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

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. Lecture Notes in Computer Science, 84-87. doi:10.1007/978-3-642-15582-6_17Faugére, J.-C. (1999). A new efficient algorithm for computing Gröbner bases (F4). Journal of Pure and Applied Algebra, 139(1-3), 61-88. doi:10.1016/s0022-4049(99)00005-5Faugère, J. C., Gianni, P., Lazard, D., & Mora, T. (1993). Efficient Computation of Zero-dimensional Gröbner Bases by Change of Ordering. Journal of Symbolic Computation, 16(4), 329-344. doi:10.1006/jsco.1993.1051Salzer, H. E. (1960). A note on the solution of quartic equations. Mathematics of Computation, 14(71), 279-279. doi:10.1090/s0025-5718-1960-0117882-

Efficient lens distortion correction for decoupling in calibration of wide angle lens cameras

© 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In photogrammetry applications, camera parameters must be as accurate as possible to avoid deviations in measurements from images. Errors increase if wide angle lens cameras are used. Moreover, the coupling between intrinsic and extrinsic camera parameters and the lens distortion model influences the result of the calibration process notably. This paper proposes a method for calibrating wide angle lens cameras, which takes into account the existing hard coupling. The proposed method obtains stable results, which do not depend on how the image lens distortion is corrected.This work was supported in part by the Universidad Politecnica de Valencia research funds (PAID 2010-2431 and PAID 10017), the Generalitat Valenciana (GV/2011/057) and the Spanish government and the European Community under Project DPI2010-20814-C02-02 (FEDER-CICYT) and Project DPI2010-20286 (CICYT). The associate editor coordinating the review of this paper and approving it for publication was Dr. Subhas C. Mukhopadhyay.Ricolfe Viala, C.; Sánchez Salmerón, AJ.; Valera Fernández, Á. (2013). Efficient lens distortion correction for decoupling in calibration of wide angle lens cameras. IEEE Sensors Journal. 13(2):854-863. https://doi.org/10.1109/JSEN.2012.2229704S85486313

Event based localization in Ackermann steering limited resource mobile robots

“© 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.”This paper presents a local sensor fusion technique with an event-based global position correction to improve the localization of a mobile robot with limited computational resources. The proposed algorithms use a modified Kalman filter and a new local dynamic model of an Ackermann steering mobile robot. It has a similar performance but faster execution when compared to more complex fusion schemes, allowing its implementation inside the robot. As a global sensor, an event-based position correction is implemented using the Kalman filter error covariance and the position measurement obtained from a zenithal camera. The solution is tested during a long walk with different trajectories using a LEGO Mindstorm NXT robot.This work was supported by FEDER-CICYT projects with references DPI2011-28507-C02-01 and DPI2010-20814-C02-02, financed by the Ministerio de Ciencia e Innovacion (Spain). This work was also supported by the University of Costa Rica.Marín, L.; Vallés Miquel, M.; Soriano Vigueras, Á.; Valera Fernández, Á.; Albertos Pérez, P. (2014). Event based localization in Ackermann steering limited resource mobile robots. IEEE/ASME Transactions on Mechatronics. 19(4):1171-1182. doi:10.1109/TMECH.2013.2277271S1171118219

GEMA2:Geometrical matching analytical algorithm for fast mobile robots global self-localization

[EN] This paper presents a new algorithm for fast mobile robot self-localization in structured indoor environments based on geometrical and analytical matching, GEMA(2). The proposed method takes advantage of the available structural information to perform a geometrical matching with the environment information provided by measurements collected by a laser range finder. In contrast to other global self-localization algorithms like Monte Carlo or SLAM, GEMA(2) provides a linear cost with respect the number of measures collected, making it suitable for resource-constrained embedded systems. The proposed approach has been implemented and tested in a mobile robot with limited computational resources showing a fast converge from global self-localization. (C) 2014 Elsevier B.V. All rights reserved.This work has been partially funded by FEDER-CICYT projects with references DPI2011-28507-C02-01 and HAR2012-38391-C02-02 financed by Ministerio de Ciencia e Innovacion and Ministerio de Economia y Competitividad (Spain).Sánchez Belenguer, C.; Soriano Vigueras, Á.; Vallés Miquel, M.; Vendrell Vidal, E.; Valera Fernández, Á. (2014). GEMA2:Geometrical matching analytical algorithm for fast mobile robots global self-localization. Robotics and Autonomous Systems. 62(6):855-863. https://doi.org/10.1016/j.robot.2014.01.009S85586362

