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

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CHAPTER 2. State of the art
manipulations.
The theoretical background of MLD models and MIPQ solvers can be found
in [5].
2.3.6
Control basis approach
Inspired by linear algebra theory where any vector of the space can be expressed
with a linear sum of vectors of the basis, the control basis approach allows to build
any controller simply combining controllers of the basis. In such combination, each
controller is in the null space of the others guaranteeing the robustness.
A real problem is how to select the simple controllers of the basis, since from
this last depends the variety of control that one can apply to the manipulation
In [46], a finite states scheme is presented for manipulation control and re-grasp
tasks. A combination of controls from the basis corresponds to each state and the
basis is made up by three simple controllers, namely: a space motion controller,
for the control of the motion in the operational space in order to avoid obstacles; a
contact configuration controller, managing the contact forces; a posture controller,
for the kinematics of the system in order to manage its redundancy. Each controller
of the basis is simple, inner closed-loop by feedback and stable. A combination
of simple controllers is also stable. A formal language to deal with this class of
control has also been developed. The work in [77] is inspired by this way to control
some manipulation tasks with robotic hands, too.
2.3.7
Adaptive control is often employed when the parameters of the model of the sys-
tem (hand plus object) are not known at all or they are partially known, and
an estimation process is then necessary. Hence, with this technique, the control
schemes can deal with unstructured environments and become more flexible for
real and practical situations.
In [40], the problem of how to manipulate an object without knowledge about
its dynamic and inertia parameters is considered. The proposed scheme is made up
of two steps, namely: in the first step the object's center of mass is estimated with
an adaptive nonlinear scheme, while in the second step the estimated parameters
are used to optimize finger velocities and internal forces, in order not to allow the
slippage of the object and to follow desired motions. The adaptive control scheme
used in [40] is depicted in Figure 2.4, and the same was used in [6, 90], while the
controller used in the latter step is a PD with an acceleration feedforward with a
forces optimization module.
Considering sliding contacts and unknown parameters of the object and friction
coefficients, in [100], it is proposed a coordinated control scheme for multi-fingered
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Summary :