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On Maintaining Connectivity of a Colony of AutonomousExplorer Mobile Robots
Jonathan Mat́ıas Palma Olate1 and Cristian Duran-Faundez2
Departamento de Ingenieŕıa Eléctrica y ElectrónicaUniversidad del B́ıo-B́ıo, Concepción, Chile.
October 21, 2014
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Indice
1 Introduction to Problem of Maintaining Connectivity.Methods of solution
2 A multi-robot exploring applicationTetheringOptimal PointOrientation Method
3 AlgorithmEvaluation Method.Simulation.
4 ConclusionConclusion and CommentsAcknowledgment
JMP & CDF (UBB) October 21, 2014 2 / 37
Introduction to Problem of Maintaining Connectivity.
Robotics.
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Introduction to Problem of Maintaining Connectivity. Methods of solution
Methods to maintain a communication link of explorerrobot.
JMP & CDF (UBB) October 21, 2014 4 / 37
Introduction to Problem of Maintaining Connectivity. Methods of solution
Methods to maintain a communication link of explorerrobot.
A) Direct Communication.
JMP & CDF (UBB) October 21, 2014 5 / 37
Introduction to Problem of Maintaining Connectivity. Methods of solution
Methods to maintain a communication link of explorerrobot.
A) Direct Communication.
-Limited coverage Transmit.
-Unique link, not robust.
-High power transmissionover long distances.
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Introduction to Problem of Maintaining Connectivity. Methods of solution
Methods to maintain a communication link of explorerrobot.
B)Communication with StaticRouter.
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Introduction to Problem of Maintaining Connectivity. Methods of solution
Methodsto maintain a communication link of explorerrobot.
B)Communication with StaticRouter.
-Previous infrastructure.
-High cost ofimplementation andmaintenance.
-Robustness to the failure ofa unit.
-A subset of the total unitsthe network participateingactively in the linkcommunication.
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Introduction to Problem of Maintaining Connectivity. Methods of solution
Methods to maintain a communication link of explorerrobot (Proposal).
C)Communication usingMobile Router.
JMP & CDF (UBB) October 21, 2014 9 / 37
Introduction to Problem of Maintaining Connectivity. Methods of solution
Methods to maintain a communication link of explorerrobot (Proposal).
C)Communication usingMobile Router.
-Dynamic deployment.
-Minimize energy and cost.
-Design flexibility.
-High level of technicalcomplexity inimplementation. today.
JMP & CDF (UBB) October 21, 2014 10 / 37
Introduction to Problem of Maintaining Connectivity. Methods of solution
Methods to maintain a communication link of explorerrobot (Proposal).
C)Communication usingMobile Router.
-Dynamic deployment.
-Minimize energy and cost.
-Design flexibility.
-High level of technicalcomplexity inimplementation. today.
JMP & CDF (UBB) October 21, 2014 11 / 37
A multi-robot exploring application Tethering
Tethering
Tethering is the robot task offollowing a mobile agent (human,robot, etc.), with all the differentrequired capabilities to it, in orderto provide network connectivity(Zickler and Veloso 2010).
The reference we propose includesthe following kind of nodes:
-A set Base Station : Gateways(GW ).
-A set Explorer Robot : Targets(TG ).
-A set Router Robots :Gangway of data (GG ).
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A multi-robot exploring application Tethering
Network Topology Options
Link type to use?Model network of interestsimple-link. Figure NetworkTopology link green.
Figure: Network Topology.
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A multi-robot exploring application Tethering
This scenario entails a set of sub-problems, including:
-Definition of a link quality metric.
-Drive router robots to optimal positions to forward data packets.
-Minimizing the amount of robot routers maintaining globalperformance.
-Addressing robustness. Which involves methods to deal withcommunication errors and incidentals such as robot failures.
-Sharing tasks. To provide ways to make robots share some tasks,e.g., to make a router robot take other router’s job allowing thesecond one to go to the base station for recharge or maintenance.
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A multi-robot exploring application Optimal Point
Definition of Link Quality Metric.
Metric quality standard ofwireless communication.
- Packet Loss Rate PLR.
- link quality indicator LQI.
- Received Signal StrengthIndicator RSSI.
0
0.5
1
1.5
2
2.5
3
01
23
45
6
−100
−90
−80
−70
−60
−50
−40
−30
−20
Metros (m)Metros (m)
RS
SI (d
B)
GW
RS
SI (
dB)
Metros (M)
Figure: Example RSSI vs Distance
JMP & CDF (UBB) October 21, 2014 15 / 37
A multi-robot exploring application Optimal Point
Optimal point (PO) to ideal model.
PO Geometric: midpoint betweenthe line formed superior andinferior units.
