Towards a “Brain-Guided” Cognitive Architecture - Bioinspired Approaches for Human-Centric Technologies - page 206

Fig. 7.1 Purely reactive system ( left panel ) vs. cognitive system ( right panel )

that the two dynamical regimes are compatible and integrated in the same structure,
allowing subjects to shift effortlessly from mental simulations of actions to real
actions and back, in agreement with the evidence coming from brain imaging.
The Passive Motion Paradigm is a force field-based mechanism of synergy
formation that allows to coordinate the motion of a redundant set of articulations
while carrying out a task, like reaching or tracking an object. Originally, it was
formulated in order to demonstrate that, when carrying out inverse kinematics with
a highly redundant system, it is not necessary to introduce an explicit optimization
process. The idea can be expressed, in qualitative terms, by means of the animated
puppet metaphor (Fig. 7.2 left panel) or the “flying hand metaphor” (Fig. 7.2 right
panel), suggested by Marc Jeannerod. The key point, in both cases, is that in
reaching movements, it is not the proximal part of the body which is pushing the
end effector to the target but the other way around: the end effector is pulled
towards the target by the force field and in turn pulls the rest of the body.
In mathematical terms, let us represent the intention to reach a target ! T by
means of a force field ! H , aimed at the target and attached to the hand ! H . 2 ! H is
mapped into an equivalent torque field ! A , acting on all the joints of the arm (vector
! ), by means of the transpose Jacobian matrix J B 3 : it is worth mentioning that the

2 In the simplest case of a linear model, this field is elastic and is characterized by a stiffness matrix
K : ! H ¼ ! H .

3 The Jacobian matrix of the arm is defined as follows: J B ¼ ∂ ! H
∂

K ! T

! . It maps motion and effort in

and ! A ¼ J B T ! H .

opposite directions: d ! H J B d !

dt

dt ¼