Information Technology Reference
In-Depth Information
Fig. 4.6
Biological mechanism of activation of coupled neural oscillators (Central Patterns
Generators)
the other hand, deficiencies or enhanced levels of dopaminergic inputs result in
movements distortion and malfunction of the locomotion system [
70
,
212
].
Coupled neuron models which have been used as CPGs are Hodkin-Huxley
neurons and FitzHugh-Nagumo neurons (Fig.
4.7
). CPG methods have been used
to control various kinds of robots, such as crawling robots and legged robots and
various modes of locomotion such as basic gait control, gait transitions control,
dynamic adaptive locomotion control, etc. [
85
].
4.8
Differential Flatness Theory
4.8.1
Definition of Differentially Flat Systems
The main principles of differential flatness theory are as follows [
58
,
177
,
200
]:
A finite dimensional system is considered. This can be written in the general form
of an ODE, i.e. S
i
.
w
;
w
;
w
; ;
w
.i/
/; i D 1;2; ;q.Theterm
w
denotes the
system variables (these variables are, for instance, the elements of the system's
state vector and the control input) while
w
.i/
, i D 1;2; ;q are the associated
derivatives. Such a system is said to be differentially flat if there is a collection
of m functions y D .y
1
; ;y
m
/ of the system variables and of their time-
