Towards a communication free coordination formulti-robot exploration

Antoine Bautin, Olivier Simonin, François Charpillet

MaIA Team - INRIA / LORIA / Henri Poincaré University

20 mai 2011

Introduction Problem Statement State of the art Proposition Simulation Conclusion

Exploration of unknown environment

Multi-robot advantagesMinimize exploration time

explore distinct part of the environment simultaneouslyredundancy of information increases accuracyrobustness

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

1 Problem StatementSpecificationNotationsAssignation criteria

2 State of the art : Frontier allocation techniquesClosest FrontierGreedy allocation

3 Proposition : Min Position allocationDescriptionAlgorithmCost Matrix computation

4 Simulation Results

5 Conclusion

Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 3/25

Introduction Problem Statement State of the art Proposition Simulation Conclusion

Outline

1 Problem StatementSpecificationNotationsAssignation criteria

2 State of the art : Frontier allocation techniquesClosest FrontierGreedy allocation

3 Proposition : Min Position allocationDescriptionAlgorithmCost Matrix computation

4 Simulation Results

5 Conclusion

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Assumptions

Robot fleet AssumptionsHomogeneous robotsCommunication ability (maps, location)

Robot abilitieslocalization and mappingmap fusion

=⇒ remains to define a multi-robot exploration strategy

Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 4/25

Introduction Problem Statement State of the art Proposition Simulation Conclusion

FrontiersFinite environmentExploration→ increase explored part of the environment

Frontier definition [Yamauchi97]Boundary between unexplored and empty/accessible areas

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Problem Statement

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Notations

DefinitionR is the set of robots, R : {R1...Rn} with n = |R| thenumber of robotsF is the set of frontiers, F : {F1...Fm} with m = |F| thenumber of frontiersC a cost matrix with Cij the cost associated with assigningrobot Ri to frontier Fj

A an assignation matrix with αij ∈ [0,1] computed asfollows :

αij =

{1 if robot Ri is assigned to Fj0 otherwise

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Frontier allocation constraints

One frontier per robot

∀im∑

j=1

αij = 1

Balanced distribution of robots among frontiers

bn/mc ≤ ∀jn∑

i=1

αij ≤ dn/me

Number of robots per frontier is roughly equal with a maximumdifference of one.

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Optimization Criteria 1

Minimize of the sum of cost at each assignation

Minimize the exploration cost by minimizing the sum of cost(typically distance to reach the frontiers)

C(A) =n∑

i=1

m∑j=1

αij Cij

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Optimization Criteria 2

Minimum of the frontier exploration maximum costTime for all frontiers to be explored is determined by themaximum exploration time among all frontiers.

Cmax(A) = max∀i

m∑j=1

αij Cij (1)

Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 10/25

Introduction Problem Statement State of the art Proposition Simulation Conclusion

Outline

1 Problem StatementSpecificationNotationsAssignation criteria

2 State of the art : Frontier allocation techniquesClosest FrontierGreedy allocation

3 Proposition : Min Position allocationDescriptionAlgorithmCost Matrix computation

4 Simulation Results

5 Conclusion

Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 10/25

Introduction Problem Statement State of the art Proposition Simulation Conclusion

Closest Frontier

Algorithm Complexity : O(n)

Input: Ci cost vector of robot i to each frontierOutput: Ai robot i assignationbegin

αij = 1 such that j = min Cij ∀j ∈ Fjend

Implicit coordination

Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 11/25

Introduction Problem Statement State of the art Proposition Simulation Conclusion

Closest Frontier

Problem : robots assigned to the same frontiers

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Greedy allocation

Algorithm Complexity : O(n2m)

while Ri has no frontier assignated doFind i, j = argmin Cij ∀Ri ∈ R, ∀Fj ∈ Fαij = 1 , R = R \Ri , F = F \ FjIF F = ∅ THEN F = Finit

end

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Limits

Coordination-complexity

Closest Frontier allocation : O(n) but low performanceGreedy Frontier allocation : O(n2m) good cooperationFrontier-based methods are inherently simplier than utilitybased (estimated information gain)

market-based [Zlot et al. 02], greedy + extra communicationwithout communication, extra computation

Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 14/25

Introduction Problem Statement State of the art Proposition Simulation Conclusion

Outline

1 Problem StatementSpecificationNotationsAssignation criteria

2 State of the art : Frontier allocation techniquesClosest FrontierGreedy allocation

3 Proposition : Min Position allocationDescriptionAlgorithmCost Matrix computation

4 Simulation Results

5 Conclusion

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Our approach

Idea“Go towards the frontier having the less robots closer”

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Our approach : Min Position

Position of a robot towards a frontierNumber of robots closer to the frontier + 1

Robots are assigned to the frontier where its position isminimum

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Min Position

Algorithm Complexity O(nm)

Input: C cost matrixOutput: αij assignation of robot Ri

foreach Fj ∈ F doPij =

∑∀k∈Rk , k 6=i, Ckj<C ij

1

endαij = 1 such that j = argmin

∀F j∈FPij

In case of equality choose the minimum cost among min Pij

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

How to compute the Cost Matrix withoutcommunication

Standard approachA* algorithm : depth-first search

Wave-front propagation from every frontier

Wave-front propagation : breadth-first search [Barraquand &Latombe 91]→ shortest path from all accesible points in the environment→ cost for every robot

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Min Position

Closest Frontier allocation

Min Position Frontier allocation

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Outline

1 Problem StatementSpecificationNotationsAssignation criteria

2 State of the art : Frontier allocation techniquesClosest FrontierGreedy allocation

3 Proposition : Min Position allocationDescriptionAlgorithmCost Matrix computation

4 Simulation Results

5 Conclusion

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Test Environments

Maze environment

Player/Stage Project [Gerkey et al. 03] - Hospital sectionAntoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 20/25

Introduction Problem Statement State of the art Proposition Simulation Conclusion

Min Position in action

video

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Results on the maze environment

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Results on the hospital environment

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Towards a real implementation

MiniPekee - Cartomatic Team participating in CAROTTE Challenge

Occupancy grid and potential field gridAntoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 24/25

Introduction Problem Statement State of the art Proposition Simulation Conclusion

Outline

1 Problem StatementSpecificationNotationsAssignation criteria

2 State of the art : Frontier allocation techniquesClosest FrontierGreedy allocation

3 Proposition : Min Position allocationDescriptionAlgorithmCost Matrix computation

4 Simulation Results

5 Conclusion

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Introduction Problem Statement State of the art Proposition Simulation Conclusion

Conclusion

Novel frontier assignation algorithm :

based on the concept of position towards a frontier

outperforms Closest Frontier exploration performance

lower complexity than standard Greedy approaches

decentralized, asynchronous featuring implicitcoordination (without communication).

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