Page 171 - Human Inspired Dexterity in Robotic Manipulation

A Grasping and Manipulation Scheme 169

Tahara et al. [10]. The virtual-object frame is defined by the position of each
fingertip and is used as the control variables instead of a measured-object
frame. In the work of Wimb€ock and Tahara, this frame was defined based
only on the position of each fingertip. In our proposed method [8], we
introduced additional dimensions of the virtual-object frame, such that it
is defined by not only the position, but also the orientation of each fingertip.
The proposed virtual-object frame and a measured-object frame are shown
in Fig. 9.2. This approach is more useful for the hand-arm system having
sufficient DOFs because it allows the utilization of not only the DOFs asso-
ciated with the position, but also those associated with the orientation of
each fingertip. This section introduces the virtual-object frame defined
based on the position and orientation of each fingertip [8].
First, the position of the virtual frame, x vir , is defined as follows:
N
1 X 3
x vir ¼ x 0i 2  , (9.1)
N
i¼1
3
where the x 0i 2  denote the position of the center of each fingertip.
Eq. (9.1) implies that x vir is the centroid of a polygon defined by the x 0i .

Fig. 9.2 Measured- and virtual-object frames.