Mathematical Studying in Control of Grasping
International Journal of Science and Qualitative Analysis
Volume 2, Issue 1, July 2016, Pages: 1-13
Received: Mar. 15, 2016; Accepted: Jun. 3, 2016; Published: Jul. 5, 2016
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Authors
Eman Mirzaieepoor, Department of Mechanical Engineering, Amirkabir University, Tehran, Iran
Mohammad Sadegh Hassanli, Department of Exercise Physiology, Jahrom University, Jahrom, Iran
Pezhman Moradi, Department of Mechanical Engineering, Jahrom University, Jahrom, Iran
Mohammad Mehdi Khoddami, Department of Mechanical Engineering, Jahrom University, Jahrom, Iran
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Abstract
The main purpose of developing of mechanical hands is to give robots the knack in order to grasp objects of varying geometric and physical properties. The complete model is a coupling of models which describe contact behavior with generally using the models of rigid-body kinematics and dynamics. The contact model fundamentally come down to the choice of components of contact force and moment which are transmitted through each contact. Mathematical properties of the complete model obviously bring about two primary grasp types whose physical interpretations provide insight for grasping and manipulation planning. A grasp with complete restraint avoids loss of contact and therefore is so secure. As will be mentioned, two primary limitation properties are force closure and form closure. A form closure grasp assurances the maintenance of contact as long as the links of the hand and the proposed object are also well verged on as rigid and as long as the joint actuators are sturdy enough. It should be noted that the main difference between force closure and also form closure grasps is the latter’s reliance on contact friction.
Keywords
Computational Linear algebra, Linear Kinematic, Linear Dynamic, Grasping, Rigid-body Models, Form Closure
To cite this article
Eman Mirzaieepoor, Mohammad Sadegh Hassanli, Pezhman Moradi, Mohammad Mehdi Khoddami, Mathematical Studying in Control of Grasping, International Journal of Science and Qualitative Analysis. Vol. 2, No. 1, 2016, pp. 1-13. doi: 10.11648/j.ijsqa.20160201.11
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Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
Murray, R.N ., Li, Z., Sastry, S.: A mathematical introduction to robotics manipulation. CRC Press, USA (1994)
[2]
Bicchi, A., Kumar, V.: Robotic grasping and contact: a review. In: Robotics and Automation, 2000. Proceedings. ICRA ’00. IEEE International Conference on. pp. 348–353. IEEE (2000)
[3]
Prattichizzo, D., Trinkle, J.: Springer Handbook of Robotics, pp. 671–700. Springer, Berlin (2008)
[4]
Roa Garzón, M.: Grasp planning methodology for 3D arbitrary shaped objects. Ph. d. thesis, Universidad Politécnica de Cataluña (2009)
[5]
Haghighi, Alireza Shourangiz, Amin Haghnegahdar, Reza Jahromi Bosheri, and Iman Zare. "Micro-embedded Skimmer in Autonomous Underwater Micro-robots." International Journal of Science and Qualitative Analysis 1, no. 3 (2015): 43-53.
[6]
Haghighi, A. Shourangiz, I. Zare, Mohammad Ahmadi Balootaki, Mohammad Orak, and Omid Zare. "Modeling of Bio-inspired Thunnus Albacares and Inchworm-gammarus with Micro Actuators in One Structure." International Journal of Science and Qualitative Analysis 1, no. 3 (2015): 54-63.
[7]
Alireza Shourangiz Haghighi, Iman Zare, AliReza Fallahi, Reza Jahromi Bosheri , Amin Haghnegahdar, "Dynamic modeling of flexible tail for bio-inspired dogfish shark (squalus Acanthias)-inchworm with multifunctional locomotion." In Electrical and Electronics Engineering, 2015. ICEEE 2015. 7th Iranian Conference on, pp. 126-132. IEEE, 2015.
[8]
AliReza Shourangiz Haghighi, Iman Zare, AliReza Fallahi, Hamid Reza Naji, Amin Bahreini. "Bio-inspired micro-robot with micro-actuators ICPF and floating collector Skimmer." In Electrical and Electronics Engineering, 2015. ICEEE 2015. 7th Iranian Conference on, pp. 133-139. IEEE, 2015.