Figure: Network: two GW and onGG
PO based on the RSSI: coordinatewhere the RSSI is equal and also thesum of them is maximum
0
0.5
1
1.5
2
0 0.5 1 1.5 2 2.5 3
−80
−70
−60
−50
−40
−30
−20
−10
Metros (m)
Metros (m)
RS
SI (d
B)
GWGW
RS
SI (
dB)
Metros (M)
Figure: RSSI to GW the network.
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A multi-robot exploring application Orientation Method
Orientation Method. Indicator MIn Dif .
Let us define VS and VI as thecommunication links between arouter robot and the neighboringnode closest to the explorer andthe base station. Obteniandiendolas relaciones.
Difa = |RSSIVS − RSSIVI |
Difd =RSSIVS−RSSIVI
Difa
Difa is relevant because POdifference of RSSI to PO it zero.Status indicators can be defined.Decrease Difa, which is calculated as:
MInDif =
{1 if Difa(k)− Difa(k − 1) < 00 otherwise
JMP & CDF (UBB) October 21, 2014 17 / 37
A multi-robot exploring application Orientation Method
Orientation Method. Indicators Max and Min link Vx.
The VX it VL farthest link and VC closer link.Decreases of RSSI values for a communication link VX , can be calculatedas:
MinVC =
{1 if RSSIVX (k)− RSSIVX (k − 1) < 00 otherwise
(1)
Increase of RSSI values for a communication link VX , which is defined as:
MaxVL =
{1 if RSSIVX (k)− RSSIVX (k − 1) > 00 otherwise
(2)
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A multi-robot exploring application Orientation Method
Actions. Discrete displacements.
The Figure presents the eightpossible actions [A1,A2, .....A8].It also implements a ninth actionA9 that is return.
Figure: Actions.
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A multi-robot exploring application Orientation Method
States based on the indicators MinDif , MinVC and MaxVL.
Are defined the state S to function. The Indicators are binariesi ∈ [1, 2.....23], having eight possible states
Si = ϕ(MinDif ,MinVC ,MaxVL)
State compact SS : Are defined the state compact SS1 and SS2..SS1 = ϕ(MinDif ,MinVC ,MaxVL); MinDif = MinVC = MaxVL = 1SS2 =otherwise
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Algorithm
Algorithm Proposal
JMP & CDF (UBB) October 21, 2014 21 / 37
Algorithm
Objectives.
-Design an algorithm that achieves converge to units in the vicinity of theoptimum point (PO), maximizing both of RSSI values link.-Design an algorithm that orientation method depends only on current andpast RSSI values, does not consider additional information of theenvironment.-Evaluate the performance of the algorithm in a simulation problemTethering.
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Algorithm
Algorithm, Heuristics based to Q-learning.
The action selection is performed by
using a Q-learning-based vector
Q(SS ×Ai ). We adopted as learningcoefficient α = 0.5, and we assign a
reward +1.
For the proposed model there are
four transitions (SSk−1 → SSk), i.e.transitions of passing from an state
SSk−1 in previous iteration k − 1 tothe current state SSk . These
transitions are: (SS1 → SS2),(SS2 → SS2), (SS1 → SS1), and(SS2 → SS2).
Require: RSSI capturesRequire: Calculation of goals and
categorizations for states SS(k) andSS(k − 1).
1: if SSk−1 = SS1 and SSk = SS2then
2: return A93: end if4: if SSk−1 = SS2 and SSk = SS2
then5: return random Ai ; i ∈ [1, 8]6: end if7: Ac = MaxAc InQ(Q,SS)8: Q(SS ,Ac)← (1− α)Q(SS ,Ac) +α[r(SS ,Ac) + λmaxA∈A
s′ Q(s
′,A
′)]
9: return Ac
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Algorithm Evaluation Method.
Evaluation performance the algorithm.
Evaluation of the proposed algorithm was by the mean and standarddeviation of a set of simulations to k = 500 iterations. The Network usedit the figure.
Model to Maintaining Connectivity the Robot Explore.
The graphs are the mean and standard deviation for 1000 simulations.
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Algorithm Evaluation Method.
Description of the Simulation, parameters an values.
parameters : valuesk : 500.Vpi :
[0, 0 0,−0.15 0,−0.3 0,−0.45 0, 0.1
].
∆Paso : 0.1(m).Model RSSI : log normal shadowing.M × P : 20.State : SS1 y SS2. .Actions : A1 A2 A3, A3, A5 A6 A7, A8 and A9.Reward : SS1 = 1 y SS2 = −1.Learning Rates : γ = 0.5 y α = 0.5.TG mov : zig zag
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Algorithm Simulation.
Simulation
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Algorithm Simulation.
Positions of units, center of mass for k = 5 iterations.