Simultaneous velocity, impact and force control

[EN] In this paper, we propose a control method to achieve three objectives simultaneously: velocity regulation during free motion, impact damping and finally force reference tracking. During impact, the parameters are switched in order to dissipate the energy of the system as fast as possible and the optimal switching criteria are deduced. The possibility of sliding regimes is analysed and the theoretical results are verified in simulations.We would like to thank the R&D&I Linguistic Assistance Office, Universidad Politecnica de Valencia (Spain), for Granting financial support for the linguistic revision of this paper. This work has been partially funded by the European project MASMICRO (Project number 500095-2), by the projects FEDER-CICYT with reference, DPI2005-08732C02-02 and DP12006-15320-C03-01, of the Ministry of Education and Science as well as by the research Project of the Generalitat Valenciana, GVPRE/2008 20080916.Zotovic Stanisic, R.; Valera Fernández, Á. (2009). Simultaneous velocity, impact and force control. Robotica. 27(7):1039-1048. https://doi.org/10.1017/S0263574709005451S1039104827710. Xu Y. , Hollerbach J. M. and Ma D. , “Force and Contact Transient Control Using Nonlinear PD Control,” Proceedings of the 1994 International Conference on Robotics and Automation (1994) pp. 924–930.Brach, R. M., & Goldsmith, W. (1991). Mechanical Impact Dynamics: Rigid Body Collisions. Journal of Engineering for Industry, 113(2), 248-249. doi:10.1115/1.2899694Chiaverini, S., & Sciavicco, L. (1993). The parallel approach to force/position control of robotic manipulators. IEEE Transactions on Robotics and Automation, 9(4), 361-373. doi:10.1109/70.246048Armstrong, B. S. R., Gutierrez, J. A., Wade, B. A., & Joseph, R. (2006). Stability of Phase-Based Gain Modulation with Designer-Chosen Switch Functions. The International Journal of Robotics Research, 25(8), 781-796. doi:10.1177/0278364906067543Volpe, R., & Khosla, P. (1993). A Theoretical and Experimental Investigation of Impact Control for Manipulators. The International Journal of Robotics Research, 12(4), 351-365. doi:10.1177/027836499301200403Impact modeling and control for industrial manipulators. (1998). IEEE Control Systems, 18(4), 65-71. doi:10.1109/37.710879Brogliato, B., Niculescu, S.-I., & Orhant, P. (1997). On the control of finite-dimensional mechanical systems with unilateral constraints. IEEE Transactions on Automatic Control, 42(2), 200-215. doi:10.1109/9.554400Brogliato, B. (1999). Nonsmooth Mechanics. Communications and Control Engineering. doi:10.1007/978-1-4471-0557-2Armstrong, B., & Wade, B. A. (2000). Nonlinear PID Control with Partial State Knowledge: Damping without Derivatives. The International Journal of Robotics Research, 19(8), 715-731. doi:10.1177/02783640022067120Controlling contact transition. (1994). IEEE Control Systems, 14(1), 25-30. doi:10.1109/37.257891Seraji, H. (1998). Nonlinear and Adaptive Control of Force and Compliance in Manipulators. The International Journal of Robotics Research, 17(5), 467-484. doi:10.1177/027836499801700501Volpe, R., & Khosla, P. (1993). A theoretical and experimental investigation of explicit force control strategies for manipulators. IEEE Transactions on Automatic Control, 38(11), 1634-1650. doi:10.1109/9.262033A nonlinear PD controller for force and contact transient control. (1995). IEEE Control Systems, 15(1), 15-21. doi:10.1109/37.341859Seraji, H., & Colbaugh, R. (1997). Force Tracking in Impedance Control. The International Journal of Robotics Research, 16(1), 97-117. doi:10.1177/027836499701600107Armstrong, B., Neevel, D., & Kusik, T. (2001). New results in NPID control: Tracking, integral control, friction compensation and experimental results. IEEE Transactions on Control Systems Technology, 9(2), 399-406. doi:10.1109/87.91139

