Application Examples in the Robotics Domain
As pointed out before in the introduction, in
the robotic domain the availability of sensorimotor
transformations are a crucial issue. In particular, the
kinematic relations are of
fundamental character. They usually describe the relationship
between joint, and actuator coordinates, and the position in
one, or several particular Cartesian reference frames.
Furthermore, the effort spent to obtain and adapt these mappings
plays an important role. Several thousand training steps, as
required by many former learning schemes, do impair the
practical usage of learning methods in the domain of robotics.
Here the wear-and-tear, but especially the needed time to
acquire the training data must be taken into account. Here, the
PSOM algorithm appears as a very suitable learning approach,
which requires only a small number of training data in order to
achieve a very high accuracy in continuous, smooth, and
high-dimensional mappings.
8.1 Robot Finger Kinematics
In section 2.2 we described the TUM robot hand,
which is built of several identical finger modules. To employ
this (or a similar dextrous) robot hand for manipulation tasks
requires to solve the forward and inverse kinematics problem for
the hand finger. The TUM mechanical design allows roughly the
mobility of the human index finger. Here, a cardanic base joint
(2 DOF) offers sidewards gyring of
and full adduction with two additional coupled joints
(one further DOF). Fig. 8.1 illustrates the workspace with a
stroboscopic image.
For the kinematics in the case of our finger,
there are several coordinate systems of interest, e.g. the joint
angles, the cylinder piston positions, one or more finger tip
coordinates, as well as further configuration dependent
quantities, such as the Jacobian matrices for force / moment
transformations. All of these quantities can be simultaneously
treated in one single common PSOM; here we demonstrate only the
most difficult part, the classical inverse kinematics. When
moving the three joints on a cubical 101010
grid within their maximal configuration space, the fingertip (or
more precisely the mount point) will trace out the “banana”
shaped grid displayed in Fig. 8.1 (confirm the workspace with
your finger!) Obviously, the underlying transformation is highly
non-linear and exhibits a pointsingularity in the vicinity of
the “banana tip”. Since an analytical solution to the inverse
kinematic problem was not derived yet, this problem was a
particular challenging task for the PSOM approach (Walter and
Ritter 1995).
