Search Control Problem
2008-12-15
FL seminar
Search Problem
Cooperative Optimal Search Control
To locate a target to be found,
deploying agents with the available resources.
„ search and rescue operations
„ detecting lost objects
with Distributed Control
Objective
FL08-21-2
„ formulate the Optimal Search Control Problem
‰ maximize the probability of finding the target
‰ reduce the control energy consumption
Mamoru Saito
„ analyze the agent’s behavior
Outline
Problem Setting
continuous-time linear system
agent：continuous-
obs. point
position：
„ review (single agent)
observation time (obs. time) :
waypoint
the obs. points set
„ Distributed Cooperative Optimal Search Control
the obs. points row
sensing accuracy
Search Area :
good bad
„ おまけ
1
0.8
0.6
0.4
0.2
0
2
Main Result
A target appears randomly and stays for
[s]
The target appears at time
1
0
−1
−2 −2
−1
0
1
2
search level ( small → good )
Cooperative Search Control
„ formulate Optimal Search Control Problem
‰ semi-optimization problem
approximate solution
„ the analysis of the agent’s behavior
Cooperative Optimal Search Control
‰ the expectation value of how many times the targets appears
without being found
‰ a necessary and sufficient condition for the agent’s state and
input to converge respectively to a periodic trajectory
position
obs. point
1
random walk based
proposed method
4
: the number of the agent
3
search level
z2−displacement[m]
0.8
2
„ Centralized Control
„ Decentralized Control
„ Distributed Control
0.6
The superscript
0.465
0.4
means the state of the -th agent.
1
0.2
0
0
1
initial position
2
3
z −displacement[m]
1
4
5
0
0
5
10
15
j
1
Problem Setting
Observation Point Information
the observation point information:
Each
Eachagent
agentisisassumed
assumedto
toreceive
receive
the
theobservation
observationpoint
pointinformation
informationfrom
fromits
itsneighbors.
neighbors.
the neighborhood of the -th agent at time
⇔
The -th agent receives the observation point information
from the -th agent at time .
the own and the other agents’ information at time
(only use visual information)
the observation point information set from
Objective
Each
Eachagent
agentisisassumed
assumedto
toreceive
receive
the
theobservation
observationpoint
pointinformation
informationfrom
fromits
itsneighbors.
neighbors.
Cooperative Semi-optimal Search Control Algorithm
I observed.
I will observe.
(communicate each other)
to
Semi-optimal Search
the gradient method
can’t be used
minimize
as
to minimize
as
the gradient method
while reducing the
control energy consumption
semi-optimal solution!
minimize
Semi-optimal Search Algorithm
as
Theorem
satisfying
exists.
renew the observation points
satisfying
exists.
The proposed algorithm
minimizes
as
(proof : omitted)
2
Semi-optimal Search Control Algorithm
Remark
Remark 1
The proposed algorithm is robust (adaptive)
for changing the number of agents (due to, e.g., failures).
renew the observation points
Remark 2
minimize
s.t.
The initial observation points is important
renew the observation point row
because the periodic trajectory largely depends on them.
them
RHC
Simulation
Simulation (g=1, D=8)
ex1.
system
25 steps
z2−displacement[m]
4
3
2
1
0
0
1
Simulation (g=1, D=8)
2
3
z −displacement[m]
4
5
4
5
1
proposed method
Simulation (g=1, D=1.5)
ex2.
8000
random walk based
proposed method
0.6
0.4
0.2
random walk based
proposed method
7000
control energy consumption
search level
0.8
25 steps
6000
5000
4
4000
z2−displacement[m]
1
3000
2000
1000
0
0
5
10
15
j
20
0
0
5
10
15
20
3
2
1
25
step k
0
search level
control energy consumption
0
proposed method
1
2
3
z1−displacement[m]
3
Simulation (g=1, D=1.5)
Simulation (g=4, D=0)
ex3.
6000
control energy consumption
random walk based
proposed method
search level
0.8
0.6
0.4
0.2
0
0
5
10
15
random walk based
proposed method
5000
100 steps
4000
4
3000
z2−displacement[m]
1
2000
1000
0
0
20
5
10
j
15
20
2
1
25
step k
search level
3
0
control energy consumption
0
1
proposed method
Simulation (g=4, D=0)
2
3
z1−displacement[m]
4
5
4
5
4
5
Simulation (g=6, D=8)
ex4.
4
3.5
control energy consumption
random walk based
proposed method
search level
0.6
0.4
0.2
random walk based
proposed method
3
100 steps
2.5
4
2
z2−displacement[m]
1
0.8
x 10
1.5
1
0.5
0
0
20
40
60
0
0
80
20
40
j
60
80
2
1
100
step k
search level
3
0
control energy consumption
0
1
Simulation (g=6, D=8)
2
3
z −displacement[m]
1
proposed method
Simulation (g=6, D=2)
ex5.
4
3
control energy consumption
random walk based
proposed method
search level
0.8
0.6
0.4
0.2
0
0
20
40
60
j
search level
80
x 10
random walk based
proposed method
2.5
100 steps
2
4
1.5
z2−displacement[m]
1
1
0.5
0
0
20
40
60
80
3
2
1
100
step k
0
control energy consumption
0
proposed method
1
2
3
z1−displacement[m]
4
Simulation (g=6, D=2)
Simulation (g=6, D=2)
ex6.
4
3.5
control energy consumption
random walk based
proposed method
search level
0.8
0.6
0.4
0.2
x 10
random walk based
proposed method
3
100 steps
2.5
4
2
z2−displacement[m]
1
1.5
1
0.5
0
0
20
40
60
0
0
80
20
40
j
60
80
2
1
100
step k
search level
3
0
control energy consumption
0
proposed method
Simulation (g=6, D=2)
3.5
control energy consumption
random walk based
proposed method
search level
0.8
0.6
0.4
0.2
4
5
Conclusion
x 10
random walk based
proposed method
3
2
3
z1−displacement[m]
Conclusion
4
1
1
Distributed Cooperative Optimal Search Control Algorithm
was proposed.
2.5
2
1.5
1
0.5
0
0
20
40
60
j
search level
80
0
0
20
40
60
80
100
step k
control energy consumption
5