Page 156 - Human Inspired Dexterity in Robotic Manipulation

Dynamic Manipulation Based on Thumb Opposability 153

(A) (B)
Fig. 8.2 Contact models of the fingertips: (A) Frictional point. (B) Rolling contact. The
contact point does not move even if the orientation of the fingertip moves. Thus,
the contact normal is also unchanged. When the fingertip rolls over the object
surface, the contact point moves. The contact normal is also changed when the
object surface is curved.

Hand

Object

(A) (B) (C)
Fig. 8.3 A hand-and-object system. (A) The overview of the system. (B) Net force on the
hand. (C) Net force on the object.

multifingered robotic hands based on thumb opposability, called blind
grasping, to reduce the requirement of object information.

8.3.2 Dynamics and Equilibrium Points of a Finger-Object
System
Fig. 8.3A shows a hand grasping an object with the circular fingertips in a
horizontal plane. The contact force is assumed to stay within the friction
cone. Then, the fingertips can roll over the object surface, and the dynamics
of a hand-and-object system is given as follows:
T
H i €q + b i ðq , _q Þ + J λ i ¼ u i (8.1)
i i i i
X T
H o €z + b o ðz, _zÞ + G λ i ¼ 0, (8.2)
i
i
where q i and z are the states of the ith hand and object, respectively, H i and
H o are their inertia matrices, b i and b o are the Coriolis, centrifugal and damp-
ing forces, J i and G i are the Jacobian matrices of the contact points with