[9]
R. Vertechy, V. Parenti-Castelli, Static and stiffness analyses of a class of over-constrained parallel manipulators with legs of type US and UPS, in: Proceedings of IEEE International Conference on Robotics and Automation (ICRA), 2007, pp. 561–567.
[10]
Yoshikawa, T. (2010). Multifingered Robot Hands: Control for Grasping and Manipulation. Annual Reviews in Control, 34(2), 199-208.
[11]
Hasegawa, Y., Shikida, M., Shimizu, T., Miyaji, T., Sakai, H., Sato, K., and Itoigawa, K. (2004). A Micromachined Active Tactile Sensor for Hardness Detection, Sensors and Actuators (A Physical), 114(2-3), 141-146.
[12]
Nikandrova, Ekaterina, and Ville Kyrki. "Category-based task specific grasping." Robotics and Autonomous Systems 70 (2015): 25-35.
[13]
Klingbeil, Ellen, Deepak Rao, Blake Carpenter, Varun Ganapathi, Andrew Y. Ng, and Oussama Khatib. "Grasping with application to an autonomous checkout robot." In Robotics and Automation (ICRA), 2011 IEEE International Conference on, pp. 2837-2844. IEEE, 2011.
[14]
Klingbeil, Ellen, Deepak Rao, Blake Carpenter, Varun Ganapathi, Andrew Y. Ng, and Oussama Khatib. "Grasping with application to an autonomous checkout robot." In Robotics and Automation (ICRA), 2011 IEEE International Conference on, pp. 2837-2844. IEEE, 2011.
[15]
M. T. Mason and J. K. Salisbury. Manipulator grasping and pushing operations. In Robot Hands and theMechanics ofManipulation. TheMIT Press, Cambridge,MA, 1985.
[16]
S. Haidacher and G. Hirzinger, "Estimating finger contact location and object pose from contact measurements in 3d grasping," in Proceedings. IEEE International Conference on Robotics and Automation (ICRA), vol. 2. IEEE, 2003, pp. 1805-1810.
[17]
Gabiccini, Marco, Antonio Bicchi, Domenico Prattichizzo, and Monica Malvezzi. "On the role of hand synergies in the optimal choice of grasping forces." Autonomous Robots 31, no. 2-3 (2011): 235-252.
[18]
Li, Jia-Wei, Hong Liu, and He-Gao Cai. "On computing three-finger force-closure grasps of 2-D and 3-D objects." Robotics and Automation, IEEE Transactions on 19, no. 1 (2003): 155-161.
[19]
Shapiro, Amir, Elon Rimon, and Joel W. Burdick. "Passive force closure and its computation in compliant-rigid grasps." In Intelligent Robots and Systems, 2001. Proceedings. 2001 IEEE/RSJ International Conference on, vol. 3, pp. 1769-1775. IEEE, 2001.
[20]
Liu, Yun-Hui, Miu-Ling Lam, and Dan Ding. "A complete and efficient algorithm for searching 3-D form-closure grasps in the discrete domain." Robotics, IEEE Transactions on 20, no. 5 (2004): 805-816.
[21]
A. Bicchi and V. Kumar. Robotic grasping and contact: a review. In International Conference on Robotics and Automation (ICRA), 2000.
[22]
A. T. Miller, S. Knoop, P. K. Allen, and H. I. Christensen. Automatic grasp planning using shape primitives. In International Conference on Robotics and Automation (ICRA), 2003.
[23]
ROS-Matlab Bridge,” http://github.com/nmichael/ipc-bridge
[24]
Robot Operating System (ROS),” http://www.ros.org
[25]
S. Allin, Y. Matsuoka, and R. Klatzky, “Measuring just noticeable differences for haptic force feedback: Implications for rehabilitation,” in Proc. IEEE Hapt. Symp., Mar. 2002, pp. 299–302.
[26]
T. Takahashi, T. Tsuboi, T. Kishida, Y. Kawanami, S. Shimizu, M. Iribe, T. Fukushima, and M. Fujita, “Adaptive grasping by mulit fingered hand with tactile sensor based on robust force and position control,” in Proc. Int. Conf. Robot. Autom., 2008, pp. 264–271.
