Page 172 - Human Inspired Dexterity in Robotic Manipulation

170 Human Inspired Dexterity in Robotic Manipulation

The orientation of the virtual-object frame located at x vir is expressed in

2 SOð3Þ, as shown in
the form of a rotational matrix R vir ¼ r x vir ,r y vir ,r z vir
Fig. 9.2, and its components are given as follows:
!
N
X
2  , ¼ (9.2)
¼ r x vir 3
r x vir r x vir r x fi
k r x vir k
i¼1
!
N
X
2  , ¼ (9.3)
¼ r x vir r y vir 3
r y vir r y vir r y fi
k r x vir r y vir k
i¼1
3
2  , (9.4)
r z vir ¼ r x vir r y vir

2 SOð3Þ represents a local frame located at the
where R fi ¼ r x fi , r y fi , r z fi
position of the center of each fingertip x 0i and denotes the corresponding
orientation in Cartesian coordinates.
9.4 CONTROL LAW BASED ON FINGER-THUMB
OPPOSABILITY
In this section, a control input is designed to regulate the position and ori-
entation of a grasped object by means of visual servoing in the presence of
considerable time delays. The basic idea of the input design is based on our
proposed grasping and manipulation method [8] that is robust to the tem-
porary loss of visual information using the virtual-object frame. The advan-
tage of the method proposed here is that it is robust not only to temporary
losses of visual information, but also with considerable time delays. This
advantage arises from the use of the virtual-object frame as the control var-
iable at all times during manipulation. The method is unaffected by any tem-
porary loss or time delay of the visual information because it is defined using
only information collected from proprioceptive sensors, such as encoders on
the joints. Simultaneously, however, the desired virtual-object frame is con-
tinuously being designed and updated using information about the
measured-object frame obtained from a visual sensor. The error between
the measured-object frame and the virtual-object frame is gradually reduced
in real time through updating.

9.4.1 Time Delay

The time delays considered here are caused by the sampling rate, the compu-
tational cost of image processing, and the latency of data communication. Sup-
pose that these time delays can be measured roughly in real time. Note that no
unstable behavior is induced even if the measured time delay is not accurate