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A general method for the numerical computation of manipulator singularity sets

AuthorsBohigas, Oriol ; Zlatanov, Dimiter; Ros, Lluís ; Manubens, Montserrat ; Porta, Josep M.
KeywordsBranch-and-prune method
Non-redundant manipulator
Linear relaxation
Singularity set computation
Issue Date2014
PublisherInstitute of Electrical and Electronics Engineers
CitationIEEE Transactions on Robotics 30(2): 340-351 (2014)
AbstractThe analysis of singularities is central to the development and control of a manipulator. However, existing methods for singularity set computation still concentrate on specific classes of manipulators. The absence of general methods able to perform such computation on a large class of manipulators is problematic because it hinders the analysis of unconventional manipulators and the development of new robot topologies. The purpose of this paper is to provide such a method for nonredundant mechanisms with algebraic lower pairs and designated input and output speeds. We formulate systems of equations that describe the whole singularity set and each one of the singularity types independently, and show how to compute the configurations in each type using a numerical technique based on linear relaxations. The method can be used to analyze manipulators with arbitrary geometry, and it isolates the singularities with the desired accuracy. We illustrate the formulation of the conditions and their numerical solution with examples, and use 3-D projections to visualize the complex partitions of the configuration space induced by the singularities.
Publisher version (URL)http://dx.doi.org/10.1109/TRO.2013.2283416
Identifiersissn: 1552-3098
e-issn: 1941-0468
Appears in Collections:(IRII) Artículos
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