Reconfiguration in Sensor NetworksPhD Defense
Karthik K Dantu
Committee
Gaurav Sukhatme (Chair)
Ramesh GovindanBhaskar
Krishnamachari (Outside member)
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Sensor Network Deployments
Marine MonitoringForest Canopy
Structural Health Monitoring
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Challenges
• Energy• Battery-operated• Lack of continuous energy supply• Long deployments
• Unpredictability• Dynamic network conditions• Remote deployments• Sporadic events – spatially and temporally
Sensor networks need to be adaptable!
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Thesis Contribution
Adaptability by reconfiguration
Functional(static)
Spatial(mobile)
Node
Network
Per-process energy
accounting
Robust connectivity in robot networks
Service reconfiguration in
tiered sensor networks
Route stability using cues in robot
networks
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Thesis Contribution
Functional ReconfigurationA. Per-Process Energy AccountingB. Reconfiguration of essential services
in a sensor network
* Post-Qual* Pre-Qual
Spatial ReconfigurationA. Go from a connected network to
a biconnected networkB. Achieve route stability using
directional and positional cues
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Outline
Functional ReconfigurationA. Per-Process Energy AccountingB. Reconfiguration of essential services
in a sensor network
Spatial ReconfigurationA. Go from a connected network to
a biconnected networkB. Achieve route stability using
directional and positional cues
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Accurate Per-Process Energy Accounting• Energy is a vital resource• Modern embedded systems are highly multi-
tasking running multiple tasks concurrently and numerous sensors
• Most of the tasks involve I/O operations like using storage, networking and sensors
• Observation: Resources currently used on the system need not be used by the process currently running
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LEAP2 Platform
• Representative platform for modern 32-bit embedded system
• Energy Management and Accounting Processor (EMAP2) ASIC continuous real-time energy monitoring across entire platform
• Measures energy usage in real-time for upto 16 individual subsystems
Address/Data Buffers
512MB NAND Flash
GPIO/Serial Busses
Ethernet
CF
GPS
USB Host
SODIMM 200 Connector
uWattFPGA
mPCIWLAN
CMOS Imager
Current Sensors
Sensor Power
Switching
CC2420
EMAP ASIC
LEAP2 Stacking Connector
Low Power Radio Module
LEAP2 Stacking Connector
MSP430
Current Sensors
Current Sensors
PwrC
ontr
ol
ADC IF
Mem
Bus
Low Power Radio Module (LRM)
Host Processor Module (HPM)Energy Management and Accounting Processor (EMAP2)Mini PCI Module (MPM)
Sensor Interface Module (SIM)
CMOS Imager Module (CIM)
8MB SRAM
64MB SDRAM
32MBNOR Flash
McIntire, D., Ho, K., Yip, B., Singh, A., Wu, W., and Kaiser, W. J. 2006. The low power energy aware processing (LEAP) embedded networked sensor system. In Proceedings of the 5th international Conference on information Processing in Sensor Networks (Nashville, Tennessee, USA, April 19 - 21, 2006).
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LEAP2 Software
• ARM-Linux Patch• Endoscope
• Scheduler measures energy on every scheduler tick
• Energy attributed to either user process or system
• User process energy consumption exposed to user space via the /proc/<pid>/stat
• Etop reads this file to provide realtime energy consumption info
Stathopoulos, T., McIntire, D., and Kaiser, W. J. 2008. The Energy Endoscope: Real-Time Detailed Energy Accounting for Wireless Sensor Nodes. In Proceedings of the 7th international Conference on information Processing in Sensor Networks), April 2008.
