators, gears and sensors. In this paper, we consider approaches to describing the model of a bipedal walking robot with elastic drives. The robot is a three-link mechanism that moves in the sagittal plane and performs verticalization (sit-to-stand transfer). Two variants of describing the dynamics of the robot are shown. In the first variant, the number of equations describing the movement of the robot is doubled due to the introduction of elastic drives, in comparison with the case when there are no elastic elements present. In the second variant, there is robot model and the elastic element dynamics model, and bothare described separately. The advantages of this method include the fact that it allows us to preserve the structure and properties of the equations of motion of the mechanism used in constructing control methods in cases when the elastic properties of the gears are not taken into account, and it also allows to conserve the structure of the generalized inertia matrix. The simulation results are presented in two described previously variants, their comparison is made. It is established that both mathematical models behave almost identically, with the most significant differences manifested in the formation of control actions generated by the regulator.

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Pensky, Oleg G., Yuriy A. Sharapov, and Kirill V. Chernikov. "Mathematical Models of Emotional Robots with a Non-Absolute Memory." Intelligent Control and Automation 04, no. 02 (2013): 115–21. http://dx.doi.org/10.4236/ica.2013.42016.

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Cuneo, J., L. Barboni, N. Blanco, M. del Castillo, and J. Quagliotti. "ARM-Cortex M3-Based Two-Wheel Robot for Assessing Grid Cell Model of Medial Entorhinal Cortex: Progress towards Building Robots with Biologically Inspired Navigation-Cognitive Maps." Journal of Robotics 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/8069654.

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This article presents the implementation and use of a two-wheel autonomous robot and its effectiveness as a tool for studying the recently discovered use of grid cells as part of mammalian’s brains space-mapping circuitry (specifically the medial entorhinal cortex). A proposed discrete-time algorithm that emulates the medial entorhinal cortex is programed into the robot. The robot freely explores a limited laboratory area in the manner of a rat or mouse and reports information to a PC, thus enabling research without the use of live individuals. Position coordinate neural maps are achieved as mathematically predicted although for a reduced number of implemented neurons (i.e., 200 neurons). However, this type of computational embedded system (robot’s microcontroller) is found to be insufficient for simulating huge numbers of neurons in real time (as in the medial entorhinal cortex). It is considered that the results of this work provide an insight into achieving an enhanced embedded systems design for emulating and understanding mathematical neural network models to be used as biologically inspired navigation system for robots.

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Trang, Thanh Trung, Wei Guang Li, and Thanh Long Pham. "A New Method to Solve the Kinematic Problem of Parallel Robots Using an Equivalent Structure." Applied Mechanics and Materials 789-790 (September 2015): 643–51. http://dx.doi.org/10.4028/www.scientific.net/amm.789-790.643.

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This paper proposed a new method to downgrade the kinematic mathematical model of parallel robots. A technique of complement mathematical models uses constraints to change the form of objective functions. An equivalent structure is used to replace the original structure of investigated robots. The difficulties encountered in solving problems having the transcendental form can be avoided by downgrading formula of the new mathematical model. The original formula which is usually in quaternary order can be downgraded to quadratic form. The main advantages of this method are understandable mathematical basis, high accuracy, and quick convergence. Carrying out solutions for pracitical kinematic problems of parallel robots becomes very promissable.

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Lee, Hai-Wu. "A study of the use of fuzzy control theory to stabilize the gait of biped robots." Robotica 34, no. 4 (July 24, 2014): 777–90. http://dx.doi.org/10.1017/s0263574714001854.

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SUMMARYThis paper designs a biped robot to perform appropriate walking exercises according to the terrain, which then walks stably on a flat environment. The concept of fuzzy logic is combined with the Linear Quadratic Regulator (LQR) controller theory to design the best method to allow the biped robot system to have a balanced and stable gait. Traditional controllers are designed using mathematical models of physical systems, but a fuzzy controller is a physical system that uses an inexact mathematical model, which involves sets and membership functions. Fuzzy controllers use fuzzification, fuzzy control rules, and defuzzification. The method and theory of control: A stable gait for robots is achieved using inverse kinematics, fuzzy concepts, the LQR controller theory, path design, and the characteristics of a dynamic equation. It is then simulated using mathematical tools to prove that the system eliminates swinging by biped robots without fuzzy control knowing beforehand the dynamic model the system is using. Proportional-Integral-Differential control achieves a stable gait design in a flat environment.

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Jeyaraman, S., A. Tsourdos, R. Zbikowski, and B. A. White. "Kripke modelling of multiple robots with decentralized cooperation specified with temporal logic." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 219, no. 1 (February 1, 2005): 15–31. http://dx.doi.org/10.1243/095965105x9506.

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Kripke models are used to formalize decentralized cooperation of a group of robots, to propose temporal logic specification of the cooperation, and to verify the correctness of the specification by checking the models. The focus is on implementing this mathematical formalism under minimalist communication and under constrained motion of the robots. Kripke models consist of, firstly, a of possible worlds (system configurations), secondly, an accessibility relation in the (transitions between the worlds), and, thirdly, a labelling function (which logical statements are true in each world). This approach represents continuous dynamics and discrete decision making of the robots in a unified way. Desirable properties of cooperation can be precisely expressed using temporal logic statements defining safety, liveness, etc. Whether a group of robots, whose behaviour is formalized with Kripke models, possesses such properties is then verified using automated model checking tools. The scenarios considered include path planning of a group of three robots moving in an obstacle-free environment, without and with communication among group members. The results show that for each scenario the mathematical formalism of Kripke models expresses the group behaviour in a transparent and tractable way. Finally, desirable properties of the decentralized cooperation, specified with temporal logic, can be verified on the Kripke models by automatic model checking software. Hence, guaranteed performance of cooperating autonomous robots can be assured in a formal, precise, and clear way.

