Singularity-theoretic methods in robot kinematics

Abstract

SUMMARYThe significance of singularities in the design and control of robot manipulators is well known, and there is an extensive literature on the determination and analysis of singularities for a wide variety of serial and parallel manipulators—indeed such an analysis is an essential part of manipulator design. Singularity theory provides methodologies for a deeper analysis with the aim of classifying singularities, providing local models and local and global invariants. This paper surveys applications of singularity-theoretic methods in robot kinematics and presents some new results.

Regularization of the Spatial Inverse Positioning Problem of Revolute Joint Manipulators

“…The second order approximation [5] of the positioning problem is (83) that is a finite number, and independent of the regularization, so the third assumption is also satisfied. The condition number of J reg ( J reg )  is upper bounded by…”

“…Singularities get great attention in the literature, analysis of singularities of robot manipulators is done e.g. in the works of Donelan [5,6] and Kieffer [7].…”

Kinematic Singularities of Robot Manipulators

“…A number of authors have sought to apply methods of mathematical singularity theory to the study of manipulator singularities, for example Gibson (1992); Karger (1996);Pai & Leu (1992); Tchoń (1991). A recent survey of this approach can be found in (Donelan, 2007b). There are several salient features.…”

“…More particularly, it describes a framework, based on the work of Müller (2006;2009) and of the author (Donelan, 2007b;2008), in which singularities of both serial and parallel manipulators can be understood.…”

Singularities of non-redundant manipulators: A short account and a method for their computation in the planar case

“…Numerous mathematical conditions aimed at characterizing singularity have been given in the literature [1][2][3][4], even for manipulators of general architecture [5][6][7][8][9]. The earliest attempt to provide a general framework to determine and classify all singular configurations can be attributed to Gosselin and Angeles [5], who proposed the use of input/output velocity equations to define the well-known "Type I" and "Type II" singularities, where the velocity of the end-effector does not determine the velocities of the actuators, and vice versa.…”