View
219
Download
2
Tags:
Embed Size (px)
Citation preview
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
5/10/2007 5
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
Tcpcpcp yxX ],[
r
r
d
dd y
x
RrrR
rRRr
y
xV
)(2
2)(20
20
020
2
22 )()( cpcp yyxxr
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
p
2
2
)(yJyxJ
yxJxJVtJ
yx
yxP
y
xP J
JVJLPFg
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
max*
1*
max1
kkk
kk
kk
kk
exee
xee
xxxxx
xxx
MAXkk Vee
1
ESkk vee
1
~~
MAX
cp
MAX
ESopt V
v
V
v )max(
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
5/10/2007 23
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 [email protected]