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.

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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.



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