Global Aerospace

Transcription

Global Aerospace

CONSTELLATION MANAGEMENT
By Matthew Kuperus Heun
Global Aerospace Corporation
http://www.gaerospace.com/
8 February 2001
Global
Aerospace
Corporation
Global
Aerospace
Corporation
Global Stratospheric Balloon Constellations
Topics
What is Constellation Management?
Options for Constellation Management
Uniform Distribution
Target Overflight
Advanced Framework
Next Steps
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Definitions
• Constellation Management is the process of maintaining
spatial distribution of balloons in constellation
• A Constellation Objective is the desired spatial distribution
of balloons
• A constellation Management Strategy is the manner of
achieving the objective
• A constellation management algorithm is formulas and
instructions that determine how each balloon should be
controlled
• A given strategy may implemented by one or more
algorithms
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Aerospace
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Example: Molecular Control
• Objective: Maintain a uniform spatial distribution
• Strategy: push each balloon away from its nearest
neighbor
• Algorithm
– For every balloon, determine nearest neighbor
– Calculate direction to nearest neighbor (a vector)
– Command TCS to maximize velocity component away from nearest
neighbor
A
C
B
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Options for Constellation
Management
• Environment information used
–
–
–
–
Parameterized Description
Successive Correction (interpolated from satellite measurements)
Assimilations (general circulation model)
Forecasts
• Level of TCS model fidelity
–
–
–
–
Omni-directional ∆ V of fixed magnitude applied at balloon
Left-right ∆ V of variable magnitude applied at balloon
∆ V proportional to true relative wind at TCS
Actual TCS Aerodynamic Model and Sophisticated TCS Control
Algorithms
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Options for Constellation
Management (2)
• Network Control Strategies
–
–
–
–
–
Randomization: break up any regional coherence by N-S motion
Molecular: push away from nearest neighbor
Macro Constellation Management: balloons moved between zones
Guided North-South motion
Gradients of artificial potentials
• Coordinate System
– Planetary
– Mesoscale (cyclone-scale)
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EXAMPLE OBJECTIVE:
UNIFORM DISTRIBUTION
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Uniform Distribution
• Balloons Drift in the Typical and Pervasive Zonal
Stratospheric Flow Pattern
• Trajectory Control System Applies a Small, Continuous
Force to Nudge the Balloon in Desired Direction
• Balloons Are in Constant Communications With a Central
Operations Facility
• Stratospheric Wind Assimilations and Forecasts Are
Combined With Balloon Models to Predict Balloon
Trajectories
• Balloon TCS Are Periodically Commanded to Adjust
Trajectory Control Steering to Maintain Overall
Constellation Geometry
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Global Constellation Without Trajectory
Control
ASSUMPTIONS
• 100 StratoSats @ 35 km
• Simulation Start: 1992-11-10
• UK Met Office Assimilation
• 4 hrs per frame
• 4 month duration
STATISTICS
1000
σ
NNSD
[km]
800
600
400
Start Date: 1992-11-10T00:00:00
35 km constant altitude flights
100 balloons, UKMO Environment
200
0
0
20
40
60
80
Time from start [days]
100
120
ILLUSTRATION OF CONTROL
EFFECTIVENESS
5 m/s Toward Equator
5 m/s Toward Poles
Global
Aerospace
Corporation
Simple, Intelligent Control
• Paired N-S Control Algorithm