Designing an Advanced Regional Research Network

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Fall detection based on the gravity vector using a wide-angle camera

Falls in elderly people are becoming an increasing healthcare problem, since life expectancy and the number of elderly people who live alone have increased over recent decades. If fall detection systems could be installed easily and economically in homes, telecare could be provided to alleviate this problem. In this paper we propose a low cost fall detection system based on a single wide-angle camera. Wide-angle cameras are used to reduce the number of cameras required for monitoring large areas. Using a calibrated video system, two new features based on the gravity vector are introduced for fall detection. These features are: angle between the gravity vector and the line from feet to head of the human and size of the upper body. Additionally, to differentiate between fall events and controlled lying down events the speed of changes in the features is also measured. Our experiments demonstrate that our system is 97% accurate for fall detection. (C) 2014 Elsevier Ltd. All rights reserved.This work was partially financed by Programa Estatal de Investigacion, Desarrollo e Innovacion Orientada a los Retos de la Sociedad (Direccion General de Investigacion Cientifica y Tecnica, Ministerio de Economia y Competitividad) under the project DPI2013-44227-R.Bosch Jorge, M.; Sánchez Salmerón, AJ.; Valera Fernández, Á.; Ricolfe Viala, C. (2014). Fall detection based on the gravity vector using a wide-angle camera. Expert Systems with Applications. 41(17):7980-7986. https://doi.org/10.1016/j.eswa.2014.06.045S79807986411

Hybrid force/position control for a 3-DOF 1T2R parallel robot: Implementation, simulations and experiments

