Chapter 2. Prehension

138 THE PHASES OF PREHENSION
method for computing a hand and muscle-level trajectory from a goal
(Step 1’). They use a muscle model and a cost function of minimum
potential energy to compute the muscle activation given an endpoint
goal location. Simplifications include bypassing a coordinate trans-
formation by using the same coordinate frame for sensing and the spa-
tial coordinates of the hand. In addition, eight muscles are controlled
by only eight motor neurons in their model, while in reality there are
thousands of motor neurons for these muscles. They do not explicitly
compute the actual endpoint, because it is implicit through the muscle
model; however explicit endpoint positioning is crucial at a planning
level. Finally, they merge velocity and trajectory into one computa-
tion.
A B
Figure 5.12. Double target experiment. (a) The first target was
turned on for two time steps, and then it was turned off. (b) The
first target was turned on for three time steps, and then turned off
(from Massone and Bizzi, 1989; reprinted by permission).
5.3.5 Generating joint torques
Kawato, Furukawa, and Suzuki (1987) offered a hierarchical
model of how this motor learning and control might be accomplished,
as seen in Figure 5.13. As a model for generating motor torques from
a desired trajectory expressed in body-centered coordinates, it
computes Step 3 of Figure 5.3. The desired motor pattern, q, is sent
from elsewhere in the brain to the motor cortex, where the motor
command, u, is computed. In this case, the motor cortex would be
computing the inverse dynamics, that is, computing the torque from