Chapter 2. Prehension

Chapter 5 - Movement Before Contact 115
1989), mean-square error of jerk3 (Flash and Hogan, 1985), and
mean-square error of torque-change (Uno, Kawato, Suzuki, 1989). A
cost function constrains the potential hand paths and velocities, in that
the CNS makes a selection out of the infinite number of possible by
minimizing this measure. One such model is the ‘minimum jerk
model’ (Flash and Hogan 1985), which suggests that the square of the
jerk of hand position integrated over the entire movement is
minimized. Flash and Hogan showed that the trajectory uniquely
defined by this criterion function agrees with experimental data in
various regions of the workspace4.
In summary, trajectory planning involves transporting the hand to
a location by a controller. Cortical areas, such as the motor and
somatosensory cortex, are critical for neural control. Sensory
information is provided by exteroceptors and/or proprioceptors. How
the CNS transforms a goal into motor commands is a critical question,
particularly in light of the fact that so many degrees of freedom exist at
the joint level, the muscle level, and particularly at the muscle fiber
level. Exacerbating this are problems such as motor equivalency,
coupled degrees of freedom, and an endless number of solutions.
Cost functions have been proposed as a way to constrain the potential
number of solutions.
5.2 Transforming a Goal into Motor Commands
Goals must be transformed into motor commands. If the goal is
specified in some extrinsic coordinate reference frame, the CNS could
possibly compute an arm trajectory also in an extrinsic coordinate
frame. This trajectory could then be transformed into an intrinsic
coordinate frame (e.g., joint angles), and then into intrinsic dynamics
(e.g., muscle activity). Along this hierarchical scheme and coming
from a robotics framework, Uno, Kawato and Suzuki (1989) put forth
a computational model for voluntary movement as seen in Figure 5.3.
Starting from the environmentally-defined goal (e.g., target location,
object size), they proposed the following computations:
1) determination of desired traectorv - the goal of the movement,
such as picking up a coffee mug in order to drink from it, is
translated into an extrinsic kinematic coordinate frame for a path
3Jerk is the rate of change of acceleration.
4The workmace is a collection of points to which the hand of an arm can reach.