[27]
X. Zhu, H. Ding, Computation of force closure grasps: An iterative algorithm, IEEE Transactions on Robotics, vol.22, no.1, pp.146-162, 2006.
[28]
C. Corcoran and R. Platt, "A measurement model for tracking hand object state during dexterous manipulation," in Proceedings. IEEE International Conference on Robotics and Automation (ICRA), 2010, pp. 4302-4308.
[29]
Ghanbari, Ahmad, Ramin Solaimani, Arash Rahmani, and Farshid Tabatabaie. "Design and simulating five-finger robot hand to grasp spherical objects." Life Science Journal 10, no. 3 (2013).
[30]
M. Yashima, T. Yamawaki, Task oriented accuracy measure for dexterous Manipulation, Proceeding of the IEEE International conference on robotics and biomimetics, Bangkok, Thailand, February, pp.21-26, 2009.
[31]
F.Reuleaux: The Kinematics of Machinery (Macmillan, New York 1876), Republished by Dover, New York (2003)
[32]
J. ButterfaÃ, M. Grebenstein, H. Liu, and G. Hirzinger, "Dlr-hand ii: Next generation of a dextrous robot hand," in Proceedings. IEEE International Conference on Robotics and Automation (ICRA), 2001, pp. 109-114.
[33]
O. Company, S. Krut, F. Pierrot, Modelling and preliminary design issues of a 4-axis parallel machine for heavy parts handling, Journal of Multibody Dynamics 216 (2002) 1–11.
[34]
T. Omata, K. Nagata: Rigid body analysis of the indeterminate grasp force in power grasps, IEEE Trans. Robot. Autom. 16(1), 46–54 (2000)
[35]
R.M. Murray, Z. Li, S.S. Sastry: A Mathematical Introduction to Robot Manipulation (CRC Press, Boca Raton 2010).
[36]
A. Saxena, “Monocular depth perception and robotic grasping of novel objects,” Ph.D. dissertation, Stanford University, pp.123-126, 2009.
[37]
E. Rimon, J. Burdick: Mobility of bodies in contact i: A 2nd order mobility index for multiple-finger grasps, IEEE Trans. Robot. Autom. 14(5), 696–708 (1998).
[38]
Thomas R. Kurfess Ph.D.,Robotics and automotion handbook, pp.406-409, CRC Press LLC, 2005, ISBN 0-8493-1804-1/05
[39]
Belter, D.; Kopicki, M.; Zurek, S.; Wyatt, J. "Kinematically optimised predictions of object motion", Intelligent Robots and Systems (IROS 2014), 2014 IEEE/RSJ International Conference on, on page(s): 4422 - 4427
[40]
A.J. Goldman, A.W. Tucker: Polyhedral convex cones. In: Linear Inequalities and Related Systems, ed. by H.W. Kuhn, A.W. Tucker (Princeton Univ., York 1956) pp. 19–40.
[41]
R. Platt, A. H. Fagg, and R. Grupen, “Learning grasp context distinctions that generalize,” in IEEE-RAS International Conference on Humanoid Robots, pp. 504 – 511, Genova, IEEE,2006.
[42]
Montana, David J. "The kinematics of contact and grasp." The International Journal of Robotics Research 7, no. 3 (1988): 17-32.
[43]
León, Beatriz, Joaquín L. Sancho-Bru, Néstor J. Jarque-Bou, Antonio Morales, and Máximo A. Roa. "Evaluation of human prehension using grasp quality measures." International Journal of Advanced Robotic Systems 9 (2012).
[44]
Yamada, Takayoshi, Toshiya Taki, Manabu Yamada, Yasuyuki Funahashi, and Hidehiko Yamamoto. "Static stability analysis of spatial grasps including contact surface geometry." Advanced Robotics 25, no. 3-4 (2011): 447-472.
[45]
De Leone, Renato, Paola Festa, and Emilia Marchitto. "A bus driver scheduling problem: a new mathematical model and a GRASP approximate solution."Journal of Heuristics 17, no. 4 (2011): 441-466.