"This is an Author's Accepted Manuscript of an article published in Cazalilla, José, Marina Vallés, Ángel Valera, Vicente Mata, and Miguel Díaz-Rodríguez. 2016. Hybrid Force/Position Control for a 3-DOF 1T2R Parallel Robot: Implementation, Simulations and Experiments. Mechanics Based Design of Structures and Machines 44 (1 2). Informa UK Limited: 16 31. doi:10.1080/15397734.2015.1030679, available online at: https://www.tandfonline.com/doi/full/10.1080/15397734.2015.1030679."[EN] A robot interacting with the environment requires that the end effector \hboxposition is tracked and that the forces of contact are kept below certain reference values. For instance, in a rehabilitation session using a robotic device, the contact forces are limited by the allowed strength of the human limbs and their complex-joints. In these cases, a control scheme which considers both position and force control is essential to avoid damage to either the end effector or the object interacting with the robot. This paper therefore develops a real-time force/position control scheme for a three-DOF parallel robot whose end effector holds a DOF one translation (1T) and two rotations (2R). The implemented hybrid force/position control considers, as a reference, the normal force on the mobile platform, which is measured by means of a load cell installed on the platform. The position control is designed to track the orientations of the robot either in joint or task space using a model-based control scheme with identified parameters. Moreover, the force control is based on a PD action. The control scheme is developed through simulations, before being applied to an actual parallel robot. The findings show that with the implemented controller, the actual robot accomplishes the reference values for the normal force on the mobile platform, while at the same time the platform accurately follows the required angular orientation.The authors wish to thank the Plan Nacional de I+D, Comision Interministerial de Ciencia y Tecnologia (FEDER-CICYT) for the partial funding of this study under the projects DPI2011-28507-C02-01 and DPI2013-44227-R. This work was also partially supported by the Fondo Nacional de Ciencia, Tecnologia e Innovacion (FONACIT-Venezuela).Cazalilla, J.; Vallés Miquel, M.; Valera Fernández, Á.; Mata Amela, V.; Díaz-Rodríguez, M. (2016). Hybrid force/position control for a 3-DOF 1T2R parallel robot: Implementation, simulations and experiments. Mechanics Based Design of Structures and Machines. 44(1-2):16-31. https://doi.org/10.1080/15397734.2015.1030679S1631441-2Åström, K. J., & Murray, R. M. (2008). Feedback Systems. doi:10.1515/9781400828739Bellakehal, S., Andreff, N., Mezouar, Y., & Tadjine, M. (2011). Force/position control of parallel robots using exteroceptive pose measurements. Meccanica, 46(1), 195-205. doi:10.1007/s11012-010-9411-zCao, R., Gao, F., Zhang, Y., Pan, D., & Chen, W. (2014). A New Parameter Design Method of a 6-DOF Parallel Motion Simulator for a Given Workspace. Mechanics Based Design of Structures and Machines, 43(1), 1-18. doi:10.1080/15397734.2014.904234Carretero, J. A., Podhorodeski, R. P., Nahon, M. A., & Gosselin, C. M. (1999). Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator. Journal of Mechanical Design, 122(1), 17-24. doi:10.1115/1.533542Clavel, R. (1988). DELTA, a fast robot with parallel geometry.Proceedings of 18th International Symposium on Industrial Robot, Lausanne, April, 91–100.Díaz-Rodríguez, M., Mata, V., Valera, Á., & Page, Á. (2010). A methodology for dynamic parameters identification of 3-DOF parallel robots in terms of relevant parameters. Mechanism and Machine Theory, 45(9), 1337-1356. doi:10.1016/j.mechmachtheory.2010.04.007Diaz-Rodriguez, M., Valera, A., Mata, V., & Valles, M. (2013). Model-Based Control of a 3-DOF Parallel Robot Based on Identified Relevant Parameters. IEEE/ASME Transactions on Mechatronics, 18(6), 1737-1744. doi:10.1109/tmech.2012.2212716Farhat, N., Mata, V., Page, Á., & Valero, F. (2008). Identification of dynamic parameters of a 3-DOF RPS parallel manipulator. Mechanism and Machine Theory, 43(1), 1-17. doi:10.1016/j.mechmachtheory.2006.12.011Garg, A., Vikram, C. S., Gupta, S., Sutar, M. K., Pathak, P. M., Mehta, N. K., … Gupta, V. K. (2014). Design and Development of In Vivo Robot for Biopsy. Mechanics Based Design of Structures and Machines, 42(3), 278-295. doi:10.1080/15397734.2014.898587Gough, V. E., Whitehall, S. G. (1962). Universal tire test machine.Proceedings of 9th International Technical Congress FISITA, pp. 117–135.García de Jalón, J., & Bayo, E. (1994). Kinematic and Dynamic Simulation of Multibody Systems. Mechanical Engineering Series. doi:10.1007/978-1-4612-2600-0Lee, K.-M., & Arjunan, S. (1991). A three-degrees-of-freedom micromotion in-parallel actuated manipulator. IEEE Transactions on Robotics and Automation, 7(5), 634-641. doi:10.1109/70.97875Li, Y., & Xu, Q. (2007). Design and Development of a Medical Parallel Robot for Cardiopulmonary Resuscitation. IEEE/ASME Transactions on Mechatronics, 12(3), 265-273. doi:10.1109/tmech.2007.897257Merlet, J.-P. (2000). Parallel Robots. Solid Mechanics and Its Applications. doi:10.1007/978-94-010-9587-7Pierrot, F., Nabat, V., Company, O., Krut, S., & Poignet, P. (2009). Optimal Design of a 4-DOF Parallel Manipulator: From Academia to Industry. IEEE Transactions on Robotics, 25(2), 213-224. doi:10.1109/tro.2008.2011412Rosillo, N., Valera, A., Benimeli, F., Mata, V., & Valero, F. (2011). Real‐time solving of dynamic problem in industrial robots. Industrial Robot: An International Journal, 38(2), 119-129. doi:10.1108/01439911111106336Steward, D. A. (1965). A platform with 6 degrees of freedom.Proceedings of the Institution of Mechanical Engineers, Part 1, vol. 15, pp. 371–386.Valera, A., Benimeli, F., Solaz, J., De Rosario, H., Robertsson, A., Nilsson, K., … Mellado, M. (2011). A Car-Seat Example of Automated Anthropomorphic Testing of Fabrics Using Force-Controlled Robot Motions. IEEE Transactions on Automation Science and Engineering, 8(2), 280-291. doi:10.1109/tase.2010.2079931Vallés, M., Díaz-Rodríguez, M., Valera, Á., Mata, V., & Page, Á. (2012). Mechatronic Development and Dynamic Control of a 3-DOF Parallel Manipulator. Mechanics Based Design of Structures and Machines, 40(4), 434-452. doi:10.1080/15397734.2012.687292Volpe, R., & Khosla, P. (1993). A theoretical and experimental investigation of explicit force control strategies for manipulators. IEEE Transactions on Automatic Control, 38(11), 1634-1650. doi:10.1109/9.262033Zarkandi, S. (2011). Kinematics and Singularity Analysis of a Parallel Manipulator with Three Rotational and One Translational DOFs. Mechanics Based Design of Structures and Machines, 39(3), 392-407. doi:10.1080/15397734.2011.559149Zeng, G., & Hemami, A. (1997). An overview of robot force control. Robotica, 15(5), 473-482. doi:10.1017/s026357479700057

