Page 157 - Human Inspired Dexterity in Robotic Manipulation

154 Human Inspired Dexterity in Robotic Manipulation

respect to the joints and object, and λ i is the contact force. Thus, at the equi-
librium, the state of the system satisfies the following equations (see Fig. 8.3B
and C):

T
J λ i ¼ u i
i
X T (8.3)
G λ i ¼ 0:
i
i
The net force of the hand must be zero to be at the equilibrium as well as
the net force of the object. Thus, the control problem is to design the control
input u i satisfying the equilibrium point (8.3) of the hand-object system
without loosing the contact (i.e., λ i must stay in the friction cone).

8.3.3 Blind Grasp Based on Thumb Opposability

Roughly speaking, passivity is a property of a dynamical system that does not
generate energy. A closed-loop system controlled by a passivity-based con-
troller satisfies the passive property [6]. It is well known that passivity-based
control methods use little information to implement it, and this property
increases the robustness.
A passivity-based controller for grasp and manipulation has been pro-
posed to stabilize an object with a pair of fingers by only using visual infor-
mation to detect the relative distance between the fingertip along the object
surface [7].
This paper explains another passivity-based controller, in which we fur-
ther eliminate preknowledge and external sensor information to increase the
robustness of grasping and manipulation [8]. This method uses thumb
opposability that has been frequently referred to as an important feature
of human hands. In this section, we explain how opposability is introduced
in the controller and why opposability is useful for maintaining stability.
First, let us consider a pair of fingertips grasping a rectangular object at an
equilibrium point, as shown in Fig. 8.3, where the hand and object have five
and three DOFs and the constraint at the fingertips constrains four DOFs.
To stabilize the object, one DOF is assigned to control the internal force
that is perpendicular to the object surface for maintaining contact. We intro-
duce a strategy based on opposability, in which the center of each fingertip is
controlled to generate the force toward that of the other finger, as shown in
Fig. 8.4A. Then, at the equilibrium point, the contact forces are apparently
balanced and can maintain the grasp. Next, a disturbance is applied to the
object to generate the rotation of the object and fingertips, as shown in