area coverage optimization using heterogeneous...
TRANSCRIPT
Area Coverage Optimization using HeterogeneousRobots
Dakota Adra and Eric JonesAdvisor: Dr. Suruz Miah
D. Adra & E. Jones (Bradley University) ACO Presentation 1 / 38
Overview1 Introduction2 Background3 Functional Requirements
InputsArea Coverage SystemOutputs
4 MAFOSS5 Networking
Network ConfigurationsROS Networking
6 Preliminary WorkModeling Density and AreaDeriving Coverage MetricSimulationsImplementation
7 Parts List8 Future Work9 Deliverables
Schedule for Completion10 References
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Introduction
Statement of the Problem
Applications
Introduction of MAFOSS
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Background
Kilinc - Cooperative Networking
Lee - Dynamic Density Area Optimization
Miah - Heterogeneous Area Coverage
Varposhti - Area Coverage via Distributed Learning Algorithm
Yu - Area Coverage via Genetic Learning Algorithms
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Functional Requirements
Heterogenous area coverage systemArea
Density sources
Agents' initial
positions
Agents' final
positionsMAFOSS Application Robot
Coverage
performance
metric
Figure: Functional Diagram of Area Coverage System
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Functional RequirementsInputs
Heterogenous area coverage systemArea
Density sources
Agents' initial
positions
Agents' final
positionsMAFOSS Application Robot
Coverage
performance
metric
Figure: Functional Diagram of Area Coverage System
Area
Density source
Agents’ initial positions
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Functional RequirementsArea Coverage System
Heterogenous area coverage systemArea
Density sources
Agents' initial
positions
Agents' final
positionsMAFOSS Application Robot
Coverage
performance
metric
Figure: Functional Diagram of Area Coverage System
MAFOSS
Application
Agent
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Functional RequirementsOutputs
Heterogenous area coverage systemArea
Density sources
Agents' initial
positions
Agents' final
positionsMAFOSS Application Robot
Coverage
performance
metric
Figure: Functional Diagram of Area Coverage System
Coverage performance metric
Agents’ final positions
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MAFOSSDiagram
USER INTERFACE
CONTROL API
Linux headers Linux headers
ROBOTIC OPERATING SYSTEM (ROS)
Console
ROS agentsROS
networking
APPLICATIONS
Control code
librobotcontrollibrary
libkhepraAPI
ROS AriaAPI
Matlab code
Figure: MAFOSS System Architecture
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MAFOSSLayers
User Interface
Applications
Robotic Operating System
Control API
USER INTERFACE
CONTROL API
Linux headers Linux headers
ROBOTIC OPERATING SYSTEM (ROS)
Console
ROS agentsROS
networking
APPLICATIONS
Control code
librobotcontrollibrary
libkhepraAPI
ROS AriaAPI
Matlab code
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NetworkingConfigurations
Internet
Router Server
Modified eduMIP Khepera IV Pioneer 3-DX
(a) Heterogeneous Configuration
Internet
Router Server
Modified eduMIP Modified eduMIP Modified eduMIP
(b) Homogeneous Configuration
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NetworkingROS Networking Diagram
publishD
esired
subscribeDesired
subscribeCurrent
publishC
urrent
MESSAGES TO
CONSOLE
ANDLOG FIL
ES
MASTER
Example:
nodenameXML=RPC = host : portTCP data = host : port
robot1 robot2
robot3
robot1XML=RPC = (robot1 id) : 1234TCP data = (robot1 id) : 2345
DATADATADATA
Figure: ROS Networking
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NetworkingROS Networking
Nodes
Topics
Master
Output Data
Example
publishD
esired
subscribeDesired
subscribeCurrent
publishC
urrent
MESSAGES TO
CONSOLE
ANDLOG FIL
ES
MASTER
Example:
nodenameXML=RPC = host : portTCP data = host : port
robot1 robot2
robot3
robot1XML=RPC = (robot1 id) : 1234TCP data = (robot1 id) : 2345
DATADATADATA
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Preliminary Work
Modeling Density and Area
Derivation of Coverage Metric
VREP and Matlab Simulations
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Preliminary WorkModeling Density and Area
First we define q to be an x-y coordinate in a square area and q to be thedesired density point in the same square area.The phi function is the measure of the density at any given point q as seenbelow.