– Only apply control when a balloon is closer than 2000 km from its
nearest neighbor
– Control direction is either N or S, depending on proximity to nearest
neighbor
AND
• Zonal Control
– Zones are: -90° --> -45°, -45° --> 0°, 0° --> 45°, 45 °--> 90°
– Count balloons in each zone
– If actual number differs from the desired, identify balloons to be
moved from or to nearby zones
– Move balloons under zonal control until destination zone is reached
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GLOBAL CONSTELLATION WITH
SIMPLE, INTELLIGENT CONTROL
ASSUMPTIONS
• 100 StratoSats @ 35 km
• Simulation Start: 1992-11-10
• UK Met Office Assimilation
• 4 hrs per frame
• 4 month duration
• 5 m/s control when separation
is < 2000 km
• Same initial conditions
STATISTICS
1000
σ
NNSD
[km]
800
Free-floating
600
400
Paired NS and
Zonal Control
200
Start Date: 1992-11-10T00:00:00
35 km altitude flights
100 balloons, UKMO Environment
0
0
20
40
60
80
Time from start [days]
100
120
Global
Aerospace
Corporation
EXAMPLE OBJECTIVE:
HURRICANE OVERFLIGHT
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Hurricane Overflight
• Track a moving target (hurricane) with multiple balloons
• As one balloon moves beyond the horizon, new balloon
enters the scene for observations
• Use full potential of TCS to maximize time over target (lift
and stall modes)
• Example strategy
– When > 90° longitude from hurricane, maintain hurricane's latitude
– When < 90° longitude from hurricane, aim directly for the eye.
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Hurricane Alberto
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•
•
•
Hurricane Alberto
UKMO winds at 35
& 20 km
Red
EFFECT OF
TRAJECTORY CONTROL
– Actual
Aerodynamic
TCS model
– ~ 2 m/s control
authority
– Maintains lat. of
Alberto
•
Blue
– Uncontrolled
– Floats with winds
•
•
4 hr/frame
4.25 days
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STRING OF PEARLS
• Hurricane
Alberto
• 20 balloons
• 3-day lookahead
• 4 hrs/frame
• 27 days
• 30 m/s easterly
winds
• Advanced TCS
(5 m/s)
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ADVANCED CONSTELLATION
MANAGEMENT FRAMEWORK
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Princeton University
• Princeton University support to GAC through subcontract
• Unique capabilities and multi-disciplinary approach
• Helped develop an advanced framework for constellation
management
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RELATED RESEARCH AREAS
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GROUP BEHAVIOR
ANALYSIS AND MODELING
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Behavior of Natural Groups
Photograph by Norton Wu
Photograph by Norton Wu
• Group-level characteristics emerge from individual-level
behaviors
• Schools/Pods/Flocks
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Distributed and
Coordinated Control
• Robotic obstacle avoidance (Khatib, Koditchek)
• Micro-satellite formation flying (McInnes, Krishnaprassad)
• Autonomous underwater vehicles for adaptive ocean
sampling (Leonard)
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Group Behavior Modeled
with Artificial Potentials
• Control derived from a gradient of artificial potentials
• Model local "traffic rules"
– Attraction
– Repulsion
• Potentials and virtual members produce emergent group
behavior
– Manipulate group geometry
– Direct group motion
• Useful for stability/robustness proofs
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u wind
u wind
u21 u31
2
u23
u32
uij
3
Repulsion
l
Attraction
u1
d0
No Interaction
Artificial Potentials
Corporation
d1 rij
uij = ∇Ψij (rij )

