Inverse Kinematics and Trajectory Planning Analysis of a Robotic Manipulator

In this work, we pretended to show and compare three methodologies used to solve the inverse kinematics of a 3 DOF robotic manipulator. The approaches are the algebraic method through Matlabreg; solve function, Genetic Algorithms (GAs), Artificial Neural Networks (ANNs). Another aspect considered is the trajectory planning of the manipulator, which allows the user to control the desired movement in the joint space. We compare polynomials of third, fourth and fifth orders for the solution of the chosen coordinates. The results show that the ANN method presented best results due to its configuration to show only feasible joint values, as also do the GA. In the trajectory planning the analysis lead to the fifth-order polynomial, which showed the smoothest solution

Direct kinematics and analytical solution to 3RRR parallel planar mechanisms

This paper presents the direct kinematic solutions to 3DOF planar parallel mechanisms. Efforts to solve the direct kinematics of planar parallel mechanisms have concentrated on RPR mechanisms due to its inherent simplicity. It is established that the direct kinematic equations of a general 3DOF planar parallel mechanism can be reduced to a univariate polynomial of degree 8. This paper presents the derivation of this univariate polynomials for both 3RRR and 3RPR mechanisms, showing the similarities and differences between the two common configurations of 3DOF planar parallel mechanisms. This paper also presents the on the direct kinematic solution to a simplified case of the 3RRR planar parallel mechanisms, where it is possible to decouple the polynomial further into two quadratic equations, describing the position and orientation of the end-effector, respectively. This result will provide an efficient computation method for a very useful configuration of planar parallel manipulators

Synthesis of the Inverse Kinematic Model of Non-Redundant Open-Chain Robotic Systems Using Groebner Basis Theory

