On asymptotic motions of robot-manipulator in homogeneous space

Anton Dekrét; Ján Bakša

Applications of Mathematics (2008)

  • Volume: 53, Issue: 6, page 535-545
  • ISSN: 0862-7940

Abstract

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In this paper the notion of robot-manipulators in the Euclidean space is generalized to the case in a general homogeneous space with the Lie group G of motions. Some kinematic subspaces of the Lie algebra 𝒢 (the subspaces of velocity operators, of Coriolis acceleration operators, asymptotic subspaces) are introduced and by them asymptotic and geodesic motions are described.

How to cite

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Dekrét, Anton, and Bakša, Ján. "On asymptotic motions of robot-manipulator in homogeneous space." Applications of Mathematics 53.6 (2008): 535-545. <http://eudml.org/doc/37799>.

@article{Dekrét2008,
abstract = {In this paper the notion of robot-manipulators in the Euclidean space is generalized to the case in a general homogeneous space with the Lie group $G$ of motions. Some kinematic subspaces of the Lie algebra $\mathcal \{G\}$ (the subspaces of velocity operators, of Coriolis acceleration operators, asymptotic subspaces) are introduced and by them asymptotic and geodesic motions are described.},
author = {Dekrét, Anton, Bakša, Ján},
journal = {Applications of Mathematics},
keywords = {local differential geometry; robotics; Lie algebra; asymptotic motion; local differential geometry; robotics; Lie algebra; asymptotic motion},
language = {eng},
number = {6},
pages = {535-545},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On asymptotic motions of robot-manipulator in homogeneous space},
url = {http://eudml.org/doc/37799},
volume = {53},
year = {2008},
}

TY - JOUR
AU - Dekrét, Anton
AU - Bakša, Ján
TI - On asymptotic motions of robot-manipulator in homogeneous space
JO - Applications of Mathematics
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 6
SP - 535
EP - 545
AB - In this paper the notion of robot-manipulators in the Euclidean space is generalized to the case in a general homogeneous space with the Lie group $G$ of motions. Some kinematic subspaces of the Lie algebra $\mathcal {G}$ (the subspaces of velocity operators, of Coriolis acceleration operators, asymptotic subspaces) are introduced and by them asymptotic and geodesic motions are described.
LA - eng
KW - local differential geometry; robotics; Lie algebra; asymptotic motion; local differential geometry; robotics; Lie algebra; asymptotic motion
UR - http://eudml.org/doc/37799
ER -

References

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  1. Bakša, J., On asymptotic motions of 3-parametric robot-manipulators, (to appear). 
  2. Helgason, S., Differential Geometry and Symmetric Spaces, Academic Press New York-London (1962). (1962) Zbl0111.18101MR0145455
  3. Karger, A., 10.1007/BF01258270, Manuscr. Math. 62 (1988), 115-126. (1988) Zbl0653.53007MR0958256DOI10.1007/BF01258270
  4. Karger, A., 10.1007/BF00822203, Acta Appl. Math. 18 (1990), 1-16. (1990) MR1047292DOI10.1007/BF00822203
  5. Kolář, I., Michor, P. W., Slovák, J., Natural Operations in Differential Geometry, Springer Berlin (1993). (1993) MR1202431
  6. Selig, J. M., Geometrical Methods in Robotics, Springer New York (1996). (1996) Zbl0861.93001MR1411680

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