[46]
Rosales, Carlos, Raúl Suárez, Marco Gabiccini, and Antonio Bicchi. "On the synthesis of feasible and prehensile robotic grasps." In Robotics and Automation (ICRA), 2012 IEEE International Conference on, pp. 550-556. IEEE, 2012.
[47]
Miller, Andrew T., Steffen Knoop, Henrik Christensen, and Peter K. Allen. "Automatic grasp planning using shape primitives." In Robotics and Automation, 2003. Proceedings. ICRA'03. IEEE International Conference on, vol. 2, pp. 1824-1829. IEEE, 2003.
[48]
Ciocarlie, Matei, Kaijen Hsiao, Edward Gil Jones, Sachin Chitta, Radu Bogdan Rusu, and Ioan A. Şucan. "Towards reliable grasping and manipulation in household environments." In Experimental Robotics, pp. 241-252. Springer Berlin Heidelberg, 2014.
[49]
Loureiro, Rui CV, and William S. Harwin. "Reach & grasp therapy: design and control of a 9-DOF robotic neuro-rehabilitation system." In Rehabilitation Robotics, 2007. ICORR 2007. IEEE 10th International Conference on, pp. 757-763. IEEE, 2007.
[50]
X. Markenscoff, L. Ni, C.H. Papadimitriou: The geometry of grasping, Int. J. Robot. Res. 9(1), pp.61–74 (1990)
[51]
D.G. Luenberger: Linear and Nonlinear Programming, 2nd edn. (Addison-Wesley, Reading 1984)
[52]
L. Han, J.C. Trinkle, Z. Li: Grasp analysis as linear matrix inequality problems, IEEE Trans. Robot. Autom. 16(6), 663–674 (2000)
[53]
Bruno Siciliano, Oussama Khatib, Handbooks of Robotics, Springer, pp. 250-252, 2008.
[54]
R. S. Johansson and J. R. Flanagan, “Coding and use of tactile signals from the fingertips in object manipulation tasks,” Nat. Rev. Neurosci., vol. 10, pp. 345–359, May 2009.
[55]
[55] Takaki, Takeshi, and Toru Omata. "Grasp force magnifying mechanism for parallel jaw grippers." In Robotics and Automation, 2007 IEEE International Conference on, pp. 199-204. IEEE, 2007.
[56]
Nuttall, A. J. G., and AJ Klein Breteler. "Compliance effects in a parallel jaw gripper." Mechanism and machine theory 38, no. 12 (2003): 1509-1522.
[57]
Romano, Joseph M., Kaijen Hsiao, Günter Niemeyer, Sachin Chitta, and Katherine J. Kuchenbecker. "Human-inspired robotic grasp control with tactile sensing." Robotics, IEEE Transactions on 27, no. 6 (2011): 1067-1079.
[58]
Sanchez, Jose, Sven Schneider, and Paul Plöger. "Safely Grasping with Complex Dexterous Hands by Tactile Feedback." In RoboCup 2014: Robot World Cup XVIII, pp. 332-344. Springer International Publishing, 2015.
[59]
Klingbeil, Ellen, Deepak Rao, Blake Carpenter, Varun Ganapathi, Andrew Y. Ng, and Oussama Khatib. "Grasping with application to an autonomous checkout robot." In Robotics and Automation (ICRA), 2011 IEEE International Conference on, pp. 2837-2844. IEEE, 2011.
[60]
Miltiadis A. Boboulos, Automation and robotics, pp.83, 2010, ISBN: 978-87-7681-696-4
[61]
C. Quennouelle, C. M.Gosselin, Instantaneous Kinemato-Static Model of Planar Compliant Parallel Mechanisms, In: Proceedings of ASME International Design Engineering Technical Conferences, Brooklyn, NY, USA, 2008.
[62]
Q. V. Le, D. Kamm, A. Kara, and A. Y. Ng, “Learning to grasp objects with multiple contact points,” Robotics and Automation (ICRA), 2010 IEEE International Conference on, pp.5062 - 5069, Anchorage, AK, IEEE, 2010.
