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