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Figovsky, Oleg L., and Oleg G. Pensky. "Robots, Digital Twins of People, Dialectical Models of Society and Economics." Economic Strategies 144 (September 20, 2020): 58–67. http://dx.doi.org/10.33917/es-5.171.2020.58-67.

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Current mathematical models of economics practically do not take into account the human factor when making management decisions and applying them to practice. Therefore, the creation of a mathematical theory of general human psychology, the dialectical development of human society and macroeconomics are becoming particularly relevant at present. This paper describes the main results of the mathematical modeling of psychological behavior, so-called digital twins, which are psychological analogs of people. Theorems explaining the dangers of artificial intelligence for people from the mentality point of view are formulated. We propose general models of dialectical development of the virtual world for digital twins, human society and macroeconomics.

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Transeth, Aksel Andreas, Kristin Ytterstad Pettersen, and Pål Liljebäck. "A survey on snake robot modeling and locomotion." Robotica 27, no. 7 (March 3, 2009): 999–1015. http://dx.doi.org/10.1017/s0263574709005414.

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SUMMARYSnake robots have the potential to make substantial contributions in areas such as rescue missions, firefighting, and maintenance where it may either be too narrow or too dangerous for personnel to operate. During the last 10–15 years, the published literature on snake robots has increased significantly. The purpose of this paper is to give a survey of the various mathematical models and motion patterns presented for snake robots. Both purely kinematic models and models including dynamics are investigated. Moreover, the different approaches to biologically inspired locomotion and artificially generated motion patterns for snake robots are discussed.

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Wang, Ling, Bai Chen, Peng Wang, Sun Chen, Qian Yun Zhu, and Ya Juan Li. "Thrust Force Modeling of the Flagella-Like Swimming Micro-Robot." Applied Mechanics and Materials 461 (November 2013): 930–41. http://dx.doi.org/10.4028/www.scientific.net/amm.461.930.

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In this paper, helix tails with rectangular cross-section were designed for propelling a kind of flagella-like swimming robot. CFD (Computational Fluid Dynamics) software was applied to analyze the major influencing factors of the robots mechanical properties. It is revealed that the thrust reaches the maximum when the helix tails cross-section width is 0.36 times the diameter. Meanwhile, the helix tails should be designed according to the requirements with the largest diameter, close to but less than 45° helix angle and multi-turns under the limitation of the workspace. Combining these simulation data with the derivation process of Resistive Force Theory, the models for the mechanical properties simulation of the swimming robot were revised, and the explicit empirical formula of propulsive force is obtained. This model lays a good foundation for the robots motion control as well as unified mathematical description for macro-scale and micro-scale robots.

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Maoudj, Abderraouf, Abdelfetah Hentout, Brahim Bouzouia, and Redouane Toumi. "On-Line Fault-Tolerant Fuzzy-Based Path Planning and Obstacles Avoidance Approach for Manipulator Robots." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 26, no. 05 (September 28, 2018): 809–38. http://dx.doi.org/10.1142/s0218488518500368.

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Manipulator robots are widely used in many fields to replace humans in complex and risky environments. However, in some particular environments the robot is prone to failure, resulting in decreased performance. In such environments, it is extremely difficult to repair the robot which interrupts the execution process. Therefore, fault tolerance plays an important role in industrial manipulators applications. In this paper, the key problems related to fault-tolerance and path planning of manipulator robots under joints failures are handled within an on-line fault-tolerant fuzzy-logic based path planning approach for high degree-of-freedom robots. This approach provides an alternative to using mathematical models to control such robots, and improves tolerance to certain faults and mechanical failures. The controller consists of two fuzzy units (i) the first unit, Fuzzy_Path_Planner, is responsible of path planning; (ii) the second unit, Fuzzy_Obstacle_Avoidance, is conceived for obstacles avoidance. Moreover, the proposed approach is capable of repelling the manipulator away from both local minima and limit cycle problems. Finally, to validate the proposed approach and show its performances and effectiveness, different tests are carried out on two six degree-of-freedom manipulator robots (ULM and PUMA560 robots), accomplishing point-to-point tasks, with and without considering some joints failures.

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Al-Yacoub, Ali, Myles Flanagan, Achim Buerkle, Thomas Bamber, Pedro Ferreira, Ella-Mae Hubbard, and Niels Lohse. "Data-Driven Modelling of Human-Human Co-Manipulation Using Force and Muscle Surface Electromyogram Activities." Electronics 10, no. 13 (June 22, 2021): 1509. http://dx.doi.org/10.3390/electronics10131509.

