By Topic

Equivolumetric partition of solid spheres with applications to orientation workspace analysis of robot manipulators

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Guilin Yang ; Mechatronics Group, Singapore Inst. of Manuf. Technol., Singapore ; I-Ming Chen

Orientation workspace analysis is a critical issue in the design of robot manipulators, especially the spherical manipulators. However, there is a lack of effective methods for such analysis, because the orientation workspace of a robot manipulator is normally a subset of SO(3) (the special orthogonal group) with a complex boundary. Numerical approaches appear more practical in actual implementations. For numerical analysis, a finite partition of the orientation workspace in its parametric domain is necessary. It has been realized that the exponential coordinates parameterization is more appropriate for finite partition. With such a parameterization, the rigid body rotation group, i.e., SO(3), can be mapped to a solid sphere D3 of radius pi with antipodal points identified. A novel partition scheme is proposed to geometrically divide the parametric domain, i.e., the solid sphere D3 of radius pi, into finite elements with equal volume. Subsequently, the volume of SO(3) can be numerically computed as a weighted volume sum of the equivolumetric elements, in which the weightages are the element-associated integration measures. In this way, we can simplify the partition scheme and also reduce the computation efforts, as the elements in the same partition layer (along the radial direction) have the same integration measure. The effectiveness of the partition scheme is demonstrated through analysis of the orientation workspace of a three-degree-of-freedom spherical parallel manipulator. Numerical convergence on various orientation workspace measures, such as the workspace volume and the global condition index, are obtained based on this partition scheme

Published in:

Robotics, IEEE Transactions on  (Volume:22 ,  Issue: 5 )