  A self-contained calibration procedure that can be performed automatically
without additional external sensors or tools is a significant advantage,
especially for complex robotic systems. Here, we show that the kinematics of a
multi-fingered robotic hand can be precisely calibrated only by moving the tips
of the fingers pairwise into contact. The only prerequisite for this is
sensitive contact detection, e.g., by torque-sensing in the joints (as in our
DLR-Hand II) or tactile skin. The measurement function for a given joint
configuration is the distance between the modeled fingertip geometries, but the
actual measurement is always zero. In an in-depth analysis, we prove that this
contact-based calibration determines all quantities needed for manipulating
objects with the hand, i.e., the difference vectors of the fingertips, and that
it is as sensitive as a calibration using an external visual tracking system
and markers. We describe the complete calibration scheme, including the
selection of optimal sample joint configurations and search motions for the
contacts despite the initial kinematic uncertainties. In a real-world
calibration experiment for the torque-controlled four-fingered DLR-Hand II, the
maximal error of 17.7mm can be reduced to only 3.7mm.
