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

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CHAPTER 2. State of the art
object impedance approach could be a good solution. In the just mentioned work,
grasping and manipulation problems are brought back to a cooperative problem
between manipulators. Knowing in advance the dynamics of the whole system, all
the "arms" are decoupled and the resultant scheme is linear: hence, an impedance
control is implemented in order to achieve a desired impedance at object level,
and not at the level of the end-effector of the "manipulators".
In [69], a robotic hand mounted on a robotic arm is considered. The proposed
control law tries to take into account the advantages to have both a robotic arm
and a robotic hand. The control scheme makes first a linearization of the system,
then it performs an impedance control law in order to give to the system the
desired mechanical behavior.
Nevertheless, one of the main advantages in using the impedance control is de-
scribed in [94], where the proprieties of strictly passivity in steady-state situations
of an impedance controller are shown. Moreover, a force control is meaningful
only if there is a contact, and then an impedance controller strictly passive can be
useful in all situations.
Starting from these considerations, in the last mentioned paper, a virtual object
with a virtual center of mass is introduced: the real center of mass is linked
both with the virtual one through a spring and with the fingertips through some
other 2D or 3D springs. Damper elements are inserted in a proper physical way:
in general, they require the measured joints velocities for their implementation,
but if these velocities cannot be available, it is hence possible to create a force
proportional to the twist acting on the virtual object instead of implementing an
observer. In this way, the force is transmitted through the springs and it is also
dissipated, creating the desired damping effect.
An impedance controller can also be found in [85], where algorithms for grasp
force optimization are studied. A specific module of the control scheme calculates
the optimal grasping forces according to various situations that could happen in a
manipulation task, such as re-grasping, fingers impact with the object, no motion
of the contact points and so on. This module is placed into a control scheme in
which each finger is controlled separately by an impedance controller.
To overcome some disadvantages related to fine manipulation ­ such as joints
friction or singularity position ­, a new control scheme has been proposed in [7],
where first a force sensor output is filtered to avoid noises, then an admittance
model computes the desired displacement. Finally, a position control generates
the finger joint torques. The admittance model is a mass-spring-damper system,
whose matrices are specified through a singular values decomposition.
Lately, the work in [93] about virtual object has been developed in [101, 102]. In
these last, the chosen control at object level allows a simpler definition of grasping
forces and a compensation of object and robot inertias. Hence, the object is
controlled by an impedance controller which is intrinsically passive. The fingers
are linked through virtual springs to a virtual object which is in turn linked to
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Summary :

## Knowing in advance the dynamics of the whole system, all the "arms" are decoupled and the resultant scheme is linear: hence, an impedance control is implemented in order to achieve a desired impedance at object level, and not at the level of the end-effector of the "manipulators". The control scheme makes first a linearization of the system, then it performs an impedance control law in order to give to the system the desired mechanical behavior. In these last, the chosen control at object level allows a simpler definition of grasping forces and a compensation of object and robot inertias.

Tags : irtual,controller,force,through,scheme,robotic,system,desired,which,situations,grasping,hence,springs
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