Geodesic
On asymptotic motions of robot-manipulator in homogeneous space
Applications of Mathematics, Tome 53 (2008) no. 6, pp. 535-545 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\Cal G$ (the subspaces of velocity operators, of Coriolis acceleration operators, asymptotic subspaces) are introduced and by them asymptotic and geodesic motions are described.
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.
DOI : 10.1007/s10492-008-0040-y
Classification : 53A17, 70B15, 70E60, 70G45
Keywords: local differential geometry; robotics; Lie algebra; asymptotic motion 
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Dekrét, Anton; Bakša, Ján. On asymptotic motions of robot-manipulator in homogeneous space. Applications of Mathematics, Tome 53 (2008) no. 6, pp. 535-545. doi: 10.1007/s10492-008-0040-y

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