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With collaborative robots and the recent developments in manufacturing technologies, physical interactions between humans and robots represent a vital role in performing collaborative tasks. Most previous studies have focused on robot motion planning and control during the execution of the task. However, further research is required for direct physical contact for human-robot or robot-robot interactions, such as co-manipulation. In co-manipulation, a human operator manipulates a shared load with a robot through a semi-structured environment. In such scenarios, a multi-contact point with the environment during the task execution results in a convoluted force/toque signature that is difficult to interpret. Therefore, in this paper, a muscle activity sensor in the form of an electromyograph (EMG) is employed to improve the mapping between force/torque and displacements in co-manipulation tasks. A suitable mapping was identified by comparing the root mean square error amongst data-driven models, mathematical models, and hybrid models. Thus, a robot was shown to effectively and naturally perform the required co-manipulation with a human. This paper’s proposed hypotheses were validated using an unseen test dataset and a simulated co-manipulation experiment, which showed that the EMG and data-driven model improved the mapping of the force/torque features into displacements.

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Filomeno Amador, Luis Daniel, and Eduardo Castillo Castañeda. "Kinematic and dynamic analysis of an omnidirectional mobile platform driven by a spherical wheel." Mechanical Sciences 13, no. 1 (February 7, 2022): 31–39. http://dx.doi.org/10.5194/ms-13-31-2022.

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Abstract. The increased use of spherical wheels has allowed mobile robots to have a higher degree of maneuverability, less complex path planning and less complex control schemes. The geometry and design of the mobile robot are the principal attributes that guarantee an omnidirectional motion. Furthermore, the platform uses an active spherical wheel and four passive spherical wheels to get the best stability when the robot uses a terminal element (Kärcher). The proposed model has been designed to improve the omnidirectional motion issues, such as vibration into the platform or lack of punctual contact between the wheel and the floor, compared to mobile robots using Mecanum wheels and more than one active wheel; due to the design concept, all the mathematical formulations, kinematics and dynamics presents how the models are validated with computer simulations.

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Raviola, Andrea, Roberto Guida, Andrea De Martin, Stefano Pastorelli, Stefano Mauro, and Massimo Sorli. "Effects of Temperature and Mounting Configuration on the Dynamic Parameters Identification of Industrial Robots." Robotics 10, no. 3 (June 29, 2021): 83. http://dx.doi.org/10.3390/robotics10030083.

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Dynamic parameters are crucial for the definition of high-fidelity models of industrial manipulators. However, since they are often partially unknown, a mathematical model able to identify them is discussed and validated with the UR3 and the UR5 collaborative robots from Universal Robots. According to the acquired experimental data, this procedure allows for reducing the error on the estimated joint torques of about 90% with respect to the one obtained using only the information provided by the manufacturer. The present research also highlights how changes in the robot operating conditions affect its dynamic behavior. In particular, the identification process has been applied to a data set obtained commanding the same trajectory multiple times to both robots under rising joints temperatures. Average reductions of the viscous friction coefficients of about 20% and 17% for the UR3 and the UR5 robots, respectively, have been observed. Moreover, it is shown how the manipulator mounting configuration affects the number of the base dynamic parameters necessary to properly estimate the robots’ joints torques. The ability of the proposed model to take into account different mounting configurations is then verified by performing the identification procedure on a data set generated through a digital twin of a UR5 robot mounted on the ceiling.

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POTKONJAK, VELJKO. "ROBOTIC HANDWRITING." International Journal of Humanoid Robotics 02, no. 01 (March 2005): 105–24. http://dx.doi.org/10.1142/s021984360500034x.

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Handwriting has always been considered an important human task, and accordingly it has attracted the attention of researchers working in biomechanics, physiology, and related fields. There exist a number of studies on this area. This paper considers the human–machine analogy and relates robots with handwriting. The work is two-fold: it improves the knowledge in biomechanics of handwriting, and introduces some new concepts in robot control. The idea is to find the biomechanical principles humans apply when resolving kinematic redundancy, express the principles by means of appropriate mathematical models, and then implement them in robots. This is a step forward in the generation of human-like motion of robots. Two approaches to redundancy resolution are described: (i) "Distributed Positioning" (DP) which is based on a model to represent arm motion in the absence of fatigue, and (ii) the "Robot Fatigue" approach, where robot movements similar to the movements of a human arm under muscle fatigue are generated. Both approaches are applied to a redundant anthropomorphic robot arm performing handwriting. The simulation study includes the issues of legibility and inclination of handwriting. The results demonstrate the suitability and effectiveness of both approaches.

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Luft, Lukas, Tobias Schubert, Stergios I. Roumeliotis, and Wolfram Burgard. "Recursive decentralized localization for multi-robot systems with asynchronous pairwise communication." International Journal of Robotics Research 37, no. 10 (March 16, 2018): 1152–67. http://dx.doi.org/10.1177/0278364918760698.

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This paper provides a fully decentralized algorithm for collaborative localization based on the extended Kalman filter. The major challenge in decentralized collaborative localization is to track inter-robot dependencies, which is particularly difficult when sustained synchronous communication between the robots cannot be guaranteed. Current approaches suffer from the need for particular communication schemes, extensive bookkeeping of measurements, overly conservative assumptions, or the restriction to specific measurement models. This paper introduces a localization algorithm that is able to approximate the inter-robot correlations while fulfilling all of the following conditions: communication is limited to two robots that obtain a relative measurement, the algorithm is recursive in the sense that it does not require storage of measurements and each robot maintains only the latest estimate of its own pose, and it supports generic measurement models. The fact that the proposed approach can handle these particularly difficult conditions ensures that it is applicable to a wide range of multi-robot scenarios. We provide mathematical details on our approximation. Extensive experiments carried out using real-world datasets demonstrate the improved performance of our method compared with several existing approaches.