0 1 2 3 4 5 6 7 8−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
Meters (M)
Met
ers
(M)
GG1
GG2
GG3
GWTG
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Algorithm Simulation.
Positions of units, center of mass for k = 100 iterations.
0 1 2 3 4 5 6 7 8−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
Meters (M)
Met
ers
(M)
GG1
GG2
GG3
GWTG
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Algorithm Simulation.
Positions of units, center of mass for k = 200 iterations.
0 1 2 3 4 5 6 7 8−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
Meters (M)
Met
ers
(M)
GG1
GG2
GG3
GWTG
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Algorithm Simulation.
Positions of units, center of mass for k = 300 iterations.
0 1 2 3 4 5 6 7 8−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
Meters (M)
Met
ers
(M)
GG1
GG2
GG3
GWTG
JMP & CDF (UBB) October 21, 2014 30 / 37
Algorithm Simulation.
Positions of units, center of mass for k = 400 iterations.
0 1 2 3 4 5 6 7 8−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
Meters (M)
Met
ers
(M)
GG1
GG2
GG3
GWTG
JMP & CDF (UBB) October 21, 2014 31 / 37
Algorithm Simulation.
Positions of units, center of mass for k = 500 iterations.
0 1 2 3 4 5 6 7 8−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
Meters (M)
Met
ers
(M)
GG1
GG2
GG3
GWTG
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Algorithm Simulation.
Mean the Difa and Standard Deviation.
0 200 400 6000
20
40
60
Iteracion (k)
RS
SI (
db)
Dif
a GG
1
((a)) Mean Difa GG1.
0 200 400 6000
20
40
60
80
Iteracion (k)R
SS
I (db
)
Dif
a GG
2
((b)) Mean Difa GG2.
0 200 400 6000
20
40
60
80
Iteracion (k)
RS
SI (
db)
Dif
a GG
3
((c)) Mean Difa GG3.
0 200 400 6000
10
20
30
40
Iteracion (k)
RS
SI (
db)
DE Difa GG
1
((d)) S deviation Difa GG1.
0 200 400 6000
10
20
30
40
50
Iteracion (k)
RS
SI (
db)
DE Dif
a GG
2
((e)) S deviation Difa GG2.
0 200 400 6000
10
20
30
40
50
Iteracion (k)
RS
SI (
db)
DE Dif
a GG
3
((f)) S deviation Difa GG3.
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Algorithm Simulation.
Mean the error of RSSI and Standard Deviation .
0 100 200 300 400 500 6000
10
20
30
40
50
60
Iteration (k)
RS
SI (
db)
Error RSSI VIError RSSI VS
((g)) Error RSSI, GG1.
0 100 200 300 400 500 6000
10
20
30
40
50
60
70
Iteration (k)
RS
SI (
db)
Error RSSI VIError RSSI VS
((h)) Error RSSI, GG2.
0 100 200 300 400 500 6000
10
20
30
40
50
60
Iteration (k)
RS
SI (
db)
Error RSSI VIError RSSI VS
((i)) Error RSSI, GG3.
0 100 200 300 400 500 6000
5
10
15
20
25
30
Iteration (k)
RS
SI (
db)
DE Error RSSI VIDE Error RSSI VS
((j)) S deviation errorGG1.
0 100 200 300 400 500 6000
5
10
15
20
25
30
Iteration (k)
RS
SI (
db)
DE Error RSSI VIDE Error RSSI VS
((k)) S deviation errorGG2.
0 100 200 300 400 500 6000
5
10
15
20
25
30
Iteration (k)
RS
SI (
db)
DE Error RSSI VIDE Error RSSI VS
((l)) S deviation errorGG3.
JMP & CDF (UBB) October 21, 2014 34 / 37
Conclusion Conclusion and Comments
Conclusion and Comments.
This paper describes a kind of application for problem and sub-problemscommunication whit explorer robots and a base station using a colony ofautonomous router robots.
The model to single link the algorithm based to RSSI for maintainingcommunication it feasible.
This heuristic is used to select the next action to perform by a roboticrouter, combining simple decisions with a Q-learning-based decision process.Simulation results over 1000 repetitions of a simulation scheme shows goodperformance of the algorithm to make converge router robots tonear-optimal positions, considering the simulated models restrictions
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Conclusion Conclusion and Comments
Acknowledgment.
This work was supported by the Research Department of the University ofBio-Bio (Project DIUBB 121910 2/R).
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Conclusion Conclusion and Comments
End.
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Introduction to Problem of Maintaining Connectivity.Methods of solution
A multi-robot exploring applicationTetheringOptimal PointOrientation Method
AlgorithmEvaluation Method.Simulation.
ConclusionConclusion and CommentsAcknowledgment
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