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In-Depth Information
v_i
v_d
Nomoto Dynamics
Model
v_cur
v
\
Tensegrity-based
Centralised Formation
Control Model
D
l
b2
/l
b1
1x2
1x2
E
3xn
Fig. 5.
Block diagram of the formation control model
A suitable PD heading controller was developed which was tuned heuristically. This
controller regulates the desired heading (
(t)) of the vehicles which maintains the tra-
jectory of the vehicle. It must also have the function of performing the change of head-
ing without excessive oscillations and in the minimum possible time.
Figure 5 shows the complete formation control setup, where
P
3
×
n
=[(
P
1
x
,
P
1
y
,
P
1
z
)
,
(
P
2
x
,
P
2
y
,
P
2
z
)
,...,
(
P
nx
,
P
ny
,
P
nz
)] is the position vector of the controlled unmanned ve-
hicles in the formation. The task was to drive the virtual leader with desired heading
angle,
ψ
and velocity,
v
from one way-point (
P
v
−
i
) to the next (
P
v
−
d
). While the con-
trolled vehicles in the formation will synchronise their positions with the virtual leader
to perform the formation manoeuvring task on the plane.
ψ
5
Implementation and Simulations
The objective in this section is to perform the formation achieving; to regulate the inter-
UV spacing between the vehicles within the prescribed communications range; to per-
form the shape transformation and carrying out the manoeuvring task in a plane. All
the parameters in the tendon-driven system [LN12] which is shown in Figure 4 are
considered to be unity.
The key control parameters are; the length of bars (
l
b
1
and
l
b
2
) which are assumed
to be of the same length of 30m at equilibrium for the formation; and the formation's
orientation angles (
β
1
and
β
2
) are set at 45 degree according to the virtual leader's body
X
B
−
axis, respectively. The length of the bars and the formation's orienta-
tion angles were changed individually as well as together for simulation purposes to
demonstrate the effectiveness of the proposed strategy.
The length of the bar (
b
1
),
l
b
1
was changed twice at 120s and 520s for a period
of 200s. The formation changing performance when the length of bar
b
,isvariedis
simulated in Figure 6. From the controller responses shown in Figure 6c, it can be seen
that the vehicles (
UV
1
&
UV
3
) experienced negative (repelling) forces at 120s when the
bar's length was dilated from 30m to 55m. Note that the controller responded to the
bar's variations because of its dependent on particular string's length. The bar's length,
l
b
1
was returned to its original length of 30m at 320s with a positive attracting force.
The control forces for the subsequent bar's length contraction performance,
l
b
1
varied
from 30m to 10m at 520s can be expected as shown in Figure 6c.
Figure 7 shows simulation results for different shape transformation tasks. Figure 7a
depicted the formation in performing turning manoeuvre while its bar (
b
2
) was dilated
and
Y
B
−
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