Many problems in motor control involve the satisfaction of constraints; in some cases the satisfaction is inherent in the mechanics of the motor system (and satisfaction takes place through execution of the motion), but in others, such as path planning, the optimum is determined before motion begins and may need to be revised as exigencies arise during its execution.
As already discussed
(Sections 2.4 and 4.2),
constraints on motion
are represented conveniently by a potential field over a
spatial map.
The potential field representation is quite general.
For example, in addition to the representation of hard
constraints, increased potential can represent the relative
difficulty of motion through a region of space. In this way,
a path can be chosen that minimizes ``work'' (as defined by
the potential function).
Further, the potential can be defined over abstract spaces;
for example, planning a path through a ``lexical space''
could be a part of sentence generation.
We will consider several ways in which an optimal path can be found by
field computation.