[63]
Kao, Imin, and Fuqian Yang. "Stiffness and contact mechanics for soft fingers in grasping and manipulation." Robotics and Automation, IEEE Transactions on20, no. 1 (2004): 132-135.
[64]
Yoshikawa, Tsuneo, Masanao Koeda, and Hiroshi Fujimoto. "Shape recognition and grasping by robotic hands with soft fingers and omnidirectional camera." InRobotics and Automation, 2008. ICRA 2008. IEEE International Conference on, pp. 299-304. IEEE, 2008.
[65]
D. Prattichizzo, A. Bicchi: Dynamic analysis of mobility and grasp ability of general manipulation systems, IEEE Trans. Robot. Autom. 14(2), 241–258 (1998).
[66]
A. Bicchi: On the problem of decomposing graspand manipulation forces in multiple whole-limb manipulation, Int. J. Robot. Auton. Syst. 13, 127–147 (1994).
[67]
Rosales, C.; Ajoudani, A.; Gabiccini, M.; Bicchi, A. "Active gathering of frictional properties from objects", Intelligent Robots and Systems (IROS 2014), 2014 IEEE/RSJ International Conference on, On page(s): 3982 – 3987.
[68]
Brown, Russell G., and Randy C. Brost. "A 3-D modular gripper design tool."Robotics and Automation, IEEE Transactions on 15, no. 1 (1999): 174-186.
[69]
Ciocarlie, Matei T., and Peter K. Allen. "Hand posture subspaces for dexterous robotic grasping." The International Journal of Robotics Research 28, no. 7 (2009): 851-867.
[70]
S. Thrun, W. Burgard, and D. Fox, Probabilistic Robotics. MIT Press, 2005, Ch. 2. Recursive State Estimation, pp. 13-38.
[71]
Sintov, Avishai, Srinivas Raghothama, Roland Menassa, and Amir Shapiro. "A common 3-finger grasp search algorithm for a set of planar objects." InAutomation Science and Engineering (CASE), 2012 IEEE International Conference on, pp. 1095-1100. IEEE, 2012.
[72]
Christopoulos, Vassilios N., and Paul Schrater. "Handling shape and contact location uncertainty in grasping two-dimensional planar objects." In Intelligent Robots and Systems, 2007. IROS 2007. IEEE/RSJ International Conference on, pp. 1557-1563. IEEE, 2007.
[73]
Phoka, Thanathorn, Pawin Vongmasa, Chaichana Nilwatchararang, Peam Pipattanasomporn, and Attawith Sudsang. "Optimal independent contact regions for two-fingered grasping of polygon." Robotica 30, no. 06 (2012): 879-889.
[74]
Zisimatos, A.G.; Liarokapis, M.V.; Mavrogiannis, C.I.; Kyriakopoulos, K.J. "Open-source, affordable, modular, light-weight, underactuated robot hands", Intelligent Robots and Systems (IROS 2014), 2014 IEEE/RSJ International Conference on, On page(s): 3207 – 3212
[75]
Bard, C.; Troccaz, J.; Vercelli, G. "Shape analysis and hand preshaping for grasping", Intelligent Robots and Systems '91. 'Intelligence for Mechanical Systems, Proceedings IROS '91. IEEE/RSJ International Workshop on, On page(s): 64 - 69 vol.1
[76]
Grosso, E.; Vercelli, G. "Grasping strategies for reconstructed unknown 3D objects", Intelligent Robots and Systems '91. 'Intelligence for Mechanical Systems, Proceedings IROS '91. IEEE/RSJ International Workshop on, On page(s): 70 - 75 vol.1
[77]
Bruno Siciliano, Oussama Khatib, Handbooks of Robotics, Springer, pp. 297-298, 2008.
[78]
G.F. Liu, J. Xu, X. Wang, Z.X. Li: On quality functions for grasp synthesis, fixture planning, and coordinated manipulation, IEEE Trans. Autom. Sci. Eng. 1(2), 146–162 (2004).
[79]
L. Han, J.C. Trinkle, Z. Li: Grasp analysis as linear matrix inequality problems, IEEE Trans. Robot. Autom. 16(6), 663–674 (2000).
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