Page 160 - Human Inspired Dexterity in Robotic Manipulation

Dynamic Manipulation Based on Thumb Opposability 157

As shown in Fig. 8.6A, a conventional impedance controller adjusts the
absolute impedance of the object. The object impedance can be replaced
with the equivalent joint impedance to uniquely determine the equilibrium
T
point by using the transformation J K x J , where J x is the object Jacobian
x x
and K x is the object stiffness. Meanwhile, as shown in Fig. 8.6B, the blind
grasping is intuitively expressed as the spring connecting between the finger-
tips to adjust for the relative force while it does not determine the absolute
motion of the object. Thus, the proposed system is redundant and ill-posed.
Therefore, the system has an infinite number of equilibrium points and the
proposed controller might generate self-motion. The self-motion can be
suppressed by the stability theory on manifolds [12]. Intuitively, this method
uses an appropriate damping to maintain the state within a bounded region
on the grasp manifold, as shown in Fig. 8.7, instead of an explicit null-space
motion.
However, the real effect of the redundancy resolutions on grasp stability
is uncertain. Therefore, we executed a comparison between the conven-
tional impedance controller and the opposed controller with the KITECH
robotic hand that has four fully actuated four-DOF fingers [5], as shown in
Fig. 8.8. In both cases, the hand stably grasped an object at the equilibrium
when no external force was applied. However, the hand showed different
behaviors to external disturbances.
The joint impedance control preserves the position of both fingertips to
grasp the object. However, when the left finger was pulled by the distur-
bance, the distance between the fingers became larger than the object’s
width and, as a result, the hand dropped the object.
Meanwhile, the blind grasping controller preserves the relative distance
between fingers. When an external disturbance was added to one of the

Constraint manifold
Stable grasp
manifold

Lower priority task
manifold

Neighborhood around
nominal equilibrium

State space

Fig. 8.7 Manifold.