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Hoorn, Johan F., and Matthijs A. Pontier. "Robot communication - human contact with androids." Information Design Journal 16, no. 3 (December 8, 2008): 236–41. http://dx.doi.org/10.1075/idj.16.3.08hoo.

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We are increasingly communicating with robots, and the design of lifelike humanoid robots will face at least five challenges. 1) Robots should meet social needs – people are getting older, lonelier, and are looking for alternatives to face-to-face contact, for instance, in coaching and therapy. 2) Robot designers assume that the better they can simulate social and affective behavior, the more effective the robotic partner is. Yet, it is not always clear what natural behavior is, nor whether maximal humanlikeness equals optimal user satisfaction. 3) Multidisciplinary design teams require transdisciplinary theory to create mutual understanding and cover the wide-ranging facets of robot design. However, combining diverse theories from different domains means confronting major unification problems. 4) Empirical approaches to robot design usually miss out on logic consistency within theory. Conversely, formalization and mathematical modeling often lack external validity. Verification before validation seems to be the new way to go. 5) Finally, if it is actually possible to create lifelike, affective, sociable androids, the cognitive models underlying their behavior may be open to abuse, for example in malicious software that spies on people.

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Gaiduk, A. R., I. A. Kalyaev, S. G. Kapustyan, and I. O. Shapovalov. "DESIGN OF THE CONTROL SYSTEM BY MOVEMENT OF ROBOTS MOBILE GROUP IN CONDITIONS OF UNCERTAINTY." Proceedings of the Southwest State University 22, no. 4 (August 28, 2018): 112–22. http://dx.doi.org/10.21869/2223-1560-2018-22-4-112-122.

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Many controlled plants, in particular mobile robots, solve various tasks in a priori uncertain conditions. In this connection their mathematical models necessary for creation of qualitative control systems are unknown. Therefore development of design methods of adaptive control systems is actuality. The big uncertainty of this control problem makes application of adaptive systems with identification by the most expedient. In article the new analytical design method of adaptive control systems by movement of mobile robots group in the uncertainty conditions is offered. This method is focused on the decision of a task of identification of the current mathematical models of robots with the subsequent design of a control system by movement of each robot. The suggested method can be realized automatically as required. It is developed on a basis of the markov method of identification, the method of analytical design of systems with control on output and impacts, and also the standard normalized transfer functions are used. As a whole this method allows to design of the adaptive control systems with desirable qualitative properties. Trial step functions of the small intensity and the original method of digital processing of the information are used at identification. Property of system invariancy of the markov parameters and their direct connection with factors of the discrete dynamic systems transfer functions are a basis of the method of digital processing of the information. It is supposed, that the mobile robots are full or can be stabilized at all possible values of their order and parameters. The suggested method can be used for creation of control systems by the various technical plants functioning in conditions of uncertainty.

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Galin, R. R., V. V. Serebrennyj, G. K. Tevyashov, and A. A. Shiroky. "Human-robot Interaction in Collaborative Robotic Systems." Proceedings of the Southwest State University 24, no. 4 (February 4, 2021): 180–99. http://dx.doi.org/10.21869/2223-1560-2020-24-4-180-199.

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Purpose or research is to find solvable tasks for increasing the effectiveness of collaborative interaction between people and robots in ergatic robotic systems, or, in other words, in collaborative robotic systems. Methods. A comprehensive analysis of works published in highly rated peer-reviewed open-access scientific publications was carried out to achieve this goal. Main terms and concepts of collaborative robotics are described in § 1 and their current understanding in the research community is also described. The structure of workspaces in interaction zone of a person and robot is described. The criteria for assigning robot to the class of collaborative ones are also described. The criteria for safe interaction of a person and robot in a single workspace is described in § 2. Various grounds for classifying human-robot interactions in collaborative RTAs are described in § 3. Results. A significant part of published works about collaborative robotics is devoted to the organization of safe man and robot interaction. Less attention is paid to the effectiveness improvement of such interaction. An up-to-date task in the problem of efficiency improvement of collaborative robotic systems is the identification of tasks that have already been solved in other areas - in particular, in the field of organizational systems management. The possibility of using the term "team" for collaborative robots in a collaborative PTC is stated in § 4. A formal problem setting of optimal distribution in teamwork of collaborative robots, similar to the problem of heterogeneous team formation in the theory of organizational systems management is proposed in § 5. Conclusions. Proposed task setting of optimal distribution of works in collaborative robots’ team shows possibility of using results obtained in group of mathematical models of commands formation and functioning for control of collaborative robotic systems in order to increase efficiency of people and robots interaction. It is prospectively to continue the search for adapting models and governance mechanisms to the theory of organizational system management and integrated activities methodology.

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Pensky, O. G., and N. V. Oschepkova. "Mathematical models for education of robots with non-absolute memory using the media." Вестник Пермского университета. Математика. Механика. Информатика, no. 3 (46) (2019): 65–71. http://dx.doi.org/10.17072/1993-0550-2019-3-65-71.

