Chapter 2. Prehension

114 THE PHASES OF PREHENSION
present above the task specification. This makes the solution of a
computation indeterminant, because the number of degrees of freedom
available in the controlled system exceeds the number of degrees of
freedom needed to specify the task. At the muscle level, the problem
is even more complicated, since there are about 33 muscles, some
having multiple compartments and attachments. Thousands of muscle
fibers combine to form these muscles. Thus at the muscle level, there
are at least 27 extra degrees of freedom above the task specification,
and at the muscle fiber level, there are thousands of extra ones. At any
level of analysis, therefore, there are many possible ways to achieve
the same goal. When a controlled system has such redundancy, one
unique solution does not exist for that the controller; therefore the
problem is ill-posed.
A further complication is that many degrees of freedom in the hu-
man arm and hand are coupled; i.e., there are nonlinear interactions
between degrees of freedom. Interdependent motions are noted for the
joints of the pectoral girdle, and muscles can be seen to contribute to
more than one degree of freedom at a joint (see Appendix A). For ex-
ample, Soechting and Terzuolo (1990) discussed a task where shoul-
der and elbow flexors are required to counteract gravity. They pointed
out that the posture could be maintained using the brachioradialis (an
elbow flexor) and anterior deltoid (a shoulder flexor), or alternatively,
using the biceps (an elbow and shoulder flexor). What mechanism is
the CNS using for making such a decision? Bernstein (1967) argued
that having redundant degrees of freedom makes it easier to control the
arm, suggesting that actions are organized as synergies in order to re-
duce the number of degrees of freedom to be controlledz. He argued
that action-related proprioceptive input is necessary since the CNS
cannot foresee and compute forces acting on several simultaneous
joints.
Finally, there are an infinitely large number of spatial paths that the
hand could follow in reaching towards an object. And for any given
path, there are an infinitely many velocity profiies that could be used.
Recalling Greene (1972), the choice can be constrained to
approximations by an executive, with lower centers fine tuning the
ballpark solution.
One way to reduce the degrees of freedom problem is to use a cost
function as a measure of the ‘goodness’ of a solution. This perfor-
mance criteria can be done on a variety of measures, such as the mini-
mal movement time, torque, potential energy (Massone and Bizzi,
2A Svnerw is a group of muscles acting within a functional and coherent unit.