Distance computation between non-holonomic motions with constant accelerations

A method for computing the distance between two moving robots or between a mobile robot and a dynamic obstacle with linear or arc-like motions and with constant accelerations is presented in this paper. This distance is obtained without stepping or discretizing the motions of the robots or obstacles. The robots and obstacles are modelled by convex hulls. This technique obtains the future instant in time when two moving objects will be at their minimum translational distance - i.e., at their minimum separation or maximum penetration (if they will collide). This distance and the future instant in time are computed in parallel. This method is intended to be run each time new information from the world is received and, consequently, it can be used for generating collision-free trajectories for non-holonomic mobile robots.This work was partially funded by the Spanish government CICYT projects: DPI2010-20814-C02-02, and DPI2011-28507-C02-01.Bernabeu Soler, EJ.; Valera Fernández, Á.; Gómez Moreno, J. (2013). Distance computation between non-holonomic motions with constant accelerations. International Journal of Advanced Robotic Systems. 10:1-15. doi:10.5772/56760S11510Urmson, C., Anhalt, J., Bagnell, D., Baker, C., Bittner, R., Clark, M. N., … Ferguson, D. (2008). Autonomous driving in urban environments: Boss and the Urban Challenge. Journal of Field Robotics, 25(8), 425-466. doi:10.1002/rob.20255Redon, S., Kheddar, A., & Coquillart, S. (2002). Fast Continuous Collision Detection between Rigid Bodies. Computer Graphics Forum, 21(3), 279-287. doi:10.1111/1467-8659.t01-1-00587Canny, J. (1986). Collision Detection for Moving Polyhedra. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-8(2), 200-209. doi:10.1109/tpami.1986.4767773Buss, S. R. (2005). Collision detection with relative screw motion. The Visual Computer, 21(1-2), 41-58. doi:10.1007/s00371-004-0269-8Fiorini, P., & Shiller, Z. (1998). Motion Planning in Dynamic Environments Using Velocity Obstacles. The International Journal of Robotics Research, 17(7), 760-772. doi:10.1177/027836499801700706Gilbert, E. G., Johnson, D. W., & Keerthi, S. S. (1988). A fast procedure for computing the distance between complex objects in three-dimensional space. IEEE Journal on Robotics and Automation, 4(2), 193-203. doi:10.1109/56.2083Bernabeu, E. J., & Tornero, J. (2002). Hough transform for distance computation and collision avoidance. IEEE Transactions on Robotics and Automation, 18(3), 393-398. doi:10.1109/tra.2002.1019476Simon, D. (2006). Optimal State Estimation. doi:10.1002/047004534