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TAKEMATSU, Ryo, Naoki SATONAKA, Wiroj THASANA, Koji IWAMURA, and Nobuhiro SUGIMURA. "A study on tolerances design of parallel link robots based on mathematical models." Journal of Advanced Mechanical Design, Systems, and Manufacturing 12, no. 1 (2018): JAMDSM0015. http://dx.doi.org/10.1299/jamdsm.2018jamdsm0015.

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Vukobratović, M., D. Katić, and V. Potkonjak. "Computer-assisted choice of electrohydraulic servosystems for manipulation robots using complete mathematical models." Mechanism and Machine Theory 22, no. 5 (January 1987): 431–39. http://dx.doi.org/10.1016/0094-114x(87)90060-7.

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Refaai, Mohamad Reda A. "An Improved Inverse Kinematics Solution for a Robot Arm Trajectory Using Multiple Adaptive Neuro-Fuzzy Inference Systems." Advances in Materials Science and Engineering 2022 (September 9, 2022): 1–12. http://dx.doi.org/10.1155/2022/1413952.

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Inverse kinematics of robots is a critical topic in the robotics field. Although there are conventional ways of solving inverse kinematics, soft computing is an important technology that has lately gained prominence due to its ability to reduce the complexity of the inverse kinematics problem. This paper presents an inverse kinematics solution using multiple adaptive neuro-fuzzy inference systems (MANFIS). Different models were established by employing various methods of identification. Subtractive Clustering (SCM), Fuzzy C-Means Clustering (FCM), and Grid Partitioning (GP) are the three methods used in this study. This work is being carried out on a 5-DOF articulated robot arm, which is commonly used in industry. A mathematical model is built based on the Denavit-Hartenberg (DH) approach. Following confirmation that the kinematic findings of the mathematical model match the actual observed values of the robot arm, two types of data sets are generated: a random data set and a systematic data set based on a trajectory. The data sets are then utilized to train and evaluate ANFIS models and choose the optimal models to develop MANFIS model. Thus, the prediction and experimental data are compared to assess the performance of the MANFIS model.

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Павлюк, Н. А. "Mathematical and algorithmic models of reconfiguration of a modular robotic system." Вестник КРАУНЦ. Физико-математические науки, no. 4 (December 29, 2020): 122–31. http://dx.doi.org/10.26117/2079-6641-2020-33-4-122-131.

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Обоснована актуальность научной проблемы разработки алгоритмических моделей и программных средств автономного соединения и взаимодействия модульных гомогенных роботов. Представлен обзор существующих модульных робототехнических устройств и модульных робототехнических систем. Рассмотрены разработанные концептуальная и теоретико-множественная модели модульной робототехнической системы. Описаны алгоритмы физического соединения и информационного взаимодействия гомогенных модульных робототехнических устройств при построении связанных пространственных структур. The relevance of a research problem is justified, which consists in development of the algorithmic models and software components for autonomous connection and interaction of the modular homogeneous robots. A review of existing modular robotic devices and modular robotic systems is presented. Developed conceptual and set-theoretic models of a modular robotic system are considered. Algorithms of physical connection and data exchange of homogeneous modular robotic devices are described in context of composition of coupled spatial structures.

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Krakhmalev, Oleg, Nikita Krakhmalev, Sergey Gataullin, Irina Makarenko, Petr Nikitin, Denis Serdechnyy, Kang Liang, and Sergey Korchagin. "Mathematics Model for 6-DOF Joints Manipulation Robots." Mathematics 9, no. 21 (November 8, 2021): 2828. http://dx.doi.org/10.3390/math9212828.

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A universal solution to an applied problem related to the study of deviations occurring in the joints of manipulation robots, for example, due to elastic deformations or gaps in them, is proposed. A mathematical (dynamic) model obtained by the Lagrange–Euler method is presented, making it possible to investigate such deviations. Six generalized coordinates, three linear and three angulars, were used to describe the variations of each joint in the dynamic model. This made it possible to introduce into consideration joints with six degrees of freedom (6-DOF joints). In addition, mathematical models for external forces acting on the links of manipulation robots are presented. When composing matrices of coefficients of equations of motion, elements identically equal to zero were excluded, which significantly increased the computational efficiency of these equations. The dynamic model based on the obtained equations can be used in the computer simulation of manipulation robots.

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Ammar Amouri, Chawki Mahfoudi, and Abdelouahab Zaatri. "Dynamic Modeling of a Spatial Cable-Driven Continuum Robot Using Euler-Lagrange Method." International Journal of Engineering and Technology Innovation 10, no. 1 (January 1, 2020): 60–74. http://dx.doi.org/10.46604/ijeti.2020.4422.

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Continuum robots are kinematically redundant and their dynamic models are highly nonlinear. This study aims to overcome this difficulty by presenting a more practical dynamic model of a certain class of continuum robots called cable-driven continuum robot (CDCR). Firstly, the structural design of a CDCR with two rotational degrees of freedom (DOF) is introduced. Then, the kinematic models are derived according to the constant curvature assumption. Considering the complexity of the kinetic energy expression, it has been approximated by the well-known Taylor expansions. This case corresponds to weak bending angles within the specified bending angle range of the robot. On the other hand, due to the low weight of the CDCR components, the gravitational energy effects can be neglected compared to those stemmed from the elastic energy. Thereafter, the corresponding dynamic model is established using Euler-Lagrange method. Static and dynamic models have been illustrated by examples. This analysis and dynamic model development have been compared with the existing scientific literature. The obtained results shown that the consistency and the efficiency of accuracy for real-time have been carried out. However, the dynamic modeling of CDCR with more than 2-DOF leads to a more complex mathematical expression, and cannot be simplified by adopting the similar assumptions and methodology used in the case of 2-DOF.

