Towards a “Brain-Guided” Cognitive Architecture - Bioinspired Approaches for Human-Centric Technologies - page 207

Fig. 7.2 Animated puppet metaphor ( left panel ). Flying hand metaphor ( right panel )

torque field has a much higher dimensionality than the force field as a consequence
of the redundancy of the arm. The torque field induces in the body schema a
distribution of incremental joint rotations, modulated by the admittance matrix A .
In turn, the joint rotation pattern is mapped into the corresponding hand motion
pattern, thus updating the attractor force field and closing the computational loop:

8
<

8
< d ! H

dt ¼

J B d !
dt

d !
dt ¼

A ! A

J B

J B T

ð 7 1 Þ

! ! :

: : Arm joint space

! H ¼ K ! T ! H

! A ¼ J B T ! H

Γ ðÞ t

Hand space

The mathematical description of the PMP summarized by ( 7.1 ) can be expressed
graphically by means of the bock diagram of Fig. 7.3 . The transient induced by the
activation of the force field is terminated when the target is reached, if it is
reachable. If the target is not reachable, for example, if it is outside the workspace,
the final posture is the one that minimizes the final positioning error. It should be
noted that all the computations in the loop are “well posed” and thus this compu-
tational model is robust and cannot fail. In any case, if the force field remains
stationary during the movement, the acquisition of the new equilibrium state occurs
in an asymptotic manner, and thus reaching time is not controlled. Such time can be
controlled by means of a technique proposed by the group of Michael Zak ( 1988 ),
called terminal attractor dynamics, which consists of a suitable nonlinear modula-
tion of the force field, which tends to diverge to infinity when time approaches the
intended deadline. The ( t ) function or nonlinear time-base generator implements

such modulation. The function can be considered as a kind of “neural pacemaker”
(Barhen et al. 1989 ), and a biologically plausible representation can be identified in
the cortico-basal ganglia-thalamocortical loop and the well-established role of the
basal ganglia in the initiation and speed control of voluntary movements. In other
words, synergy formation requires a symphonic director, not a mere metronome,
namely, a coordination entity that, in addition to giving the tempo, recruits the

Γ