0
Research Papers

Optimal-Regularity for Serial Redundant Robots

[+] Author and Article Information
Nir Shvalb

Department of Industrial Engineering,
Ariel University,
Ariel 4076113, Israel
e-mail: nirsh@ariel.ac.il

Tal Grinshpoun

Department of Industrial Engineering,
Ariel University,
Ariel 4076113, Israel
e-mail: talgr@ariel.ac.il

Oded Medina

Department of Mechanical Engineering,
Ariel University,
Ariel 4076113, Israel
e-mail: odedmedina@gmail.com

Manuscript received May 15, 2016; final manuscript received December 15, 2016; published online March 24, 2017. Assoc. Editor: Andreas Mueller.

J. Mechanisms Robotics 9(3), 031015 (Mar 24, 2017) (5 pages) Paper No: JMR-16-1144; doi: 10.1115/1.4035532 History: Received May 15, 2016; Revised December 15, 2016

A configuration of a mechanical linkage is defined as regular if there exists a subset of actuators with their corresponding Jacobian columns spans the gripper's velocity space. All other configurations are defined in the literature as singular configurations. Consider mechanisms with grippers' velocity space m. We focus our attention on the case where m Jacobian columns of such mechanism span m, while all the rest are linearly dependent. These are obviously an undesirable configuration, although formally they are defined as regular. We define an optimal-regular configuration as such that any subset of m actuators spans an m-dimensional velocity space. Since this densely constraints the work space, a more relaxed definition is needed. We therefore introduce the notion of k-singularity of a redundant mechanism which means that rigidifying k actuators will result in an optimal-regularity. We introduce an efficient algorithm to detect a k-singularity, give some examples for cases where m = 2, 3, and demonstrate our algorithm efficiency.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Chirikjian, G. S. , and Burdick, J. W. , 1995, “ The Kinematics of Hyper-Redundant Robot Locomotion,” IEEE Trans. Rob. Autom., 11(6), pp. 781–793. [CrossRef]
Shvalb, N. , Moshe, B. B. , and Medina, O. , 2013, “ A Real-Time Motion Planning Algorithm for a Hyper-Redundant Set of Mechanisms,” Robotica, 31(8), pp. 1327–1335.
Sujan, V. A. , and Dubowsky, S. , 2004, “ Design of a Lightweight Hyper-Redundant Deployable Binary Manipulator,” ASME J. Mech. Des., 126(1), pp. 29–39. [CrossRef]
Ota, T. , Degani, A. , Zubiate, B. , Wolf, A. , Choset, H. , Schwartzman, D. , and Zenati, M. A. , 2006, “ Epicardial Atrial Ablation Using a Novel Articulated Robotic Medical Probe Via a Percutaneous Subxiphoid Approach,” Innovations (Philadelphia, PA), 1(6), pp. 335–340. [CrossRef] [PubMed]
Medina, O. , Shapiro, A. , and Shvalb, N. , 2015, “ Motion Planning for an Actuated Flexible Polyhedron Manifold,” Adv. Rob., 29(18), pp. 1195–1203. [CrossRef]
Medina, O. , Shapiro, A. , and Shvalb, N. , 2015, “ Kinematics for an Actuated Flexible n-Manifold,” ASME J. Mech. Rob., 8(2), p. 021009. [CrossRef]
Craig, J. J. , 2005, Introduction to Robotics: Mechanics and Control, Vol. 3, Pearson Prentice Hall, Upper Saddle River, NJ.
de Wit, C. C. , Siciliano, B. , and Bastin, G. , 2012, Theory of Robot Control, Springer Science & Business Media, Berlin.
Siciliano, B. , 1990, “ Kinematic Control of Redundant Robot Manipulators: A Tutorial,” J. Intell. Rob. Syst., 3(3), pp. 201–212. [CrossRef]
Sciavicco, L. , and Siciliano, B. , 2012, Modelling and Control of Robot Manipulators, Springer Science and Business Media, Berlin.
Gosselin, C. , and Angeles, J. , 1990, “ Singularity Analysis of Closed-Loop Kinematic Chains,” IEEE Trans. Rob. Autom., 6(3), pp. 281–290. [CrossRef]