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Per-Process Energy Accounting: Caveats• System operation dominated by I/O operations
• Userspace processes get switched out due to delay• Latency of execution in kernel
• Kernel needs to track such interactions• System call interface (SCI) in *nix kernel used
for userspace-kernel transition• Single point of entry/exit in kernel
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Function call
SCI functioning in Linux (ARM)
TIME
process LibraryCall
kernelentry.S
System call
Flash
fwrite()
r7 = __NR_writeswitch to kernel (swi)
write()
vector_swicall
sys_call_table[r7]
sys_write()
donereturn
ret_from_syscall
return numbytes
writesuccessful
Processblocked
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Modifications to SCI
• Implement two new system calls sys_initiate and sys_terminate
• Call sys_initiate on invocation of every system call • Record the process id, timestamp and system call
number• The original system call is then invoked• On completion, control returns to the kernel where we
invoke sys_terminate• sys_terminate calculates the energy spent for this
system call and accurately allocates that to the corresponding process
• State for that call is then purged
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Resource Accountant
sys_initiate()(keep state)
Modifications to SCI
TIME
kernelentry.S
System call
Flash
done
return
ret_from_syscall
… call sys_initiate
vector_swicall
sys_call_table[r7] …
Resource Accountant
sys_terminate()(energy accounting)
call sys_terminate()
write(<params>)
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Modifications to SCI: Discussion
• There are a lot of system calls invoked• Eg: At bootup, about 7000 system calls before login
• For efficiency, we are currently only monitoring a small subset (sys_open, sys_close, sys_read, sys_write)
• These system calls account for majority of the system calls placed and energy consumed during the experiments
• Need to maintain state across system calls to keep track of file and socket identifiers
• Compared against our implementation of Endoscope
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Experimental Setup
• LEAP2 running a copy (cp) of a large file from compact flash to compact flash
• Concurrently running calc1, compute intensive CPU-bound process that performs some computation and goes to sleep
• Multiple system services running in the background• Ext2 filesystem and virtual memory tuned to minimize
buffering• Show energy consumption of Processor (PXA), Memory
(SDRAM) and Compact Flash (CF)
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cp and calc1: endoscope v2
Processor Speed = 104 MHz
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cp and calc1: Resource Accountant (RA)
Processor Speed = 104 MHz
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Effect of Processor Frequency Scaling
• Bottleneck is read/write from and to compact flash
• CPU can drive reading/writing even at lowest processor frequency (104 MHz)
• Processor energy consumption increases at higher frequencies
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cp and calc1: endoscope v2
Processor Speed = 312 MHz
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cp and calc1: Resource Accountant
Processor Speed = 312 MHz
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cp and calc1: endoscope v2
Processor Speed = 624 MHz
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cp and calc1: Resource Accountant
Processor Speed = 624 MHz
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Resource Accountant: Discussion
• Effective when I/O interaction takes some timeEg: GPS and other high latency sensors, flash writes
etc.• Intensive to monitor every system call
• System needs to be tailored for monitoring the significant operations only
• Does not account for optimizations at lower levels of kernel (eg: Delayed writes by ext2 fs, dirty page caching by VM, DMA, non-blocking drivers)
• Need driver support for end-end accuracy
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Related Work
Authors Work
Banga et al. Resource containers: a new facility for resource management in server systems (OSDI 1999)
Zeng et al. ECOSystem: managing energy as a first class operating system resource (ASPLOS 2002)
Rajkumar et al. Resource Kernels (MMCN 1998)
Fonseca et al. Quanto: Tracking energy in networked embedded systems. (OSDI 2008)
Stathopoulos et al. The Energy Endoscope (IPSN 2008)
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Outline
Functional ReconfigurationA. Per-Process Energy AccountingB. Reconfiguration of essential services
in a sensor network
Spatial ReconfigurationA. Go from a connected network to
a biconnected networkB. Achieve route stability using
directional and positional cuesKarthik Dantu and Gaurav S. Sukhatme, "Rethinking data-fusion based services in sensor networks," In the Third IEEE Workshop on Embedded Networked Sensors (Emnets), 2006.
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Motivation – Tiered Sensor Networks
Mote-class sensor node
Microserver node
Base Station
Transit Network
Sensor node
Gateway
Gateway
Sensor node
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Tiered Sensor Networks
• Microservers: More powerful processor and radio
• Tradeoff true distributedness for saving on communication
• Data collection from motes followed by computation at microserver
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SDP Formulation of Localization
Eijrxx jiij ),(|||| 22
Rkiik Eikdxx ),(|||| 22
Connectivity-based constraints
Range-based constraints
Pratik Biswas, Yiyu Ye, “Semidefinite programming for ad hoc wireless sensor networks localization”, In
Proceedings of conference on Information Processing in Sensor Networks (IPSN) 2004.
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SDP Formulation of Localization
jiEji kjkjjiEji ijij RR ,,,,
)()(min
Eji kjjiEji ij ,,,
1);0;1();0;1( 00 ZTs.t. 1);1;0();1;0( 00 ZT
2);1;1();1;1( 00 ZT^
2)();();( ijijijijT
ij deZe 00R
kjkjkjijT
ij EjkdeZe ,)();();(^
200
jiEjireZe ijijijT
ij ,,)();();(^
200
0,,,,,,, kjkjijijkjkjijij
Pratik Biswas, Yiyu Ye, “Semidefinite programming for ad hoc wireless sensor networks localization”, In Proceedings of conference on Information Processing in Sensor Networks (IPSN) 2004.