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Sawai, Kana, Yutaka Nomaguchi, and Kikuo Fujita. "Fundamental framework toward optimal design of product platform for industrial three-axis linear-type robots." Journal of Computational Design and Engineering 2, no. 3 (March 11, 2015): 157–64. http://dx.doi.org/10.1016/j.jcde.2015.03.002.

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Abstract This paper discusses an optimization-based approach for the design of a product platform for industrial three-axis linear-type robots, which are widely used for handling objects in manufacturing lines. Since the operational specifications of these robots, such as operation speed, working distance and orientation, weight and shape of loads, etc., will vary for different applications, robotic system vendors must provide various types of robots efficiently and effectively to meet a range of market needs. A promising step toward this goal is the concept of a product platform, in which several key elements are commonly used across a series of products, which can then be customized for individual requirements. However the design of a product platform is more complicated than that of each product, due to the need to optimize the design across many products. This paper proposes an optimization-based fundamental framework toward the design of a product platform for industrial three-axis linear-type robots; this framework allows the solution of a complicated design problem and builds an optimal design method of fundamental features of robot frames that are commonly used for a wide range of robots. In this formulation, some key performance metrics of the robot are estimated by a reduced-order model which is configured with beam theory. A multi-objective optimization problem is formulated to represent the trade-offs among key design parameters using a weighted-sum form for a single product. This formulation is integrated into a mini–max type optimization problem across a series of robots as an optimal design formulation for the product platform. Some case studies of optimal platform design for industrial three-axis linear-type robots are presented to demonstrate the applications of a genetic algorithm to such mathematical models.

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Kalani, Hadi, Alireza Akbarzadeh, and Hossein Bahrami. "Application of statistical techniques in modeling and optimization of a snake robot." Robotica 31, no. 4 (November 16, 2012): 623–41. http://dx.doi.org/10.1017/s0263574712000616.

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SUMMARYThis paper provides a general framework based on statistical design and Simulated Annealing (SA) optimization techniques for the development, analysis, and performance evaluation of forthcoming snake robot designs. A planar wheeled snake robot is considered, and the effect of its key design parameters on its performance while moving in serpentine locomotion is investigated. The goal is to minimize energy consumption and maximize distance traveled. Key kinematic and dynamic parameters as well as their corresponding range of values are identified. Derived dynamic and kinematic equations of n-link snake robot are used to perform simulation. Experimental design methodology is used for design characterization. Data are collected as per full factorial design. For both energy consumption and distance traveled, logarithmic, linear, and curvilinear regression models are generated and the best models are selected. Using analysis of variance, ANOVA, effects of parameters on performance of robots are determined. Next, using SA, optimum parameter levels of robots with different number of links to minimize energy consumption and maximize distance traveled are determined. Both single and multi-criteria objectives are considered. Webots and Matlab SimMechanics software are used to validate theoretical results. For the mathematical model and the selected range of values considered, results indicate that the proposed approach is quite effective and efficient in optimization of robot performance. This research extends the present knowledge in this field by identifying additional parameters having significant effect on snake robot performance.

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de Melo, Leonimer Flavio, and Jose Fernando Mangili Junior. "Trajectory Planning for Nonholonomic Mobile Robot Using Extended Kalman Filter." Mathematical Problems in Engineering 2010 (2010): 1–22. http://dx.doi.org/10.1155/2010/979205.

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In the mobile robotic systems, a precise estimate of the robot pose with the intention of the optimization in the path planning is essential for the correct performance, on the part of the robots, for tasks that are destined to it. This paper describes the use of RF digital signal interacting with beacons for computational triangulation in the way to provide a pose estimative at bidimensional indoor environment, where GPS system is out of range. This methodology takes advantage of high-performance multicore DSP processors to calculate ToF of the order about ns. Sensors data like odometry, compass, and the result of triangulation Cartesian estimative, are fused for better position estimative. It uses a mathematical and computational tool for nonlinear systems with time-discrete sampling for pose estimative calculation of mobile robots, with the utilization of extended Kalman filter (EKF). A mobile robot platform with differential drive and nonholonomic constraints is used as a base for state space, plants and measurements models that are used in the simulations and validation of the experiments.

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Kovalchuk, Alexander, and F. Akhmetova. "Denavit-Hartenberg Coordinate System for Robots with Tree-like Kinematic Structure." IAES International Journal of Robotics and Automation (IJRA) 5, no. 4 (December 1, 2016): 244. http://dx.doi.org/10.11591/ijra.v5i4.pp244-254.