Srivatsan, R. A. , Bandyopadhyay, S. , and Ghosal, A. , 2013, “ Analysis of the Degrees-of-Freedom of Spatial Parallel Manipulators in Regular and Singular Configurations,” Mech. Mach. Theory, 69, pp. 127–141. [CrossRef]
Shvalb, N. , Shoham, M. , Bamberger, H. , and Blanc, D. , 2009, “ Topological and Kinematic Singularities for a Class of Parallel Mechanisms,” Math. Probl. Eng., 2009, p. 249349. [CrossRef]
Liu, G. , Lou, Y. , and Li, Z. , 2003, “ Singularities of Parallel Manipulators: A Geometric Treatment,” IEEE Trans. Rob. Autom., 19(4), pp. 579–594. [CrossRef]
Tsai, L.-W. , 1996, “ Kinematics of a Three-DOF Platform With Three Extensible Limbs,” Recent Advances in Robot Kinematics, Springer, Berlin, pp. 401–410.
Zlatanov, D. , Fenton, R. , and Benhabib, B. , 1995, “ A Unifying Framework for Classification and Interpretation of Mechanism Singularities,” ASME J. Mech. Des., 117(4), pp. 566–572. [CrossRef]
Zlatanov, D. , Bonev, I. A. , and Gosselin, C. M. , 2002, “ Constraint Singularities of Parallel Mechanisms,” IEEE International Conference on Robotics and Automation (ICRA), Washington, DC, May 11–15, pp. 496–502.
Zlatanov, D. S. , Fenton, R. G. , and Benhabib, B. , 1998, “ Classification and Interpretation of the Singularities of Redundant Mechanisms,” ASME Paper No. DETC98/MECH-5896.
Conconi, M. , and Carricato, M. , 2009, “ A New Assessment of Singularities of Parallel Kinematic Chains,” IEEE Trans. Rob., 25(4), pp. 757–770. [CrossRef]
Villard, G. , 2003, “ Computation of the Inverse and Determinant of a Matrix,” Algorithms Seminar, INRIA, Le Chesnay, France, pp. 29–32.
Muller, M. E. , 1959, “ A Note on a Method for Generating Points Uniformly on n-Dimensional Spheres,” Commun. ACM, 2(4), pp. 19–20. [CrossRef]
Marsaglia, G. , 1972, “ Choosing a Point From the Surface of a Sphere,” Ann. Math. Stat., 43(2), pp. 645–646. [CrossRef]
Hunt, K. H. , 1978, Kinematic Geometry of Mechanisms, Vol. 7, Oxford University Press, Oxford, UK.
Blanc, D. , and Shvalb, N. , 2012, “ Generic Singular Configurations of Linkages,” Topol. Appl., 159(3), pp. 877–890. [CrossRef]
West, D. B. , 2001, Introduction to Graph Theory, 2nd ed., Prentice Hall, Upper Saddle River, NJ.
Wang, X. , and Hu, Y. , 2009, “ Reordering and Partitioning Jacobian Matrices Using Graph-Spectral Method,” Intelligent Robotics and Applications, Springer, Berlin, pp. 696–705.
Garey, M. R. , and Johnson, D. S. , 1979, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman & Co., New York.

Figures

Grahic Jump Location
Fig. 1

Ignoring the obstacle, the depicted configuration is regular. Taking the obstacle into account will result with a singular configuration, since joints 2,3,…,7 are linear dependent.

Grahic Jump Location
Fig. 2

A three-singular configuration: rigidifying two joints of{3, 5, 8} and one of {1, 6} will result in an optimal-regular configuration

Grahic Jump Location
Fig. 3

An optimal-regular configuration

Grahic Jump Location
Fig. 4

A two-singular configuration: dropping joint 4 and one of the joints 3 or 5 will result in an optimal-regular configuration

Grahic Jump Location
Fig. 5

The bipartite graph where four vectors in J are perpendicular to two vectors in A

Grahic Jump Location
Fig. 6

The calculation time needed when searching for a six vector linear dependencies of redundant serial robots with degrees-of-freedom ranging from 8 to 30. The dashed line presents the naïve approach. The vertical error bars indicate the 1.5 standard deviations of 20experiments.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In