0Z
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Hierarchical Overlapped Coordination
Consider an optimization problem of the form -
min f (x)0)( Xh0)( Xg
subject to
Where h and g are functions and X
Rn
Nestor Michelena, Hyungju Park, Panos Papalambros and Devadatta Kulkarni, “Hierarchical Overlapping coordination under non-linear constraints”, American Institute of Aeronautics and Astronautics, 1998.
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Functional Dependence Table
hi
hN1
h1
gi
g1
gN1
x1
x i
xn
1 0 1 …
.
.
.
Columns correspond to the variables in the problem Rows correspond to constraints
Table with entries such that (i,j)th entry is 1 if constraint i
involves variable j, and zero otherwise
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Rearrange FDT
B1
A1
B2
A2
B p
A p
h1
g1
h2
g2
h p
g p
x0
x1
x p. . .
.
.
.
.
.
.
0 0
0
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Problem reformulation
min f i (d ,X i)
h i(d ,X i
) 0
g i (d ,X i) 0
subject to
i1,..., pFor each
X0d
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HOC Algorithm
1. Fix linking variables and solve problem by solving independent sub problems
2. Fix linking variables to their values determined in step 1 and solve problem by solving sub problems
3. Go to step 1 with fixed values of -linking variables determined by step 2
4. Repeat until convergence is achieved
X0
p
X 0
p
Nestor Michelena, Hyungju Park, Panos Papalambros and Devadatta Kulkarni, “Hierarchical Overlapping coordination under non-linear constraints”, American Institute of Aeronautics and Astronautics, 1998.
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Partitioning the Nodes
Motes Microservers
1
111
1
1 1 1
11
1 11
222
2
22
2222
2
2 2
1,2
1,2
1,2
1,2
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Partitioning: The Basic Idea
Motes Microservers
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SDP Relaxation for Localization
Pratik Biswas, Yiyu Ye, “Semidefinite programming for ad hoc wireless sensor networks localization”, In Proceedings of conference on Information Processing in Sensor Networks (IPSN) 2004.
jiEji kjkjjiEji ijij RR ,,,,)()(min
Eji kjjiEji ij ,,,
1);0;1();0;1( 00 ZTs.t.1);1;0();1;0( 00 ZT
2);1;1();1;1( 00 ZT ^2)();();( ijijijij
Tij deZe 00
Rkjkjkjij
Tij EjkdeZe ,)();();(
^200
jiEjireZe ijijijT
ij ,,)();();(^
2000,,,,,,,
kjkjijijkjkjijij
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Simulation Setup
• Nodes distributed uniformly randomly in a square of side 100 units
• Radius of communication assumed to be 20 units• Semi-centralized simulations had four master
nodes
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Centralized - Error vs. Iterations
Error vs. Iteration Centralized Formulation (Degree = 8)
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Distributed – Error vs. Iterations
Error vs. Iteration in Semi-Centralized Formulation (Degree = 8)
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Multiple masters
Error vs. Number of Master Nodes in Semi-Centralized Formulation
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Error – Edge Effects
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Service Reconfiguration - Summary
• Framework adaptable to services that can be framed as an optimization problem
• Spatial distribution of sensor nodes lends itself to partitioning automatically
• Partitioning can be done with a simple broadcast from master nodes
• Formulation for lifetime-aware routing presented
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Related Work
Authors Work
Niculescu et al. Localized Positioning in Ad hoc Networks (Adhoc Networks 2003)
Pratik Biswas Semidefinite Programming Approaches to Distance Geometry Problems (Phd. thesis 2007)
Savvides et al. Dynamic Fine-grained Localization (MOBICOM 2001)Aspnes et al. Theory of Network Localization (IEEE TMC 2006)
Chang et al. Maximum Lifetime Routing in Wireless Sensor Networks (ToN 2004)
Michelena et al. Hierarchical Overlapping coordination under non-linear constraints (AIAA 1998)
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Functional Reconfiguration - Summary• Per-Process Energy Accounting
• Demonstrated problem of accurate energy accounting in current embedded systems
• Designed resource accountant in the OS to perform energy accounting
• Prototype implementation on LEAP2/Linux shows accurate results
• Service Reconfiguration in Tiered Sensor Networks• Proposed semi-centralized framework for reconfiguring
services in tiered sensor networks• Evaluation done on two services – Localization and Power-
aware routing
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Outline
Functional ReconfigurationA. Per-Process Energy AccountingB. Reconfiguration of essential services
in a sensor network
Spatial ReconfigurationA. Go from a connected network to
a biconnected networkB. Achieve route stability using
directional and positional cues
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Robot Networks
Marine observation Urban search and rescue
Formation control Collaborative taskingTarget tracking
Robust connectivity between the robots!