d0 
Ψ = k  ln(rij ) + 
rij 

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WSB ANALYSIS AND MODELING
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Weak Stability Boundary
(WSB) Theory
• Chaos principles used to control spacecraft for low-energy
routes in space
• Operationally demonstrated in 1991 by Japanese
spacecraft, Hiten, by performing new type of lunar transfer
• Upcoming uses
– SMART1 (ESA, 2003)
– Lunar A (Japan, 2003)
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WSB Theory (2)
• WSB is a multi-dimensional position/velocity surface
• WSB theory can provide significant and controlled
trajectory modification in regions of high atmospheric
instability
• WSBs do not exist everywhere
• WSBs exist near vortex pairs
• Trajectory control possible when balloon is maneuvered to
get on WSB
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ADVANCED FRAMEWORK FOR
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Motivation for
Advanced Framework
Polar Vortex
StratWarms
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Advanced Framework
Corporation
Region I
Regroup here!
Control by artificial potentials
WSB defined threshold
No control action
Stay on WSB
through ∆Vs
WSB
Region II–Chaotic Flow
Control by WSB
No control action
WSB defined threshold ∆V to achieve WSB defined here
Region I–“Steady” Flow
Control by artificial potentials
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Artificial Potentials in
Uniform Velocity Field
Corporation
7000
2 vehicles, 1
virtual leader
Vehicle 2
Vehicle 3
Virtual leader
6000
u wind = 20 m/s
Kilometers from Start
5000
uleader = 20 m/s
4000
3000
Stable formation
is achieved in
uniform flow
field
2000
1000
0
35
35.5
36
36.5
37
37.5
38
38.5
39
39.5
40
North Latitude
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Non-uniform Velocity Field
4
12
x 10
Kilometers from Start
10
2 vehicles, 1
virtual leader
Vehicle 2
Vehicle 3
Virtual leader
8
•
A 3rd order polynomial
variation of east-west
velocity w.r.t latitude
•
A constant south-north
drift of 1 m/s
•
Artificial Potential
provides stable group
control in non-uniform
flow field
6
4
2
0
35
36
37
38
39
40
41
North Latitude
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WSB Velocity
Magnitude
WSB Surface
Perform “instantaneous”
∆V to alter trajectory
Perform ∆V to enter
WSB Region on WSB
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Example WSB Simulation
2.5
Nominal Trajectory
Maneuvered Trajectory
2
Y (scale: 1 unit = 5000 Km)
1.5
∆V = −5 m/s introduced
tangentially at X = -.1
units
1
0.5
Causes a shift of about
2000 km in 12 days
WSB region
0
-0.5
-1
-1.5
-1
“Instantaneous” ∆V
-0.5
0
X (scale: 1 unit = 5000 Km)
0.5
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Continuous force application
would cause significant
trajectory change
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Advanced Framework for
Constellation Management
• Combines Artificial Potentials and Weak Stability Boundary
theory
– Artificial Potentials --> emergent group behavior
– Weak Stability Boundary --> high level of control in chaotic regions
• Intelligence in adaptive control algorithms allows one to
work with imperfect knowledge of atmosphere to achieve
network objectives
• Parameterized description of atmosphere may be sufficient
for control algorithms
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Exciting New Research
• To the best of our knowledge, first use of gradients of an
artificial potential to determine control strategies in
presence of non-uniform external flow fields for multivehicle systems
• First generalization of WSB for arbitrary force fields
• First demonstration of non-space application of WSB
(atmosphere)
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Applications to StratCon
• Artificial potentials concept simplifies analysis and control
algorithms
– Unified framework
– Algorithms consist of different arrangement of virtual vehicles
• Point attractors for eye of hurricane or other scientific targets
• Zone repellers for no-fly zones
• Line attractors for constant-latitude control
– Analysis process and calculation of TCS commands remains
constant
• WSB may provide options for significant trajectory control
capability from bounded and under-actuated control
systems in regions of high instability
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Application to StratCon
Operations
Corporation
Location &
Environment
Gondola
calculates
TCS commands
TCS
Commands
Constellation
Geometry &
Environments
Constellation
Operations
Center
TWA
Constellation
Geometry &
Atm. Param.
Observed Strat.
Winds &
In-situ Data
Improved
Stratospheric
Forecasts
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Stratospheric
Forecast
Center
Standard Sat.
& In-situ
Observations
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Corporation
Possible Future Directions
for Advanced Framework
• Atmosphere parameterization
• In-depth analysis of AP/WSB
– Formal analysis of potentials for parameterized atmosphere
– Stability analyses for various balloon configurations
– Experiments (water)
• Develop systematic design methodology for AP/WSB
– Systematize stable arrangements and describe by parameters
– Find AP prescriptions for moving from one arrangement to another
– Find WSB prescriptions for continuous force application
• Investigate Implementation issues and design constraints
– Bounded and underactuated control systems
– Frequency of control law updates
•GlobalAssess
Performance — Try 41It!
Aerospace Corporation
MKH–February 2001
SUMMARY
Global
Aerospace
Corporation
SUMMARY
• Analyzed uniformly distributed constellation
• Have begun study of hurricane chaser application
• AP/WSB control framework developed for stratospheric
circulation
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Global Aerospace

Transcription

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