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<p class="MDPI17abstract"><span lang="EN-US">The paper presents a modified Denavit-Hartenberg coordinate system resulted from joint application of graph theory and the Denavit-Hartenberg coordinate system, which was developed to describe the kinematics of robot actuators with a linear open kinematic chain. It allows forming mathematical models of actuating mechanisms for the robots with tree-like kinematic structures. The work introduces the concept of primary and auxiliary coordinate systems. It considers an example of making the links’ reachability matrix and reachability graph for the tree-like actuating mechanism of a robotic mannequin. The use efficiency of the proposed modified Denavit-Hartenberg coordinate system is illustrated by the examples giving the mathematical description of the kinematics and dynamics of specific robots’ tree-like actuating mechanisms discussed in the previously published papers. It is shown that the proposed coordinate system can also be successfully applied to describe the actuating mechanisms of robots with a linear open kinematic chain, which is a particular case of the tree-like kinematic structure. The absence of branching joints in it does not require introducing auxiliary coordinate systems and the parameters f(i) and ns(i) are necessary only for the formal notation of equations, which have similar forms for the tree-like and linear chains. In this case, the modified and traditional coordinate systems coincide.</span></p>

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Ijspeert, Auke. "Decoding the mechanisms of gait transition in the salamander using robots and mathematical models." Comparative Biochemistry and Physiology Part A: Molecular & Integrative Physiology 153, no. 2 (June 2009): S136. http://dx.doi.org/10.1016/j.cbpa.2009.04.247.

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Baba, Isa Abdullahi, Bashir Abdullahi Baba, and Parvaneh Esmaili. "A Mathematical Model to Study the Effectiveness of Some of the Strategies Adopted in Curtailing the Spread of COVID-19." Computational and Mathematical Methods in Medicine 2020 (October 13, 2020): 1–6. http://dx.doi.org/10.1155/2020/5248569.

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In this paper, we developed a model that suggests the use of robots in identifying COVID-19-positive patients and which studied the effectiveness of the government policy of prohibiting migration of individuals into their countries especially from those countries that were known to have COVID-19 epidemic. Two compartmental models consisting of two equations each were constructed. The models studied the use of robots for the identification of COVID-19-positive patients. The effect of migration ban strategy was also studied. Four biologically meaningful equilibrium points were found. Their local stability analysis was also carried out. Numerical simulations were carried out, and the most effective strategy to curtail the spread of the disease was shown.

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Winston, Sheldon Ijau, and Annisa Jamali. "Axis manipulation to solve Inverse Kinematics of Hyper-Redundant Robot in 3D Space." Journal of Integrated and Advanced Engineering (JIAE) 2, no. 2 (September 24, 2022): 113–22. http://dx.doi.org/10.51662/jiae.v2i2.81.

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A solution based on inverse kinematics is required for the robot's end effector, also known as its tip, to reach a target. Current methods for solving the inverse kinematics solution for a hyper-redundant robot in three 3D are generally complex, difficult to visualize, and time-intensive. This requires the development of new algorithms for solving inverse kinematics in a quicker and more efficient manner. In this study, an axis manipulation using a geometrical approach is used. Initially, a general algorithm for a 2 m-link hyper-redundant robot in 3D is generated. The method employed a repetitive basic inverse kinematics solution of a two-link robot on virtual links. The virtual links are generated using a specific geometric proposition. Finally, the 3D solution is generated by rotating about the global z-axis. This method reduces the mathematical complexity required to solve the inverse kinematics solution for a 2-m-link robot. In addition, this method can manage variable link manipulators, thereby eliminating singularity. To demonstrate the effectiveness of the model, numerical simulations of hyper redundant models in 3D are presented. This new geometric approach is anticipated to enhance the performance of hyper-redundant robots, enabling them to be of greater assistance in fields such as medicine, the military, and search and rescue.

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Signa, Alessandro, Antonio Chella, and Manuel Gentile. "Cognitive Robots and the Conscious Mind: A Review of the Global Workspace Theory." Current Robotics Reports 2, no. 2 (April 6, 2021): 125–31. http://dx.doi.org/10.1007/s43154-021-00044-7.

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Abstract Purpose of Review The theory of consciousness is a subject that has kept scholars and researchers challenged for centuries. Even today it is not possible to define what consciousness is. This has led to the theorization of different models of consciousness. Starting from Baars’ Global Workspace Theory, this paper examines the models of cognitive architectures that are inspired by it and that can represent a reference point in the field of robot consciousness. Recent Findings Global Workspace Theory has recently been ranked as the most promising theory in its field. However, this is not reflected in the mathematical models of cognitive architectures inspired by it: they are few, and most of them are a decade old, which is too long compared to the speed at which artificial intelligence techniques are improving. Indeed, recent publications propose simple mathematical models that are well designed for computer implementation. Summary In this paper, we introduce an overview of consciousness and robot consciousness, with some interesting insights from the literature. Then we focus on Baars’ Global Workspace Theory, presenting it briefly. Finally, we report on the most interesting and promising models of cognitive architectures that implement it, describing their peculiarities.

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Kozov, Aleksei V. "MODELS AND DESIGNING METHODS FOR THE DYNAMICALLY RECONFIGURABLE GROUP CONTROL SYSTEM FOR MOBILE ROBOTS." АВТОМАТИЗАЦИЯ ПРОЦЕССОВ УПРАВЛЕНИЯ 63, no. 1 (2021): 130–39. http://dx.doi.org/10.35752/1991-2927-2021-1-63-130-139.

