A Riemannian-Geometry Approach for Modeling and Control of Dynamics of Object Manipulation under Constraints
A Riemannian-geometry approach for modeling and control of dynamics of object manipulation under holonomic or non-holonomic constraints is presented. First, position/force hybrid control of an endeffector of a multijoint redundant (or nonredundant) robot under a holonomic constraint is reinterpreted...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | Journal of Robotics |
| Online Access: | http://dx.doi.org/10.1155/2009/892801 |
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| Summary: | A Riemannian-geometry approach for modeling and control of
dynamics of object manipulation under holonomic or non-holonomic
constraints is presented. First, position/force hybrid control of
an endeffector of a multijoint redundant (or nonredundant) robot
under a holonomic constraint is reinterpreted in terms of
“submersion” in Riemannian geometry. A force control
signal constructed in the image space of the constraint gradient
is regarded as a lifting (or pressing) in the direction orthogonal
to the kernel space. By means of the Riemannian distance on the
constraint submanifold, stability of position control under
holonomic constraints is discussed. Second, modeling and control
of two-dimensional object grasping by a pair of multijoint robot
fingers are challenged, when the object is of arbitrary shape. It
is shown that rolling contact constraints induce the Euler
equation of motion, in which constraint forces appear as wrench
vectors affecting the object. The Riemannian metric is introduced
on a constraint submanifold characterized with arclength
parameters. An explicit form of the quotient dynamics is expressed
in the kernel space with accompaniment of a pair of first-order
differential equations concerning the arclength parameters. An
extension of Dirichlet-Lagrange's stability theorem to
redundant systems under constraints is suggested by introducing a
Morse-Lyapunov function. |
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| ISSN: | 1687-9600 1687-9619 |