Chapter 2. Prehension

134 THE PHASES OF PREHENSION
A B
Figure 5.9. Six degree of freedom manipulator having learned two
different sequences of four goal locations. Some of the goals in A
and B are in the same Cartesian location. The network was able to
choose different inverse kinematic solutions, using temporal
constraints to provide a context for the decision. (from Jordan,
1988; reprinted by permission).
goals. Figure 5.9b shows another learned sequence which has two
goal locations in common with the sequence in Figure 5.9a.
However, even though the two target points are the same, the network
generates different joint configurations. These configurations depend
upon the temporal context in which the target point was embedded.
Since the arm was bent upwards at the elbow in Figure 5.9b, the con-
figuration chosen is a smooth transition from the previous one.
Jordan’s model solves the inverse kinematic problem of generating
joint angles from a goal location, addressing the underdetermined
aspect of the problem. Using an adaptive constraint network that in-
corporates constraints at relevant levels, he offers a solution to motor
equivalence problems (see Jordan 1989 or 1990 for further elaboration
of these ideas). For configurational constraints that depend more on
the structural properties of a particular manipulator, single unit and
multiple unit constraints are maintained locally, acting as small filters
to focus error-reducing adaptation. For temporal constraints that allow
adaptation to occur within a historical context of the way nearby joints
are changing, the error-reducing algorithm acts with knowledge of the
previous state. While an intriguing model for trajectory learning, the
question remains, how does the system learn the constraints in the first
place? These had to be placed by Jordan himself. An interesting en-
hancement of the model would be for the system to learn the con-
straints in the workplace.