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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
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 2/25
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
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 3/25
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
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 5/25
Introduction Problem Statement State of the art Proposition Simulation Conclusion
Problem Statement
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 6/25
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
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 7/25
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.
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 8/25
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
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 9/25
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
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 12/25
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
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 13/25
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
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 14/25
Introduction Problem Statement State of the art Proposition Simulation Conclusion
Our approach
Idea“Go towards the frontier having the less robots closer”
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 15/25
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
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 16/25
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
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 17/25
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
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 18/25
Introduction Problem Statement State of the art Proposition Simulation Conclusion
Min Position
Closest Frontier allocation
Min Position Frontier allocation
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 19/25
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 19/25
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
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 21/25
Introduction Problem Statement State of the art Proposition Simulation Conclusion
Results on the maze environment
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 22/25
Introduction Problem Statement State of the art Proposition Simulation Conclusion
Results on the hospital environment
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 23/25
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
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 24/25
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).
Antoine Bautin, Olivier Simonin, François Charpillet Coordination for multi-robot exploration 25/25
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