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High adaptability is an important requirement for the control system over a group of mobile robots operating in a nondeterministic changing environment. The group control system must ensure that the group task is completed when the structure of the group or the environment changes. Such adaptability can be achieved through dynamic reconfiguration of the control system. The article discusses the mathematical models of a dynamically reconfigurable system from the standpoint of computer-aided design. A review of mathematical models of variable structure system, reconfigurable control systems and their design methods is presented. The paper deals with set-theoretic, analytical, discrete-event models of variable structure systems and methodologies of designing reconfigurable systems. It is shown that the existing design methods do not fully provide the required adaptability of designed group control system. The paper compares the group control system and the reconfigurable multiprocessor computing system and shows how to increase adaptability and autonomy of designed control system using principles of reconfigurable computing systems designing.

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Sun, Na, Quan Qiu, Zhengqiang Fan, Tao Li, Chao Ji, Qingchun Feng, and Chunjiang Zhao. "Intrinsic Calibration of Multi-Beam LiDARs for Agricultural Robots." Remote Sensing 14, no. 19 (September 28, 2022): 4846. http://dx.doi.org/10.3390/rs14194846.

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With the advantages of high measurement accuracy and wide detection range, LiDARs have been widely used in information perception research to develop agricultural robots. However, the internal configuration of the laser transmitter layout changes with increasing sensor working duration, which makes it difficult to obtain accurate measurement with calibration files based on factory settings. To solve this problem, we investigate the intrinsic calibration of multi-beam laser sensors. Specifically, we calibrate the five intrinsic parameters of LiDAR with a nonlinear optimization strategy based on static planar models, which include measured distance, rotation angle, pitch angle, horizontal distance, and vertical distance. Firstly, we establish a mathematical model based on the physical structure of LiDAR. Secondly, we calibrate the internal parameters according to the mathematical model and evaluate the measurement accuracy after calibration. Here, we illustrate the parameter calibration with three steps: planar model estimation, objective function construction, and nonlinear optimization. We also introduce the ranging accuracy evaluation metrics, including the standard deviation of the distance from the laser scanning points to the planar models and the 3σ criterion. Finally, the experimental results show that the ranging error of calibrated sensors can be maintained within 3 cm, which verifies the effectiveness of the laser intrinsic calibration.

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Wang, Yingxu. "Classic Probability Revisited (I): Mathematical Models of an Extended Probability Theory." PROOF 2 (March 17, 2022): 77–85. http://dx.doi.org/10.37394/232020.2022.2.10.

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Part I of this paper presents a set of extended mathematical models of probability theory in order to explain the nature, properties, and rules of general probability. It is found that probability is a hyperstructure beyond those of the traditional monotonic and one-dimensional discrete structures. The sample space of probability is not invariant in general cases. Types of vents in the sample space may be refined as joint or disjoint and dependent, independent, or mutuallyexclusive. These newly identified properties lead to a three-dimensional dynamic model of probability structures constrained by the type of sample spaces, the relation of events, and the dependency of events. A set of algebraic operators on the mathematical structures of the general probability theory is derived based on the extended mathematical models of probability. It is revealed that the Bayes’ law needs to be extended in order to fit more general contexts on variant sample spaces and complex event properties in fundamental probability theories. The revisited probability theory enables a rigorous treatment of uncertainty events and causations in formal inference, qualification, quantification, and semantic analysis in contemporary fields such as cognitive informatics, computational intelligence, cognitive robots, complex systems, soft computing, and brain informatics.

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Kamleshwar, Sahil. "Robotics and Automation." International Journal for Research in Applied Science and Engineering Technology 9, no. VII (July 30, 2021): 2852–56. http://dx.doi.org/10.22214/ijraset.2021.35723.

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Cloud infrastructure and its extensive set of Internet-enabled resources have the potential to provide significant benefits to robots and flexible systems. We look for robots and data-switching programs or code from the network to support their performance, that is, when not all sense, calculation, and memory are integrated into the standalone system. This survey is designed for four possible Cloud benefits: 1) Big Data: access to photo libraries, maps, trajectories, and descriptive data; 2) Cloud Computing: access to the same grid computer with the demand for mathematical analysis, reading, and movement planning; 3) Integrated Robots Learning: robots that share tracking, control policies, and results; and 4) Census: use of crowdourcing to tap people's skills for image and video analysis, classification, reading, and error retrieval. The cloud can also improve robots and flexible systems by providing access to: a) data sets, publications, models, measurements, and simulation tools; b) open competitions for designs and programs; and c) open source software.

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Birlescu, Iosif, Manfred Husty, Calin Vaida, Bogdan Gherman, Paul Tucan, and Doina Pisla. "Joint-Space Characterization of a Medical Parallel Robot Based on a Dual Quaternion Representation of SE(3)." Mathematics 8, no. 7 (July 3, 2020): 1086. http://dx.doi.org/10.3390/math8071086.

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The paper proposes a mathematical method for redefining motion parameterizations based on the joint-space representation of parallel robots. The study parameters of SE(3) are used to describe the robot kinematic chains, but, rather than directly analyzing the mobile platform motion, the joint-space of the mechanism is studied by eliminating the Study parameters. From the loop equations of the joint-space characterization, new parameterizations are defined, which enable the placement of a mobile frame on any mechanical element within the parallel robot. A case study is presented for a medical parallel robotic system in which the joint-space characterization is achieved and based on a new defined parameterization, the kinematics for displacement, velocities, and accelerations are studied. A numerical simulation is presented for the derived kinematic models, showing how the medical robot guides the medical tool (ultrasound probe) on an imposed trajectory.

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Journal articles on the topic 'Robots Mathematical models'

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