φ(q) = exp(−0.5 ∗ ‖(q− q)2‖
σ2) (1)
Where σ in equation in (1) represents the spread of density throughout anarea.
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Preliminary WorkModeling Density and Area Cont.
Further simplification of equation (1) yields:
φ(q) = exp(−0.5 ∗ ‖((x − x)2 + (y − y)2)‖
σ2) (2)
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Preliminary WorkModeling Density and Area Cont.
The figure below shows an example of a square area that could potentiallybe mapped in such a way.
V1 V2
V3
Agent 1
Agent 2
Agent 3
High
Density
Point
Figure: Plot of Agents in their Respective Voronoi Cells
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Preliminary WorkModeling Density and Area Cont.
The density is applied over each x-y coordinate in a square area. Thefigure below shows a density region represented in three-dimensional space.
0
150
0.2
0.4
0.6
100 150
0.8
100
1
5050
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure: Plot of Density with One Density Region
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Preliminary WorkDeriving Coverage Metric
Now that density has been defined we can look at the coverage metric.The coverage metric, H for i number of agents is defined as the following:
H =n∑
i=1
∫Vi
φ(q)f (r2i )dQ (3)
Where f (r2i ) is a function that models sensor characteristics with idealparameters.
f (r2i ) = α ∗ e−βr2i (4)
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Preliminary WorkDeriving Coverage Metric Cont.
To find each Voronoi region p[i ] such that H is maximized it is necessaryto find dH
dp[i ] and set it equal to zero. For an individual case it can be shown
that:
dH
dp[i ]=
d
dp[i ]
n∑i=1
Hi =n∑
i=1
∫Vi
f (r2i )φ(q)dQ (5)
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Preliminary WorkDeriving Coverage Metric Cont.
By ignoring the all other indices other than the current agent index i andmanipulation the derivative variables the derivative of the introduced rangecan be found to be:
dH
dp[i ]=
dHi
dp[i ]=
d
dp[i ]
∫Vi
f (r2i )φ(q)dQ =
∫Vi
df (ri2)
dri 2dri
2
p[i ]φ(q)dQ (6)
dridp[i ]
=d
dp[i ]
√(x − x [i ]])2 + (y − y [i ]])2 (7)
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Preliminary WorkDeriving Coverage Metric Cont.
dri2
dp[i ]=
d
dx[i ]dy[i ][(x − x [i ])2 + (y − y [i ])2] = (8)
(−2x + x [i ]) + (−2y + y [i ]) = −2(q− p[i ]) (9)
Using the previous equations, we are able to simplify the derivative evenfurther:
dH
dp[i ]=
∫Vi
[−2φ(q)df
dri 2](q− p[i])dQ (10)
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Preliminary WorkDeriving Coverage Metric Cont.
The quantity [−2φ(q) dfdri 2
] shown in the previous equation is introduced as
the modified φ(q) function. This function takes into account the sensorparameters. We call this new function φ(q,p[i ]). From the previousequation:
dH
dp[i ]=
∫Vi
φ(q,p[i ])(q− p[i ])dQ (11)
Using properties of integrals, we split the integral into two:
dH
dp[i ]=
∫Vi
qφ(q,p[i ])dQ− p[i ]
∫Vi
φ(q,p[i ])dQ (12)
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Preliminary WorkDeriving Coverage Metric Cont.
dH
dp[i ]=
∫Vi
φ(q,p[i ])dQ∫Vi
qφ(q,p[i ])dQ∫Viφ(q,p[i ])dQ
− p[i ]
∫Vi
φ(q,p[i ])dQ (13)
We know that the mass is defined as the integral of our density functionrelative to a bounded area Vi . As such the modified mass is expressed asMVi
=∫Viφ(q,p[i ])dQ. The modified centroid is expressed as any point
within the bounded area scaled by our modified φ(q,p[i ]) function.