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Robot Network Biconnectivity Problem
Given a connected robot network, can they reassemble themselves with minimum movement to form a biconnected robot network? Minimum total sum distance: NP-
Hard!
Karthik Dantu, Prakhar Goyal, and Gaurav S. Sukhatme. Relative bearing estimation from commodity radios. In International Conference of Robotics and Automation (ICRA), May 2009.
Karthik Dantu and Gaurav S. Sukhatme, Biconnected Robot Networks, In submission to Transactions in Robotics Oct 2009.
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Definitions: Biconnectivity
Biconnected Graph: Given a graph G(V, E), every vertex in V has atleast two vertex disjoint paths to every other node in V
Biconnected Component: Subgraph of a given graph that is biconnected
Articulation Point:Vertices in a connected graph that connects two biconnected components. This edge or vertex is the only path between the two biconnected components
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Achieving Biconnectivity
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Biconnectivity Algorithm: Introduction• Conservative approach: Move one robot at a
time• Iterative: Improves connectivity of the network
with iteration• Each iteration potentially adds one new edge• Only needs bearing measurement to neighbors• Three phases in each iteration
• Compute biconnected components• Identify potential neighbors • Command movement
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Biconnectivity Algorithm
•Phase I – Distributed biconnected components computationE.J.H. Chang. Echo algorithms: Depth parallel operations on general graphs. IEEE Transactions on Software Engineering, 8(4):391–401, 1982.• Phase II – Identify nodes
to move• Articulation points compute bearing of
all neighbors• Identify nodes to move
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Biconnectivity Algorithm - II
• Phase III - Move nodes• Articulation points
negotiate for least expensive move
• Least expensive node is chosen
• Command is sent based on relative angle – according to table shown
Node 1
Node 2 Q1 Q2 Q3 Q4
Q1 -al - 45
135 - ah
-al
180 - ah
45 - al
ah - 135
al - 270
90 - ah
Q2 45 - al
135 - ah
90 - al
270 - ah
135 - al
315 - ah
Q3 135 - al
315 - ah
180 - al
360 - ah
Q4 225 - al
415 - ah
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Biconnectivity Algorithm: Simulation
• Simulations done using Player/Stage simulator
• Studied various randomly generated topologies (connected)
• Results shown for 16-node and 20-node networks
• Results averaged over 25 simulation trials
actual
computed• Study error in
• Relative Bearing• Translation
executed
• Turn angle
commanded
executed
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Robustness to Bearing Error
Gaussian error with zero mean, deviation shown on x-axis
Algorithm robust to large bearing error (upto 30°)!
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Robustness to Odometry Error
Gaussian error with zero mean and deviation as a percentage of the
command given
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Robustness to turn angle error
Gaussian error with zero mean and deviation as shown on x-axis
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Robot Experiments
• iRobot Create with e-boxes• Antenna raised for better
signal strength readings• Use radio to compute
relative bearing• OLSR routing protocol• Neighbor list obtained from
routing table
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Robot Experiments - bearing computation• Sample signal strength in the robot
neighborhood according to pattern• Measure 100 samples at each point • Perform 3-D Principal Component
Analysis• Assume major axis as the direction of
neighbor • Experimented with wifi and zigbee
radios• Varied step size to study effect on
bearing estimation• Chosen step size 2 m
Step size
Karthik Dantu, Prakhar Goyal, and Gaurav S. Sukhatme. Relative bearing estimation from commodity radios. In International Conference of Robotics and Automation (ICRA), May 2009.
