Chapter 4
CLIK algorithm for
dexterous manipulation
A kinematic model for object manipulation using a multi-fingered robotic hand has
been derived in this chapter. The model allows the object's pose to be computed
from the joint variables of each finger, called active joints, as well as from a set
of contact variables modeled as passive joints [66]. Suitable conditions have been
derived, ensuring that a given motion can be imposed to the object using only the
active joints. A closed-loop inverse kinematics algorithm (CLIK [89]) has been re-
arranged in this contest, in order to compute finger contact variables, once given
the desired trajectory of the object. Both the schemes based on the transpose and
on the inverse of the Jacobian matrix can be adopted in the proposed framework.
Further, as already sentenced in Chapter 2, the manipulation system can be
redundant also if the single fingers are not: this is due to the presence of the
additional degrees of freedom (DOFs) provided by the contact variables. These
redundant DOFs can be suitably exploited to satisfy a certain number of secondary
tasks, aimed at ensuring grasp stability and manipulation dexterity, besides the
main task corresponding to the desired motion of the object.
Simulations are presented to show the performance of the proposed re-arranged
CLIK and the results presented in this chapter can be also found in the following
papers [60, 62].
4.1
Kinematics of objet and fingers
Consider a robotic hand composed by n
f
rigid fingers, numbered from 1 to n
f
,
holding a rigid object, and let q
i
denote the joint vector of finger i, with n
i
components. To derive the kinematic mapping between the joint variables of the
fingers and the pose (position and orientation) of the object, it is useful introducing
an object frame
o
attached to the object, usually chosen with the origin in the
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