[EN] One of the most important elements of a robot's control system is its Inverse Kinematic Model (IKM), which calculates the position and velocity references required by the robot's actuators to follow a trajectory. The methods that are commonly used to synthesize the IKM of open-chain robotic systems strongly depend on the geometry of the analyzed robot. Those methods are not systematic procedures that could be applied equally in all possible cases. This project presents the development of a systematic procedure to synthesize the IKM of non-redundant open-chain robotic systems using Groebner Basis theory, which does not depend on the geometry of the robot's structure. The inputs to the developed procedure are the robot's Denavit-Hartenberg parameters, while the output is the IKM, ready to be used in the robot's control system or in a simulation of its behavior. The Groebner Basis calculation is done in a two-step process, first computing a basis with Faugere's F4 algorithm and a grevlex monomial order, and later changing the basis with the FGLM algorithm to the desired lexicographic order. This procedure's performance was proved calculating the IKM of a PUMA manipulator and a walking hexapod robot. The errors in the computed references of both IKMs were absolutely negligible in their corresponding workspaces, and their computation times were comparable to those required by the kinematic models calculated by traditional methods. The developed procedure can be applied to all Cartesian robotic systems, SCARA robots, all the non-redundant robotic manipulators that satisfy the in-line wrist condition, and any non-redundant open-chain robot whose IKM should only solve the positioning problem, such as multi-legged walking robots.This research was partially funded by Plan Nacional de I+D+i, Agencia Estatal de Investigacion del Ministerio de Economia, Industria y Competitividad del Gobierno de Espana, in the project FEDER-CICYT DPI2017-84201-R.Guzmán-Giménez, J.; Valera Fernández, Á.; Mata Amela, V.; Díaz-Rodríguez, MÁ. (2020). Synthesis of the Inverse Kinematic Model of Non-Redundant Open-Chain Robotic Systems Using Groebner Basis Theory. Applied Sciences. 10(8):1-22. https://doi.org/10.3390/app10082781S122108Atique, M. M. U., Sarker, M. R. I., & Ahad, M. A. R. (2018). Development of an 8DOF quadruped robot and implementation of Inverse Kinematics using Denavit-Hartenberg convention. Heliyon, 4(12), e01053. doi:10.1016/j.heliyon.2018.e01053Flanders, M., & Kavanagh, R. C. (2015). Build-A-Robot: Using virtual reality to visualize the Denavit-Hartenberg parameters. Computer Applications in Engineering Education, 23(6), 846-853. doi:10.1002/cae.21656Özgür, E., & Mezouar, Y. (2016). Kinematic modeling and control of a robot arm using unit dual quaternions. Robotics and Autonomous Systems, 77, 66-73. doi:10.1016/j.robot.2015.12.005Wang, X., Han, D., Yu, C., & Zheng, Z. (2012). The geometric structure of unit dual quaternion with application in kinematic control. Journal of Mathematical Analysis and Applications, 389(2), 1352-1364. doi:10.1016/j.jmaa.2012.01.016Barrientos, A., Álvarez, M., Hernández, J. D., del Cerro, J., & Rossi, C. (2012). Modelado de Caden as Cinemáticas mediante Matrices de Desplazamiento. Una alternativa al método de Denavit-Hartenberg. Revista Iberoamericana de Automática e Informática Industrial RIAI, 9(4), 371-382. doi:10.1016/j.riai.2012.09.004Virgil Petrescu, R. V., Aversa, R., Apicella, A., Mirsayar, M., Kozaitis, S., Abu-Lebdeh, T., & Tiberiu Petrescu, F. I. (2017). Geometry and Inverse Kinematic at the MP3R Mobile Systems. Journal of Mechatronics and Robotics, 1(2), 58-65. doi:10.3844/jmrsp.2017.58.65Chen, S., Luo, M., Abdelaziz, O., & Jiang, G. (2017). A general analytical algorithm for collaborative robot (cobot) with 6 degree of freedom (DOF). 2017 International Conference on Applied System Innovation (ICASI). doi:10.1109/icasi.2017.7988522Bouzgou, K., & Ahmed-Foitih, Z. (2014). Geometric modeling and singularity of 6 DOF Fanuc 200IC robot. Fourth edition of the International Conference on the Innovative Computing Technology (INTECH 2014). doi:10.1109/intech.2014.6927745Mahajan, A., Singh, H. P., & Sukavanam, N. (2017). An unsupervised learning based neural network approach for a robotic manipulator. International Journal of Information Technology, 9(1), 1-6. doi:10.1007/s41870-017-0002-2Duka, A.-V. (2014). Neural Network based Inverse Kinematics Solution for Trajectory Tracking of a Robotic Arm. Procedia Technology, 12, 20-27. doi:10.1016/j.protcy.2013.12.451Toshani, H., & Farrokhi, M. (2014). Real-time inverse kinematics of redundant manipulators using neural networks and quadratic programming: A Lyapunov-based approach. Robotics and Autonomous Systems, 62(6), 766-781. doi:10.1016/j.robot.2014.02.005Rokbani, N., & Alimi, A. M. (2013). Inverse Kinematics Using Particle Swarm Optimization, A Statistical Analysis. Procedia Engineering, 64, 1602-1611. doi:10.1016/j.proeng.2013.09.242Jiang, G., Luo, M., Bai, K., & Chen, S. (2017). A Precise Positioning Method for a Puncture Robot Based on a PSO-Optimized BP Neural Network Algorithm. Applied Sciences, 7(10), 969. doi:10.3390/app7100969Köker, R. (2013). A genetic algorithm approach to a neural-network-based inverse kinematics solution of robotic manipulators based on error minimization. Information Sciences, 222, 528-543. doi:10.1016/j.ins.2012.07.051Rokbani, N., Casals, A., & Alimi, A. M. (2014). IK-FA, a New Heuristic Inverse Kinematics Solver Using Firefly Algorithm. Computational Intelligence Applications in Modeling and Control, 369-395. doi:10.1007/978-3-319-11017-2_15Buchberger, B. (2001). Multidimensional Systems and Signal Processing, 12(3/4), 223-251. doi:10.1023/a:1011949421611Kendricks, K. D. (2013). A kinematic analysis of the gmf a-510 robot: An introduction and application of groebner basis theory. Journal of Interdisciplinary Mathematics, 16(2-03), 147-169. doi:10.1080/09720502.2013.800304Wang, Y., Hang, L., & Yang, T. (2006). Inverse Kinematics Analysis of General 6R Serial Robot Mechanism Based on Groebner Base. Frontiers of Mechanical Engineering in China, 1(1), 115-124. doi:10.1007/s11465-005-0022-7Abbasnejad, G., & Carricato, M. (2015). Direct Geometrico-static Problem of Underconstrained Cable-Driven Parallel Robots With $n$ Cables. IEEE Transactions on Robotics, 31(2), 468-478. doi:10.1109/tro.2015.2393173Rameau, J.-F., & Serré, P. (2015). Computing mobility condition using Groebner basis. Mechanism and Machine Theory, 91, 21-38. doi:10.1016/j.mechmachtheory.2015.04.003Xiguang Huang, & Guangpin He. (2009). Forward kinematics of the general Stewart-Gough platform using Gröbner basis. 2009 International Conference on Mechatronics and Automation. doi:10.1109/icma.2009.5246088Uchida, T., & McPhee, J. (2012). Using Gröbner bases to generate efficient kinematic solutions for the dynamic simulation of multi-loop mechanisms. Mechanism and Machine Theory, 52, 144-157. doi:10.1016/j.mechmachtheory.2012.01.015Faugère, J.-C. (2010). FGb: A Library for Computing Gröbner Bases. 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An Overview of Kinematic and Calibration Models Using Internal/External Sensors or Constraints to Improve the Behavior of Spatial Parallel Mechanisms

This paper presents an overview of the literature on kinematic and calibration models of parallel mechanisms, the influence of sensors in the mechanism accuracy and parallel mechanisms used as sensors. The most relevant classifications to obtain and solve kinematic models and to identify geometric and non-geometric parameters in the calibration of parallel robots are discussed, examining the advantages and disadvantages of each method, presenting new trends and identifying unsolved problems. This overview tries to answer and show the solutions developed by the most up-to-date research to some of the most frequent questions that appear in the modelling of a parallel mechanism, such as how to measure, the number of sensors and necessary configurations, the type and influence of errors or the number of necessary parameters

