Page 176 - Human Inspired Dexterity in Robotic Manipulation

174 Human Inspired Dexterity in Robotic Manipulation

Eqs. (9.14), (9.15) state that the error norm between the differences between
the measured- and virtual-object frames at t A and at t B is smaller than that
between the measured-object frames at t A and at t B , where the error norm
of the object orientation is represented by a rotational angle around the
equivalent rotational axis. In other words, the physical meaning of these
conditions is that the change in the difference between the measured-object
frame and the virtual-object frame must be smaller than the discretization
error due to the low sampling rate. The measured-object frame will ulti-
mately converge to the desired state if these conditions are satisfied in every
servo loop.

9.5 NUMERICAL SIMULATION

This section presents the results of numerical simulations to verify the effec-
tiveness of the proposed controller. A three-fingered hand-arm model as
shown in Fig. 9.1 was utilized in the simulations [6]. As it is mentioned
in Section 9.2, this model consists of a five-DOF arm component and a
three-fingered hand component with one five-DOF finger and two four-
DOF fingers. A triangular prism is considered as the grasped object as an
example of a polyhedral object. The specific parameters of the hand-arm sys-
tem and the grasped object are shown in Table 9.1. In this table, Y i is the
perpendicular distance from the center of mass of the object O c.m. to the
ith surface of the object, and θ ti is the internal angle of the corresponding
triangular cross section of the object. Table 9.2 shows the desired nominal
grasping force and gains. Assume that under the initial conditions, the hand-
arm system has already grasped the object. The parameters of this system in
the initial state are shown in Table 9.3.
Two types of simulations were conducted to demonstrate the advantages
of the proposed method. One simulation used the proposed visual servoing
method. The other used our previously proposed visual servoing method,
which directly utilizes the position and orientation of the measured-object
frame as control variables [7]. The previous method uses control inputs
for position and orientation control of the measured-object frame, u p real
, respectively, instead of u p and u o . These control inputs are given
and u o real
as follows:
N
T
X
u p ðtÞ¼ K p J ðtÞ x d xðt t delay Þ , (9.19)
0i
real
i¼1