We call it CVi=
∫Vi
qφ(q,p[i ])dQ∫Viφ(q,p[i ])dQ .
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Preliminary WorkDeriving Coverage Metric Cont.
Therefore we can express:
dH
dp[i ]= MVi
CVi− p[i ]MVi
= 0 (14)
MVi(CVi
− p[i ]) = 0 (15)
CVi= p[i ] (16)
In conclusion, as the mass can not be zero, the coverage is maximizedwhen the position of the agent is equal to the modified centroid of abounded area.
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Preliminary WorkLine Following in Matlab
Figure: Line Following Simulation in Matlab
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Preliminary WorkLine Following in VREP
(a) VREP Start (b) VREP In Progress
(c) VREP Finished
Play Video
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Preliminary WorkLeader Follower in Matlab
Figure: Coverage PlotD. Adra & E. Jones (Bradley University) ACO Presentation 28 / 38
Preliminary WorkLeader Follower in VREP
Play Video
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Preliminary WorkArea Coverage Algorithm in Matlab Start
(a) Coverage Plot (b) MATLAB Plot
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Preliminary WorkArea Coverage Algorithm in Matlab Cont.
(a) Coverage Plot (b) MATLAB Plot
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Preliminary WorkArea Coverage Algorithm in Matlab End
(a) Coverage Plot (b) MATLAB Plot
Play Videos
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Preliminary WorkImplementation
ROS Networking
PID Control for Actuator Commands
MATLAB Robotics Systems Toolbox
Play rosNetworking video
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Parts List
Vendor Part Quantity
Digikey JST SH Jumper 6 Wire Assembly 3Digikey JST SH Jumper 4 Wire Assembly 6Amazon SanDisk Ultra 8GB Memory Card 3Amazon USB 2.0 Male to Micro B cable (3 Pcs) 1Amazon 10 Sets of Mini Micro ZH 2Pin JST 1Amazon 20 M2.5x30mm Socket Head Cap Screws 1Ren. Robotics Beaglebone Blue 3Ren. Robotics Robotics eduMIP Kit 3Polulu Pololu Ball Caster with 1” Ball 5
Table: Parts List
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Future Work
eduMIP homogeneous implementation
Pioneer and eduMIP implementation
Pioneer, eduMIP, and Khepera implementation
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Deliverables
2018 2019
November December January February March
47 48 49 50 51 52 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Homogeneous Static
Heterogeneous Static
Homogeneous Vary
Heterogeneous Vary
Figure: Timeline for Completion
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References
D. Kilinc, M. Ozger, and O. B. Akan, (2015)
On the maximum coverage area of wireless networked control systems withmaximum cost-efficiency under convergence constraint
In: IEEE Transactions on Automatic Control 60(7), 1910 – 1914.
D.-M. S. G. Lee and M. Egerstedt, (2015)
Multirobot control using timevarying density functions
In: IEEE Transactions on Robotics 31(2), 489 – 493.
M. S. Miah and J. Knoll, (2018)
Area coverage optimization using heterogeneous robots: Algorithm andimplementation
In: IEEE Transactions on Instrumentation and Measurement 67(6), 1380 – 1388.
S. A. M. Varposhti, P. Saleh and M. Dehghan, (2016)
Distributed area coverage in mobile directional sensor networks
In: 2016 8th International Symposium Telecommunications (IST) 0(0), 18 – 23.
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References Cont.
G. X. Z. Yu, G. Shan and X. Duan, (2018)
Method of multi-sensor optimal deployment for area coverage
In: 2018 International Conference on Electronics Technology (ICET) 0(0), 116 –119.
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