Chapter 2. Prehension

Chapter 5 - Movement Before Contact 131
profiles can be constructed to generate a muscle length, given a desired
speed and muscle length, using a difference vector. Excellent reviews
of pointing, aiming and the role of vision are provided in Meyer et al.
(1990) and Proteau and Elliott (1992).
5.3.3 Generating joint level trajectories
Jordan (1988) used a recurrent artificial neural network10 to
generate joint angles from one or more desired hand locations in a
body coordinate frame (Step 2 in Figure 5.3). A goal location was
specified in a two dimensional space, as seen in the inset to Figure 5.8
where two goal locations are shown. Jordan simulated a non-anthro-
pomorphic manipulator with six degrees of freedom: two translational
(in the x and y directions) and four revolute joints". As seen below,
any other configuration of joints could have been used, modelling an
anthropomorphic arm or even a finger or two.
The neural network architecture is seen in Figure 5.8. In the
bottom half of the figure, six input units, here called plan units,
encode a sequence of goal locations. This sequence of goal locations
is translated into a sequence of joint angles at the articulatory layer
(one unit for each joint controller or manipulator degree of freedom).
Two target units specify the Cartesian coordinates of the end point of
the arm. For a given arm configuration, as specified by the six articu-
latory units, the Model Network determines the end point of the arm.
Jordan added two units (here called state units) to create recurrent
connections from the target units back into the network, thus allowing
time-varying sequences of configurations to be computed (in the
Sequential Network).
Jordan's algorithm involves two phases of computations. During
the training phase, the system learns the forward kinematics using the
Model Network (top half of the figure). As a training set, random
static configurations are presented to the articulatory layer. The actual
end point of the manipulator is computed by summing up weighted
activation values of the articulatory units and then the weighted
activation values on the hidden layer. This computed endpoint is then
compared to the desired location of the end point. If there is a
difference, the generalized delta rule is used to change the weights
between the articulatory units, hidden layer, and target units in order to
l%or a more detailed discussion of artificial neural networks, see Appendix C.
A revolute joint is like the hinge joint of the elbow.