In order to enhance dexterity in execution of robot tasks, a
redundant number of degrees-of-freedom (DOF) is adopted for
design of robotic mechanisms like robot arms and multi-fingered
robot hands. Associated with such redundancy in DOFs relative
to the number of physical variables necessary and sufficient
for description of a given task, an extra performance index
is introduced for controlling such a redundant robot in order
to avoid arising of ill-posedness of inverse kinematics from
the task space to the joint space. This paper shows that such
an ill-posedness problem of DOF redundancy can be resolved in
a natural way on the basis of construction of sensory feedback
signals from the task space and a novel concept named "stability
on a manifold". To show this, two illustrative robot tasks are
analyzed in details, which are 1) posture control of an object
via rolling contact by a redundant multi-DOF finger and 2)
stable pinching and object manipulation by a pair of multi-DOF
robot fingers.