Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
local differential geometry; robotics; Lie algebra; asymptotic motion
local differential geometry; robotics; Lie algebra; asymptotic motion
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.
References:
[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). MR 0145455 | Zbl 0111.18101
[3] Karger, A.: Geometry of the motion of robot manipulators. Manuscr. Math. 62 (1988), 115-126. DOI 10.1007/BF01258270 | MR 0958256 | Zbl 0653.53007
[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. DOI 10.1007/BF00822203 | MR 1047292
[5] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry. Springer Berlin (1993). MR 1202431
[6] Selig, J. M.: Geometrical Methods in Robotics. Springer New York (1996). MR 1411680 | Zbl 0861.93001
Search
Partner of
