Chapter 2. Prehension

Chapter 5 - Movement Before Contact 135
5.3.4 Generating muscle level commands
Using Jordan’s Sequential Network, Massone and Bizzi (1989)
drove a planar three-joint manipulator at the muscle level instead of at
the joint level. The manipulator has four pairs of antagonist muscles:
shoulder flexor and extensor, double joint flexor and extensor, elbow
flexor and extensor, and the wrist flexor and extensor. As seen in the
bottom of Figure 5.10, the plan units are simplified sensory views of
the world in a shoulder-centered reference frame (centered in the same
workspace as the manipulator). Each plan unit has a receptive field
that covers nine pixels of the 15 x 15 pixel body coordinate frame.
The activation of each plan unit is the sum of the pixel values within its
receptive field. The advantage of this type of coding, called coarse
coding, is that the network can generalize better and learn faster
(Hinton, McClelland, & Rumelhart, 1986). The output units represent
‘motor neurons’, each unit controls one of the eight muscles. Thus
the computation being performed here is Step l’, computing a trajec-
tory in body coordinates from a goal location.
Using the generalized delta rule, Massone and Bizzi trained the
network to generate a trajectory of muscle activations from a goal lo-
cation. This inverse problem uses the mass-spring model so that the
arm trajectory is generated following the virtual trajectory of equilib-
rium configurations defined by the elastic properties of muscles.
However, it is still an ill-posed problem, and a cost function is needed
to determine a unique solution. Massone and Bizzi used a minimum
potential-energy cost function as their criterion, so that when the sys-
tem of muscles is perturbed by an external force, the manipulator set-
tles into a configuration of minimum potential energy, thus computing
muscle activations for a given x,y goal location of the endpoint. The
velocity is constrained by a bell-shaped velocity profile. The output is
a set of eight-dimensional vectors of muscle activations, each vector
corresponding to an equilibrium position.
In simulations of the learning phase, various endpoint trajectories,
six time steps in length covering the workspace, were presented to the
network. Using the minimum potential energy criteria for generating
arm configurations, the network produced straight-line movements
and bell-shaped velocity profiles, and was even able to generalize joint
reversals, as seen in Figure 5.11.
In analyzing the weights produced on the connections, Massone
and Bizzi observed reciprocal inhibition between agonist-antagonist
pairs and evidence of synergies between all hidden units. For exam-
ple, positive correlations were found between flexors and extensors