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Planning Problems Complexity Results Conclusion
Dynamic Connected Cooperative Coverage Problem
Complexity
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
April 4, 2019
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Information Gathering Missions
Search and Rescue
Building fire XAvalanches XForest fire
Terrain analysis
Landmine detection XSmart farmHazardous locationSoil pollution
Security
PatrolEvacuation XProject RETINA
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Project RETINA
Planning
Sumo/LogicA
FBK
Drones/Sensors
Rainbow
JCP
Simpulse
Experts
SDIS 35
DGA
Data Analysis
Bright Cape
Tellus Env
UCIT
RYAX
FBK
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Motivation
Goal
Minimize expert allocation
Time critical decisionmaking
Narrow the search
Observe the evolution of afire
Approach
Unmanned AutonomousVehicles (UAVs)
Interconnected with thesupervision station
Coverage
Reachability
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Outline
1 Planning Problems
2 Complexity Results
3 Conclusion
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Preliminaries
Topological graph
G = 〈V ,→, 〉V a finite set of nodes containing B;
→⊆ V × V movement edges;
⊆ V × V undirected communication edges.
Configuration
c = 〈c1, . . . , cn〉 element of V n such that〈Va, ∩ Va × Va〉 is connected with Va = {B, c1, . . . , cn}
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Topological Graph Example
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Preliminaries
Execution
e = 〈c1, . . . , c`〉 sequence of element of V n such that c i → c i+1
Covering Execution
e = 〈c1, . . . , c`〉 such that c1 = c` = 〈B, . . . ,B〉for all v ∈ V , there exists i ∈ {1, `} with v ∈ c i
Properties:
Anonymity (〈1, 5, 6〉 ≡ 〈6, 5, 1〉)Meet-collision allowed (〈2, 4, 2〉)Head-on-collision allowed (〈〈3, 4, 1〉, 〈4, 3, 5〉〉)
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Mission Example
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Mission Example
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Mission Example
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Mission Example
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Mission Example
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Mission Example
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Mission Example
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Mission Example
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Mission Example
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Mission Example
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Mission Example
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Problems
Reachability
In: a topological graph G and a
configuration c;
Out: does there exists an execution to
reach c in G?
Coverage
In: a topological graph G and n ∈ N;
Out: does there exists a covering
execution with n agents in G?
bReachability
In: a topological graph G , a
configuration c and ` ∈ N in unary;
Out: does there exists an execution of
at most ` steps to reach c in G?
bCoverage
In: a topological graph G , n ∈ N and
` ∈ N in unary;
Out: does there exists a covering
execution of at most ` steps with n
agents in G?
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Outline
1 Planning Problems
2 Complexity Results
3 Conclusion
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Overview
Reachability Coverage bReachability bCoverageDirected PSPACE-c PSPACE-c
NP-c [HS12]
NP-c
Neighbor
Communicable PSPACE-c [TBR+18]PSPACE-c
Undirected ?Sight
Moveablein LOGSPACE in LOGSPACE
NP-c
Complete
Communicationin LOGSPACE
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Directed Topological Graphs
→ and arbitrary
Theorem
Reachabilitydir and Coveragedir are
PSPACE-complete.
Theorem
bReachabilitydir and bCoveragedir are
NP-complete.
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Neighbor-Communicable Topological Graphs
→⊆
Theorem
Reachabilitync and Coveragenc are
PSPACE-complete.
Theorem
bReachabilitync and bCoveragenc are
NP-complete.
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Sight-Moveable Topological Graphs
if v v ′ then there existsρ = 〈ρ0, . . . , ρm〉 such that ρ0 = v ,ρm = v ′, v ρi and ρi → ρi+1 for alli ∈ {0,m − 1}
Theorem
Reachability sm and Coveragesm are in
LOGSPACE.
Theorem
bReachability sm and bCoveragesm are
NP-complete.
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Complete Communication Topological Graphs
= V × V
Theorem
Reachability cc and Coveragecc are in
LOGSPACE.
Theorem
bReachability cc is in LOGSPACE.
Theorem
bCoveragecc is NP-complete
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Outline
1 Planning Problems
2 Complexity Results
3 Conclusion
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
Future Work
Known needs
Time critical plan generation
Short plans
Minimize re-planning
Avoid loss of drones from disconnection
Handle environment modification
Allow manual override
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem
Planning Problems Complexity Results Conclusion
References I
G. A. Hollinger and S. Singh, Multirobot coordination withperiodic connectivity: Theory and experiments, IEEETransactions on Robotics 28 (2012), no. 4, 967–973.
Davide Tateo, Jacopo Banfi, Alessandro Riva, FrancescoAmigoni, and Andrea Bonarini, Multiagent connected pathplanning: Pspace-completeness and how to deal with it,Proceedings of the Thirty-Second AAAI Conference onArtificial Intelligence, New Orleans, Louisiana, USA, February2-7, 2018, 2018.
T. Charrier, A. Queffelec, O. Sankur, F. Schwarzentruber
Dynamic Connected Cooperative Coverage Problem