Automatic selection of the Groebner Basis' monomial order employed for the synthesis of the inverse kinematic model of non-redundant open-chain robotic systems

This is an Author's Accepted Manuscript of an article published in José Guzmán-Giménez, Ángel Valera Fernández, Vicente Mata Amela & Miguel Ángel Díaz-Rodríguez (2023) Automatic selection of the Groebner Basis¿ monomial order employed for the synthesis of the inverse kinematic model of non-redundant open-chain robotic systems, Mechanics Based Design of Structures and Machines, 51:5, 2458-2480, DOI: 10.1080/15397734.2021.1899829 [copyright Taylor & Francis], available online at: http://www.tandfonline.com/10.1080/15397734.2021.1899829[EN] The methods most commonly used to synthesize the Inverse Kinematic Model (IKM) of open-chain robotic systems strongly depend on the robot's geometry, which make them difficult to systematize. In a previous work we presented a systematic procedure that relies on Groebner Bases to synthesize the IKM of non-redundant open-chain robots. This study expands the developed procedure with a methodology for the automatic selection of the basis' monomial order. The procedure's inputs are the robot's Denavit-Hartenberg parameters and the movement range of its actuators, while the output is the synthesized IKM, ready to be used in the robot's control system or in a simulation of its behavior. This procedure can synthesize the IKM of a wide range of open-chain robotic systems, such as Cartesian robots, SCARA, non-redundant multi-legged robots, and all non-redundant manipulators that satisfy the in-line wrist condition. The procedure's performance is assessed through two study cases of open-chain robots: a walking hexapod and a PUMA manipulator. The optimal monomial order is successfully identified for all cases. Also the output errors of the synthesized IKMs are negligible when evaluated in their corresponding workspaces, while their computation times are comparable to those required by the kinematic models calculated by traditional methods.This research was partially funded by Plan Nacional de IthornDthorni, Agencia Estatal de Investigacion del Ministerio de Economia, Industria y Competitividad del Gobierno de Espana, in the project FEDER-CICYT DPI201784201-R.Guzmán-Giménez, J.; Valera Fernández, Á.; Mata Amela, V.; Díaz-Rodríguez, MÁ. (2023). Automatic selection of the Groebner Basis' monomial order employed for the synthesis of the inverse kinematic model of non-redundant open-chain robotic systems. Mechanics Based Design of Structures and Machines. 51(5):2458-2480. https://doi.org/10.1080/15397734.2021.18998292458248051

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

Parallel Manipulators

In recent years, parallel kinematics mechanisms have attracted a lot of attention from the academic and industrial communities due to potential applications not only as robot manipulators but also as machine tools. Generally, the criteria used to compare the performance of traditional serial robots and parallel robots are the workspace, the ratio between the payload and the robot mass, accuracy, and dynamic behaviour. In addition to the reduced coupling effect between joints, parallel robots bring the benefits of much higher payload-robot mass ratios, superior accuracy and greater stiffness; qualities which lead to better dynamic performance. The main drawback with parallel robots is the relatively small workspace. A great deal of research on parallel robots has been carried out worldwide, and a large number of parallel mechanism systems have been built for various applications, such as remote handling, machine tools, medical robots, simulators, micro-robots, and humanoid robots. This book opens a window to exceptional research and development work on parallel mechanisms contributed by authors from around the world. Through this window the reader can get a good view of current parallel robot research and applications

Novel Artificial Neural Network Application for Prediction of Inverse Kinematics of Robot Manipulator

The robot control problem can be divided into two main areas, kinematics control (the coordination of the links of kinematics chain to produce desire motion of the robot), and dynamic control (driving the actuator of the mechanism to follow the commanded position velocities). In general the control strategies used in robot involves position coordination in Cartesian space by direct or indirect kinematics method. Inverse kinematics comprises the computation need to find the join angles for a given Cartesian position and orientation of the end effectors. This computation is fundamental to control of robot arms but it is very difficult to calculate an inverse kinematics solution of robot manipulator. For this solution most industrial robot arms are designed by using a non-linear algebraic computation to finding the inverse kinematics solution. From the literature it is well described that there is no unique solution for the inverse kinematics. That is why it is significant to apply an artificial neural network models. Here structured artificial neural network (ANN) models an approach has been proposed to control the motion of robot manipulator. In these work two types of ANN models were used. The first kind ANN model is MLP (multi-layer perceptrons) which was famous as back propagation neural network model. In this network gradient descent type of learning rules are applied. The second kind of ANN model is PPN (polynomial poly-processor neural network) where polynomial equation was used. Here, work has been undertaken to find the best ANN configuration for the problem. It was found that between MLP and PPN, MLP gives better result as compared to PPN by considering average percentage error, as the performance index