Cooperative Electronic Chaining using Small Unmanned Aircraft

Cory Dixon & Eric W. Frew

Infotech@Aerospace May 10, 2007

5/10/2007 2

Chaining with Mobile Vehicles

• Fuel range >> communication range for small vehicles

• Operational Range determined by the limiting value, communication range

• Limited size and power for antenna and electronics, e.g. no satellite or OTH communication capabilities

• Team of cooperative vehicles• Can utilize ad hoc communication network or radio

repeater• Extends communication range using relay nodes• Adds robustness to aircraft loss

• Chaining Solution Method• Multivariable Extremum Seeking Control• Form communication performance field from SNR • Decentralized control to maximize end-to-end chain

throughput

Cooperative electronic chaining is the formation of a linked communication chain using a team of mobile vehicles, acting as communication relays in an ad hoc network, that maximizes the end-to-end throughput of the chain while allowing the end nodes of the chain to move independently in an unknown, dynamic environment.

Long Range Sensing

OTH Communications

5/10/2007 3

Robust Chaining and Extremum Seeking

Position Based

Robust SNR Based

Typical ES

Self-Exciting ESJ

HPFLPFC x

HPF

LGVF Vehicle

k x

Plant

s

s + hs

a cos( t) sin( t + )

+

Optimal Communication Chain Extremum Seeking Control

x1 x2 x3 x4 x5 x6

S1

S2S3 S4

S5x

x

5/10/2007 4

USFS/NASA: Small UAS Communication Repeater*

• Mission Objectives• Provide real time voice relay (command channel) between ICP and fire line.

• Thermal imaging capabilities

• Near real time data relay capabilities of the thermal imagery

• Payload• COTS Transcrypt Transpeater III radio portable repeater unit for single

channel voice communications relay

• 2 USFS field radios set up to relay "command" channel communications in half duplex mode. Radios configured for 2 watts radiated power

• Thermal imaging with FLIR Micron microbolometer camera

• Mission Coordination• UAS must be positioned so that it can see the ICP and the fire fighters.

• Frequency Management: As altitude increase the possibility for interference increases

• Airspace Coordination: The position of the UAS needs to be known by other aircraft.

*Tom Zajkowski, Eleventh Biennial USDA Forest Service Remote Sensing Application Conference, Salt Lake City, Utah, April 24-28, 2006

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Overview

• Introduction• Problem Setup and Related Work• Decentralized Chaining• Extremum Seeking Controller• Simulation & Conclusion

5/10/2007 6

Vehicle Dynamics & UA Constraints

• Bicycle Kinematics• Control inputs

• Vehicle cannot turn on itself

• Can be applied to wider class of nonholonomic vehicles over unicycle

• Unmanned Aircraft (UA)• Assume vehicle has autopilot system controlling

• Attitude, altitude, airspeed, waypoint navigation

• Orbital controller (LGVF)

• UA Performance Constraints• Constant, bounded speed: 0 < VMIN ≤ VO ≤ VMAX

• Steering input: |u| ≤ uMAX

• RF Sensor located close to CG (i.e. no forward boom)

uV

Vy

Vx

sin

cos

Bicycle Kinematics

2

tan

V

g

Aircraft Dynamics

00 V

TVz ],[

5/10/2007 7

Communication environment is hard to predict in real world scenarios

Communications Model

• Maintain communication link?• Typically position based

• Received Power

• Signal-to-noise Ratio

• Shannon Channel Capacity

• C ≤ CMIN Range ≤ RangeMAX

2kdPrx

-1000 -500 0 500 1000

-1000

-500

0

500

1000

X-Location [m]

Y-L

ocat

ion

[m]

SNR Field Lines

Communication Range

Radio Environment

Throughput vs. Range

SNRBC 1log2

0/ NPSNR rx

Position Based

ri

ji ri

jiri

ji

• Environment can invalidate range based control• Obstructions• Localized noise sources• Antenna patterns

-1000 -500 0 500 1000

-1000

-500

0

500

1000

X-Location [m]

Y-L

ocat

ion

[m]

SNR Field Lines

)(

)(),()()(

jj

jijijjijijijij xN

rPrxSNRfrrKrP

Performance Field

ii

ii

2kdPRX

C ≤ CMIN S ≥ SMIN

5/10/2007 8

Standard ES Control

• Extremum Seeking Control• Model free

• Actual mapping unknown• Known to have an extremum• Quadratic near extremum

• Gradient-based adaptive control• Inject dither signal to linear system• Demodulate output signal to estimate gradient

• Our approach:• Use orbital motion of vehicle within environment to

provide dither signal (self-excitation: Krstic and Wang, 2000)

• Add “virtual” center point dynamics to kinematic model

• Decentralized ES• Treat as coupled multi-variable case• Note: motion of a vehicle changes the field

measured by the neighbor (tri-diagonal coupled system)

Extremum Seeking control is to find a set point in a closed loop system that achieves an extremum of an unknown reference-to-output objective function.

),(maxarg)(*

tftm

tatt sin)(ˆ)(

5/10/2007 9

Vehicle Steering using ES:Kristic et al.

