Part B | 21.1
484 Part B Autonomous Ocean Vehicles, Subsystems and Control
–0.8
–0.4
Goal
Goal
Start
Start
0
0.4
0.8
a)
1
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0.6
0.4
0.2
0
–0.2
–0.4
–0.6
–0.8
–1
–1
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Goal
Start
0
0.5
1
c)
1
0.8
0.6
0.4
0.2
0
–0.2
–0.4
–0.6
–0.8
–1
–0.8
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0
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b)
1
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0.6
0.4
0.2
0
–0.2
–0.4
–0.6
–0.8
–1
Fig. 21.1a–c Highway test cases.
(a) 2 ideal jets. Faster jet on left
(black arrows). Level-set optimal
path rides the faster jet. (b) Two ideal
jets in opposite directions. Level-set
optimal path first rides top jet to get
to an upstream position of opposing
lower jet. It then crosses the opposing
jet as quickly as possible to reach goal.
(c) This case includes one truncated
jet (at twice the vehicle velocity)
that is effectively an impenetrable
obstacle. The second jet is a transverse
jet, similar to the bottom jet in (b).
Here the level-set optimal path
moves around the truncated jet to
reach an upstream position of lower
jet. It then crosses the lower jet as
quickly as possible to reach the goal
(after [21.13])
2
6
10
14
4
8
12
16 18
a)
2.5
2
1.5
1
0.5
2
6
10
14
4
8
12
16 18
c)
2.5
2
1.5
1
0.5
2
6
10
14
4
8
12
16 18
b)
2.5
2
1.5
1
0.5
Fig. 21.2a–c Vorticity of the flow
past an island (gray oval) overlaid
with white streamlines. (a) All-to-all
broadcast with swarms while crossing
strong eddy field in optimal time – 11
swarms of 11 members each, avoid
island, utilize eddies/wakes, reform
swarms, and communicate. (b) All
back to ship optimal recovery of
large swarm formation of vehicles –
formation of 100 vehicles to return to
ship for pick up, avoid island, utilize
eddies/wakes to return in shortest
time. (c) Maintain swarm formation
with coordination based on local
gradients or dynamics – 3 swarms
of 24 members (line, triangle,
square), avoid island, shortest time
(after [21.10, 12, 14])
flows past an island. The circular island is an obstacle
to both the flow and to the vehicles. The flow is fast
enough to cause the shedding of vortices off the leeward
side of the island.
The first swarm example is an all-to-all broadcast to
swarm leaders, in which 11 swarms of 11 members each
optimally cross the strong eddy field in the wake of the
island while exchanging information with each other:
484 Part B Autonomous Ocean Vehicles, Subsystems and Control
–0.8
–0.4
Goal
Goal
Start
Start
0
0.4
0.8
a)
1
0.8
0.6
0.4
0.2
0
–0.2
–0.4
–0.6
–0.8
–1
–1
–0.5
Goal
Start
0
0.5
1
c)
1
0.8
0.6
0.4
0.2
0
–0.2
–0.4
–0.6
–0.8
–1
–0.8
–0.4
0
0.4
0.8
b)
1
0.8
0.6
0.4
0.2
0
–0.2
–0.4
–0.6
–0.8
–1
Fig. 21.1a–c Highway test cases.
(a) 2 ideal jets. Faster jet on left
(black arrows). Level-set optimal
path rides the faster jet. (b) Two ideal
jets in opposite directions. Level-set
optimal path first rides top jet to get
to an upstream position of opposing
lower jet. It then crosses the opposing
jet as quickly as possible to reach goal.
(c) This case includes one truncated
jet (at twice the vehicle velocity)
that is effectively an impenetrable
obstacle. The second jet is a transverse
jet, similar to the bottom jet in (b).
Here the level-set optimal path
moves around the truncated jet to
reach an upstream position of lower
jet. It then crosses the lower jet as
quickly as possible to reach the goal
(after [21.13])
2
6
10
14
4
8
12
16 18
a)
2.5
2
1.5
1
0.5
2
6
10
14
4
8
12
16 18
c)
2.5
2
1.5
1
0.5
2
6
10
14
4
8
12
16 18
b)
2.5
2
1.5
1
0.5
Fig. 21.2a–c Vorticity of the flow
past an island (gray oval) overlaid
with white streamlines. (a) All-to-all
broadcast with swarms while crossing
strong eddy field in optimal time – 11
swarms of 11 members each, avoid
island, utilize eddies/wakes, reform
swarms, and communicate. (b) All
back to ship optimal recovery of
large swarm formation of vehicles –
formation of 100 vehicles to return to
ship for pick up, avoid island, utilize
eddies/wakes to return in shortest
time. (c) Maintain swarm formation
with coordination based on local
gradients or dynamics – 3 swarms
of 24 members (line, triangle,
square), avoid island, shortest time
(after [21.10, 12, 14])
flows past an island. The circular island is an obstacle
to both the flow and to the vehicles. The flow is fast
enough to cause the shedding of vortices off the leeward
side of the island.
The first swarm example is an all-to-all broadcast to
swarm leaders, in which 11 swarms of 11 members each
optimally cross the strong eddy field in the wake of the
island while exchanging information with each other: