AFOSR MURI
ONR YIA
Coordinated UAV Operations:
Perspectives and New Results
Vishwesh Kulkarni
Joint Work with
Jan De Mot, Sommer Gentry, Tom Schouwenaars, Vladislav Gavrilets, and Prof. Eric Feron
at the Laboratory for Information and Decision Systems, MIT.
AFOSR MURI. Salem, MA. June 4, 2002.
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Overview
• Efficient multi-agent operations require robust, optimal coordination policies.
• UAV specifications constrain deployable coordination policies.
• How may we improve our understanding of these constraints?
• How may we use it to synthesize more efficient coordination policies?
Obstacles
Danger Zones
Efficiency =
1
cost per UAV
??
Number of UAVs
• Coordinated Path Planning
• Surveillance
We view spatial distribution of the UAVs as a key factor and present original
results concerning the UAV separations and the UAV placements.
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Coordinated Path Planning (CPP)
CPP Problem Setting
• UAVs need to go from a point s to a point t.
• Environment is dynamic and uncertain.
• UAVs cooperate by sharing the acquired local information.
• UAVs have limited resources.
GOAL: Optimize the traversal efficiency.
Questions
• What is the spatial distribution under an optimal policy?
 We have characterized the separation bounds.
• How many UAVs are needed?
 We do not know the full answer yet!
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Related Past Works
Multi-Agent Exploration of Unknown Environments
Probabilistic map building of Burgard et al [2002] uses deterministic
value iteration to determine the next optimal observation point.
The market architecture of Zlot et al [2002] auctions off the next optimal
observation points obtained by solving a TSP.
• The end goal is spanning rather than CPP.
CPP as Multi-Agent MDPs
• Boutilier et al [2000]. We consider partially observable MDPs.
• Greedy policy pursuit-evasion games of Hespanha et al [2002].
agent
known region
unknown region
new region
We present new results in a coordinated target acquisition setting using DP.
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Our CPP Problem
Terrain is mapped into regions having payoffs.
Terrain traversal becomes graph traversal.
• UAVs share local information.
• Partially known, uncertain environment
• On-board sensors reduce uncertainty in a
direction dependent manner.
• Lookahead link costs are deterministic, others i.i.d.
...
...
s
G2
...
S1
t
...
Si
SN
Goal: Find a path for each agent that minimizes the expected aggregate cost.
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The CPP Separation Results
Cluster Separation Lemma
1.5
Using optimal paths for two agents in G7 , configurations C0 ,
C1 , and C2 do not evolve into configurations Cl with l > 2.
The UAV separation is bounded in
2.5
2
0.5
2
3
G7 .
2.5
1
Conjecture 1: The UAV separation is bounded in Gm .
Extra nodes should not affect the separation adversely.
2
1.5
1.5
2.5
1
3
0.5
1
2
1
3
2.5
3
1.5
1
1.5
2.5 2.5
1
G7, infinite horizon, discount factor a = 0.8
Conjecture 2: The UAV separation is bounded in Gm
in a pair-wise sense.
Conjecture 1 should hold pair-wise in the n-agent setting.
 Communication power, hierarchy tier sizes
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Surveillance as CPP
Surveillance Problem Setting
• Terrain as regions with dynamic, uncertain payoffs.
• UAVs face dynamic, uncertain threats.
• Limited communication capacity and efficiency.
• Efficiency decreases with distance.
• UAVs cooperate by repositioning and handoffs.
Goal: Maximize the net minimal spare UAV capacity.
efficiency
Questions
• What is the spatial distribution under an optimal policy?
 Characterized by the separation results.
• How many UAVs are needed?
 We do not know the full answer yet!
AFOSR MURI. Salem, MA. June 4, 2002.
1
log(1  SNR)
2
SNR
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Related Efficiency Results
Commonalities with Cellular Network Concepts
• i.i.d. uniformly distributed payoffs
•
r a path loss decrease in efficiency
• How many
Network Capacity
• O (1/ n ) capacity
…
Gupta-Kumar [2000]
capacity
…
Grossglauser-Tse [2000]
• Dumb Antennas
…
Viswanath et al [2002]
• Space-Time Codes
…
Tarokh et al [2000]
• O(1)
• Techniques to exploit the UAV mobility
Cellular network understanding has promise in the UAV setting.
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Future Directions
•
Extensions for larger and heterogeneous clusters
 Dynamic program modifications
•
More incremental on-board information gathering
 Gradual link cost change from i.i.d. to deterministic
 Sets of possible link cost distributions
•
Separation and efficiency properties for large scale systems
 Curse of dimensionality
probability
1
 Neuro-Dynamic programming for approximate solutions
link cost
•
To add or not to add (a UAV) …
efficiency per UAV
 Brute force iterative DP-based solution
 Binary search for an optimum number
??
number of UAVs
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Questions ??
http://www.mit.edu/people/vishwesh/
[email protected]
Joint work being done at MIT with Prof. Eric Feron’s group, supported
by his AFOSR MURI and ONR Young Investigator Award grants.
Thank You !
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