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Biconnectivity: 5-node Topology
Trial 1 Trial 2Edge Actual
angleMeasured angle(T1)
Bearing error (T1)
Measured angle(T2)
Bearing Error (T2)
3-4 5 9.3 4.3 -12.4 17.4
3-2 120 148.1 28.1 166.8 46.8
3-1 -160 -147.2 12.8 -129.1 30.9
4-3 170 202.5 32.5 148.2 21.8
4-5 -30 -18.3 11.7 -4.3 25.7
5-4 150 172.1 22.1 175.4 25.4Average bearing error is 24.32°
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Related Work - Biconnectivity
Authors Work
Ahmadi et al. Keeping in Touch: Maintaining Biconnected Structure by Homogeneous Robots (AAAI 2006)
Poduri et al. Using Local Geometry for Tunable Topology Control in Sensor Networks (IEEE TMC 2009)
Tarjan Depth first search and Linear Graph Algorithms (SIAM J Computing 1972)
Frederickson et al. On the Relationship between the Biconnectivity Augmentation and Travelling Salesman Problems (TCS
1981)
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Thesis Contribution
Functional ReconfigurationA. Per-Process Energy AccountingB. Reconfiguration of essential services
in a sensor network
Spatial ReconfigurationA. Go from a connected network to
a biconnected networkB. Achieve route stability using
directional and positional cues
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Robot Networks
Marine observation Urban search and rescue
Formation control Collaborative taskingTarget tracking
Temporal robustness of routes using mobility cues
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Route Stability: Problem
• Control algorithms expect a stable graph • Routing protocol optimizes data forwarding
path• Path stability not a requirement for routing• Frequent route switches confuse control
algorithm• Requirement unique to robot networks
Karthik Dantu and Gaurav S. Sukhatme. Connectivity vs. control: Using directional and positional cues to stabilize routing in robot networks. In International Conference on Robot Communication and Coordination (ROBOCOMM) April 2009.
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Route Stability: Example
B
A
C DE
F
G
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Route Stability: Example
B
A
C DE
F
G
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Route Stability: Example
B A
C
DE
FG
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Route Stability: Example
BA
C
DE
F
G
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Route Stability: Example
B
A
C DE
F
G
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Route Stability: Our solution
• Robot networks have information about direction of movement and possibly position
• This can be used to choose routes that are more likely to be stable
• Modify OLSR - a popular adhoc routing protocol
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Stability Metric: Direction Cue
Direction Cue
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Stability Metric: Location and Direction Cue
• Stability metric is equal to the link duration
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Modifying OLSR: Route computation
• Added direction information base and position information base
• Modified Hello messages to incorporate direction, position and stability
• New routes are picked based on the best stability value instead of shortest path
• If a route exists, it is not modified unless the stability value falls below a threshold
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Simulation Setup
• Ns-2 with OLSR implementation from U Murcia, Spain• Deploy robots in 500x500 area• Mobility of robots is based on random waypoint mobility
model• Radius of communication is approximately 50 units –
propagation model is two ray ground• Results are averaged over 10 trials each• Percentage decrease in number of route switches is
measured as the success metric
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Effectiveness – Direction Cue Only
Speed of travel vs. Route Stability
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Effectiveness – Direction and Location Cue
Speed of travel vs. Route Stability
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Effectiveness – Direction and Location Cue
Density vs. Route Stability
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Effect of error in location cue
Gaussian error with zero mean and deviation as a percentage of the radius of
communication
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Effect of error in direction cue
Gaussian error with zero mean and deviation in degrees on x-axis
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Simulation Results
• Directional cues improve stability by about 8%-10%
• Direction and position together improves route stability by about 15%-20%
• Error in position is not very detrimental to the route stability unless the error is high
• Error in direction has a greater impact on route stability
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Related Work – Route Stability
Ko and Vaidya Using Location Information to Improve Reactive Routing in MANETs by Using Directional Flooding(Wireless Networks 2000)
Karp and Kung Greedy Perimeterless State Routing for Wireless Networks (Mobicom 2000)
Ramachandran et al.
Route Stability in Static Mesh Networks(PAM 2007)
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Thesis Contribution
Functional ReconfigurationA. Per-Process Energy AccountingB. Reconfiguration of essential services
in a sensor network
Spatial ReconfigurationA. Go from a connected network to
a biconnected networkB. Achieve route stability using
directional and positional cues
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F i g h t O n !