• Source Seeking with Nonholonomic Unicycle Without Position Measurement• Part I: Tuning Forward Velocity

• Part II: Tuning Angular Velocity

)cos(0

tavv ES

0

)cos(

vv

tES

5/10/2007 10

References & Related Work

• Communication and Control• Connectivity & Limited Range Communications

(Beard and McLain, 2003), (Spanos and Murray, 2004)• Controlled mobility to Improve/Maintain Network Performance

(Goldenberg et al., 2004), (Dixon and Frew, 2005), (Frew et al., 2006) – “Establishment and Maintenance of a Delay Tolerant Network through

Decentralized Mobility Control”

• Vehicle Control in a Sampled Environment• Cooperative Level Set Tracking (Boundary Tracking)

(Hsieh et al., 2004), (Marthaler & Bertozzi, 2003)• Cooperative Gradient Climbing

(Bachmayer et al., 2002), (Ogren et al., 2004)• Adaptive Sampling Utilizing Vehicle Motion

(Fiorelli et al., 2003)(Krstic et al, 2006) – “Source Seeking with Nonholonomic Unicycle without Position Measurement -

Part I: Tuning of Forward Velocity “

• Extremum Seeking (Peak Seeking)(Ariyur and Krstic 2003) – “Real-Time Optimization by Extremum-Seeking Control”• Multivariable

(Ariyur and Krstic, 200?), (Rotea, 2000)• Discrete Time

(Krstic, 2002)

5/10/2007 11

Overview

• Introduction• Problem Setup and Related Work• Decentralized Chaining• Extremum Seeking Controller• Simulation & Conclusion

5/10/2007 12

• Maximize end-to-end throughput• Only looking at physical layer effects

• throughput => channel capacity

• Constant data stream with no buffering

• Maximum chain capacity is determined by minimum link capacity

• Shannon Channel Capacity

Maximizing Chain Throughput

SNRBC 1log2

),(min,

ji

jiNji

chain xxCT

iNi

iNi

SNRC

minmaxminmax

),(minmaxmax,

ji

jiNjix

chain xxCTk

-1000 -500 0 500 1000

-1000

-500

0

500

1000

X-Location [m]

Y-L

ocat

ion

[m]

SNR Field Lines

Radio Environment

=> The SNR provides a robust metric of communication performance capability and can be locally sampled by individual vehicles

1 62 3 4 5

5/10/2007 13

Maximin SNR Field

x x

Initial Setup Optimal Maximin Solution

5/10/2007 14

Decentralized Performance Map

• Performance Function• Use the SNR of each neighbor link to

form the feedback signal • Can form different mappings to

accomplish different communication goals

},,,min{ ,11,,11,2 jjjjjjjjEEundirected SSSSJ

jjjjdirection SSJ ,11, 1,,1 jjjjdirection SSJ

1,1, jjjjsharingnon SSJ

1 62 3 4 5

5/10/2007 15

Overview

• Introduction• Problem Setup and Related Work• Decentralized Chaining• Electronic Chaining ES Controller• Simulation & Conclusion

5/10/2007 16

LGVF Orbital Controller

• Lyapunov Vector Guidance Field • Loiter circles at radius Ro about a center point Xcp

• Lyapunov Function

• Globally stable guidance field

• Heading tracking controller

220

2 )(),( RryxV

)( dku

Guidance Vector Field

Vehicle Trajectory

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)(2

2)(20

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d

dd x

y

arctan

5/10/2007 17

Electronic Chaining for Nonholonomic Vehicles

• Dither Signal (self exciting)• Provided by motion of the vehicle, within the field• Demodulation signal is directly deirived from the vehicle motion

• Virtual Center Point• Control motion of center point and allow LGVF controller to control UA steering• Limit dynamics of center point so UA can track and maintain an orbit• For stability VCP ≤ VMAX , good results are obtained when VCP < VMAX s.t. ≤ MAX

5/10/2007 18

Extremum Seeking Analysis: Path Gradient

• Time derivative of Cost Function

• Path Gradient

• Low-pass filtering generates gradient control update

• Gradient estimate is always in direction of true gradient

kP JJ p

k

kPP JJp

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)(yJyxJ

yxJxJVtJ

yx

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xP J

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2)(~

Motion of Vehicle within Performance Field

0~

~

Jg

Jg

5/10/2007 19

Linear Convergence Rate Bound

• Assumptions• Vehicle speed is small compared to environment• Initial error is very large

• Linear Convergence to optimal set-point

• Optimal Performance Metric

** )1()( xkxxkx

MAXkk Vxx 1

1max1

max1

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MAX

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Bounded Vehicle Motion

Positional Error Convergence

MAXVxkx *)(

5/10/2007 20

Overview

• Introduction• Problem Setup and Related Work• Decentralized Chaining• Extremum Seeking Controller• Simulation & Conclusion

5/10/2007 21

Multi-UA Simulation

• Radio Parameters

Measured values obtained from AUGNet MNR

• K = 2350

• = 3.2

• Noise is 1/1000th power of other nodes

• UA ParametersAres UAV with Piccolo Autopilot

• V = 30 m/s

• Max Bank Angle = 30 deg=> Max Turn Rate = 0.19 rad/sec

5/10/2007 22

Minimum SNR in Chain

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Bounded Convergence Rate

5/10/2007 24

Extension to Relaying for Multiple Nodes

5/10/2007 25

Conclusion

• Electronic Chaining• Connect two disconnected network (radio) nodes• Maximize end-to-end throughput• Can be formulated as tracking the peak of a performance function, that is difficult to predict

• Self-exciting Extremum Seeking• Model free, adaptive controller based on motion of vehicle• SNR as Control Input

• Does not require any additional communication• Is extensible from one node to many nodes• Provides a robust measure of link quality and bandwidth

• Simulation Results• Show that the ES controller can be used as decentralized controller• Chain responds to dynamic environment

• Uknown, dynamic noise• Unpredictable movement of end nodes

• Future work• Obtain COA • Experimental testing with Ares UAS and AUGNet 802.11b system

5/10/2007 26

Ares Measurement of RSSI using AUGNet MNR

5/10/2007 27

http://recuv.colorado.edu

Questions and Comments are Welcomed!

Thanks for ComingCory.Dixon@Colorado.edu