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Moti on Trajectory ( b ar, b 1 perfo r m dilation)
Motion Trajectory (bar, b 1 perform contraction)
t=550
t=900
Dil a tion star t at 120 s and con t raction st art at 5 2 0s for a p eriod o f 200s, r e spectiv el y
320
.
0.01
t=500
180
t=850
t=450
300
0.005
160
t=400
t=800
0
t=350
140
280
t=300
t=750
-0.005
120
260
t=250
-0.01
100
t=700
100
200
300
400
500
600
700
800
900
1000
t=200
240
80
UV 1 Trajectory
UV3 Trajectory
Virtual leader
UV 1
UV2
UV3
UV 4
t=650
0.01
60
t=150
UV 1 trajectory
UV 3 trajectory
Virtual leader
UV1
UV 2
UV 3
UV4
220
t=600
0.005
40
t=100
t=550
200
0
20
t=50
t=500
t=0
180
.
-0.005
0
.
.
0
50
100
150
200
250
140
160
180
200
220
240
260
280
300
320
-0.01
100
200
300
400
500
600
700
800
900
1000
x position (m)
x position (m)
Time (s)
(a) b 1 Dilation Performance
(b) b 1 Contraction Performance
(c) Control Forces Performance
Fig. 6. Varying of bar's length, l b 1 for shape changing performance
Motion Trajectory (bar, b 2 perform dilation)
M otion T r aject or y (For m ation R otation )
Motion Trajectory (b 1 perform contraction while b 2 perform dilation)
UV 1 Trajectory
UV2 Trajectory
UV3 Trajectory
UV 4 Trajectory
Virtual Leader
UV1
UV 2
UV 3
UV 4
t=1600
t=1550
560
820
960
t=2350
UV 1 Trajectory
UV2 Trajectory
UV 3 Trajectory
UV 4 Trajectory
Virtual Leader
UV1
UV 2
UV 3
UV4
t=1500
.
540
t=2300
940
800
t=2700
920
t=2650
520
t=2250
t=1450
780
.
900
t=2600
500
t=2200
.
760
.
t=1400
t=2150
880
480
t=2550
740
UV2 Trajectory
UV 4 Trajectory
Virtual leader
UV1
UV 2
UV 3
UV4
.
t=1350
t=2100
860
460
t=2500
720
t=1300
t=2050
840
t=2450
440
700
t=2000
t=1250
t=2400
820
420
t=2350
t=1200
t=1950
.
380
400
420
440
460
480
500
520
540
560
580
180
200
220
240
260
280
300
320
340
360
40
60
80
100
120
140
160
180
200
220
240
x position (m)
x position (m)
x position (m)
(a) Formation turning
(b) Formation rotating
(c) Formation transformation
Fig. 7. Different Shape Transformation
from 30m to 55m for a period of 200s. The formation rotation is also performed in
this work which is shown in Figure 7b. This rotation of the formation is accomplished
by increasing the value of
β 2 angles from 45 to 65 degree respectively at time
2000s for a period of 200s. This may useful for obstacle avoidance purposes. Finally,
an overall shape transformation has been performed in Figure 7c by contracting b 1 and
dilating the b 2 simultaneously at 2370s. Note that there is no crossover or any collisions
between any of the vehicles in the formation.
β 1 and
6Con lu ion
In this paper, a new formation control methodology using the concept of cross-tensegrity
structure has been proposed. In this dynamic tensegrity-based formation control, the po-
sition of the controlled vehicles in the formation changes with respect to bars' length.
This virtual change for shape transformation is not possible in the application of tenseg-
rity concept in architecture and mechanical structures. The presented approach allows
more flexibility over a wide range of different shape switching using the predictable
tendon response under the prescribed communication's range. The proposed method is
also scalable to any number of pair of autonomous vehicles in the formation and is only
limited by the communication bandwidth. Extension to 3D motion is possible using
 
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