Trojan Cricket Club
SC Badminton
Armando
UCLA Ascent Lab
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Publications (Thesis-related)JOURNAL • Karthik Dantu, and Gaurav S. Sukhatme. Biconnected robot networks. In
Submission to Transactions on Robotics, October 2009.• Karthik Dantu and Gaurav S. Sukhatme. Service Reconfiguration in Tiered
Sensor Networks, In preparation.CONFERENCES AND WORKSHOPS• Karthik Dantu, and Gaurav S. Sukhatme, “Per-Process Energy Accounting:
Handling Asynchrony in Embedded Systems”, In Submission Dec 2009. • Karthik Dantu and Gaurav S. Sukhatme. Connectivity vs. control: Using
directional and positional cues to stabilize routing in robot networks. In International Conference on Robot Communication and Coordination (ROBOCOMM) April 2009
• Karthik Dantu, Prakhar Goyal, and Gaurav S. Sukhatme. Relative bearing estimation from commodity radios. In International Conference of Robotics and Automation (ICRA), May 2009.
• Jesse Butterfield, Karthik Dantu, Brian P. Gerkey, Odest C. Jenkins, and Gaurav S. Sukhatme. Autonomous biconnected networks of mobile robots. In IEEE Workshop on Wireless Multihop Communications in Networked Robotics (WMCNR), Apr 2008.
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Publications (Thesis-related)
5. Dustin McIntire, Timothy Chow, Karthik Dantu, Mansi Shah, Thanos Stathapoulos, Gaurav S. Sukhatme, William J. Kaiser The Low Power Energy Aware Processing (LEAP) Software Applications - Poster and Demonstration, In IPSN-SPOTS ’07: Proceedings of the 5th international conference on Information processing in sensor networks.
6. Karthik Dantu and Gaurav S. Sukhatme. Detecting and Tracking level sets of scalar fields using a robotic sensor network. In IEEE International Conference on Robotics and Automation (ICRA), pages 3665–3672, Apr 2007.
8. Karthik Dantu and Gaurav S. Sukhatme. Rethinking data-fusion based services in tiered sensor networks. In IEEE Emnets ’06: Third Workshop on Embedded Networked Sensors,May 2006.
9. Karthik Dantu, Mohammad H. Rahimi, Hardik Shah, Sandeep Babel, Amit Dhariwal, and Gaurav S. Sukhatme. Robomote: enabling mobility in sensor networks. In IPSN-SPOTS ’05: Proceedings of the 5th International Conference on Information Processing in Sensor Networks.
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Publications (Other)
1. Anand Joshi, Mi Zhang, Ritesh Kadmawala, Karthik Dantu, Sameera Poduri, and Gaurav S. Sukhatme OCRdroid: A Framework to Digitize Text Using Mobile Phones In ICST International Conference on Mobile Computing, Applications and SErvices (MobiCASE),October 2009
2. Avinash Parnandi, Ken Le, Pradeep Vaghela, Aalaya Kolli, Karthik Dantu, Sameera Poduri and Gaurav S. Sukhatme, “Coarse In-Building Localization with Smartphones”, to appear in ICST International Workshop on Innovative Mobile User Interactivity (IMUI ’09) alongwith MobiCASE 2009, October 2009, San Diego, USA.
3. Dheeraj Kota, Neha Laumas, Urmila Shinde, Saurabh Sonalkar, Karthik Dantu, Sameera Poduri and Gaurav S. Sukhatme, “deSCribe: A Personalized Tour Guide and Navigational Assistant”, to appear in ICST International Workshop on Innovative Mobile User Interactivity (IMUI ’09) alongwith MobiCASE 2009, October 2009, San Diego, USA.
4. John Caffrey, Ramesh Govindan, Erik Johnson, Bhaskar Krishnamachari, Sami Masri, Gaurav S. Sukhatme, Krishna K. Chintalapudi, Karthik Dantu, Sumit Rangwala, Avinash Sridharan, Ning Xu, and Marco Zuniga. Networked sensing for structural health monitoring. In International Workshop of Structural Control Jun 2004.
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Publications (Non-thesis related)
5. Krishna Chintalapudi, Jeongyeup Paek, Omprakash Gnawali, Tat S. Fu, Karthik Dantu, John Caffrey, Ramesh Govindan, Erik Johnson, and Sami Masri. Structural damage detection and localization using netshm. In IPSN-SPOTS ’06: Proceedings of the 5th international conference on Information processing in sensor networks.
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Lifetime Aware Routing
j iBij Sj
AjijiqQijq:
),(),(),(
kBi0),( ijq
Max Tsystem
and for every i V
Mkikq 0),( and
s.t.
i iBj Bj
irt Eijqejiqe ),(.),(.
where
i iBj Bjirt
ii Eijqejiqe
ET),(.),(.
calc1 and scp: Resource Accountant