| Title:
|
On asymptotic motions of robot-manipulator in homogeneous space (English) |
| Author:
|
Dekrét, Anton |
| Author:
|
Bakša, Ján |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
53 |
| Issue:
|
6 |
| Year:
|
2008 |
| Pages:
|
535-545 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\Cal G$ (the subspaces of velocity operators, of Coriolis acceleration operators, asymptotic subspaces) are introduced and by them asymptotic and geodesic motions are described. (English) |
| Keyword:
|
local differential geometry |
| Keyword:
|
robotics |
| Keyword:
|
Lie algebra |
| Keyword:
|
asymptotic motion |
| MSC:
|
53A17 |
| MSC:
|
70B15 |
| MSC:
|
70E60 |
| MSC:
|
70G45 |
| idZBL:
|
Zbl 1199.53016 |
| idMR:
|
MR2469064 |
| DOI:
|
10.1007/s10492-008-0040-y |
| . |
| Date available:
|
2010-07-20T12:38:05Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140339 |
| . |
| Reference:
|
[1] Bakša, J.: On asymptotic motions of 3-parametric robot-manipulators.(to appear). |
| Reference:
|
[2] Helgason, S.: Differential Geometry and Symmetric Spaces.Academic Press New York-London (1962). Zbl 0111.18101, MR 0145455 |
| Reference:
|
[3] Karger, A.: Geometry of the motion of robot manipulators.Manuscr. Math. 62 (1988), 115-126. Zbl 0653.53007, MR 0958256, 10.1007/BF01258270 |
| Reference:
|
[4] Karger, A.: Classification of three-parametric spatial motions with transitive group of automorphisms and three-parametric robot manipulators.Acta Appl. Math. 18 (1990), 1-16. MR 1047292, 10.1007/BF00822203 |
| Reference:
|
[5] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry.Springer Berlin (1993). MR 1202431 |
| Reference:
|
[6] Selig, J. M.: Geometrical Methods in Robotics.Springer New York (1996). Zbl 0861.93001, MR 1411680 |
| . |
