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# Grasp and Manipulation of Objects with a Multi-Fingered Hand ...

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CHAPTER 4. CLIK algorithm for dexterous manipulation
· hard finger with friction: vector
i
is constant, while vector
i
may vary (i.e.,
the finger is not allowed to slide on the object surface, but the orientation
of
f
i
with respect to
c
i
may vary);
· soft finger with friction: vector
i
is constant, as well as the last parameter
of vector
i
, corresponding to the rotation about the Z axis of
c
i
(i.e., the
finger is not allowed to slide and to twist about the normal to the surface of
the object).
Hence, assuming that the type of contact remains unchanged during task execu-
tion, the variable parameters at each contact point are grouped in a (n
c
i
× 1)
vector
i
of contact variables, with n
c
i
5.
4.3
Classification of grasps
On the basis of (4.9), it is possible to make a kinematic classification of the
grasp [82].
A grasp is said to be redundant if the null space of the matrix
~
J
i
= J
i
J
i
is non-null, for at least one finger i. In this case, the mapping between the joint
variables of the "extended" finger i and the object's velocity is many to one:
motions of active and passive joints of the extended finger are possible when the
object is locked. Notice that a single finger could be redundant if the null space
of J
i
is non-null, i.e., in the case of a kinematically redundant finger; in this case,
motions of the active joints are possible when both the passive joints and the
object are locked. On the other hand, for the type of contacts considered here
(point contact), the null space of J
i
is always null: this implies that motions of
the passive joints are not possible when the active joints and the object are locked.
In typical situations, the fingers of the robotic hand are not redundant, but the
extended fingers may be redundant thanks to the presence of the additional DOFs
provided by the passive joints.
A grasp is indeterminate if the intersection of the null spaces of [-J
i
G
T
i
],
for all i = 1, . . . , n
f
, is non-null. In this case, motions of the object and of the
passive joints are possible when the active joints of all the fingers are locked. The
kinematic indetermination derives from the fact that the motion of the object
cannot be completely controlled by finger motions, but depends on the dynamics
of the system [67]. An example of indeterminate grasp may be that of a box
grasped by two hard-finger opposite contacts: in this case, the box may rotate
about the axis connecting the two contact points while the fingers are locked.
It is worth pointing out that, also in the case of redundant and indeterminate
grasps, for a given object's pose and a configuration of the fingers, the value of the
contact variables is uniquely determined.
46

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Summary :

## In this case, the mapping between the joint variables of the "extended" finger i and the object's velocity is many to one: motions of active and passive joints of the extended finger are possible when the object is locked. On the other hand, for the type of contacts considered here (point contact), the null space of J i is always null: this implies that motions of the passive joints are not possible when the active joints and the object are locked.

Tags : joints,object,case,contact,redundant,passie,ector,locked,null,motions,fingers,possible,grasp
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