@inproceedings{recio:1994:sig,
	title = {On the symbolic insimplification of the general $6{R}$-manipulator
	kinematic equations},
	address = {New York, NY 10036, USA},
	author = {T. Recio and M. J. Gonz{\'a}lez-L{\'o}pez},
	booktitle = {{ISSAC} '94: Proceedings of the 1994 International Symposium on Symbolic
	and Algebraic Computation: July 20--22, 1994, Oxford, England, United
	Kingdom},
	editor = { {ACM}},
	pages = {354--358},
	publisher = {ACM Press},
	url = {http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p354-recio/},
	year = {1994},
	biburl = {http://www.bibsonomy.org/bibtex/2fcc73aa671e0b7fbe47ef289495b0e61/dmartins},
	description = {robotica-bib},
	abstract = {When symbolically solving inverse kinematic problems for robot classes,
	we deal with computations on ideals representing these robot's geometry.
	Therefore, such ideals must be considered over a base field {\em
	K\/}, where the parameters of the class (and also the possible relations
	among them) are represented. In this framework we shall prove that
	the ideal corresponding to the general 6R manipulator is real and
	prime over {\em K\/}. The practical interest of our result is that
	it confirms that the usual inverse kinematic equations of this robot
	class do not add redundant solutions and that this ideal cannot be
	``factorized'', establishing therefore, Kov{\'a}cs [7] conjecture.
	We prove also that this root class has six degrees of freedom (i.e.
	the corresponding ideal is six-dimensional), even over the extended
	field {\em K\/}, which is the algebraic counterpart to the fact that
	the 6R manipulator is completely general. Our proof uses, as intermediate
	step, some dimensionality analysis of the Elbow manipulator, which
	is a specialization of the {\em 6R\/}.},
	subject = {{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
	General. {\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS
	AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical
	problems and computations. {\bf I.2.9} Computing Methodologies, ARTIFICIAL
	INTELLIGENCE, Robotics, Manipulators. {\bf F.2.1} Theory of Computation,
	ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
	and Problems, Computations on matrices.}, thesaurus = {Manipulator kinematics; Symbol manipulation}, bibdate = {Thu Mar 12 08:41:19 MST 1998}, acknowledgement = {#ack-nhfb#}, isbn = {0-89791-638-7}, classification = {C3390M (Manipulators)}, affiliation = {Dept. de Matematicas, Estadistica y Comput., Cantabria Univ., Santander,
	Spain},
	keywords = {6R Elbow General Ideal; Inverse Kinematics; Kovacs Robot Robotics; Six Symbolic Symbolically algorithms; class; computation; conjecture; degrees equations; freedom; insimplification; kinematic manipulator manipulator; of problems; solving; theory; verification }
}