Mobile Sensor Networks for
Informative Forecasting
Han-Lim Choi
Postdoctoral Associate
Dept. Aeronautics & Astronautics
Massachusetts Institute of Technology
Nov. 10, 2009
Research Theme:
Networked Information Systems
• Planning of Sensor Networks
– Allocate sensing resources to
extract information
– Information quantification in
large-scale systems
– Balance between information
and energy
[ChoiPhD] H.-L. Choi, “Adaptive sampling and
forecasting with mobile sensor networks,” PhD Thesis,
MIT.
• Multi-Agent Task Planning
– Distributed task allocation over
a network of autonomous
agents
– Realities in dynamic, uncertain
environment
– Interaction with humans
[ChoiTRO09] H.-L. Choi, L. Brunet, and J. P. How,
“Consensus-based decentralized auctions for robust task
allocation,” IEEE Transactions of Robotics, 25(4), 2009.
Introduction
• Forecasting of Environmental Systems
– Increasing potential damages due to adverse environmental
conditions (e.g., snow storms, hurricanes)
– Need accurate forecasting of future environmental conditions
• Intelligent Measurement Systems
– Under limited sensing and computation resources
– Allocate fixed or redeployable sensors to gather information
directed by particular interests
Han-Lim Choi (MIT), Nov. 10
3
Introduction
• This research
– Theoretical framework for intelligent measurement systems for
improved forecasting of large-scale systems
• Applications
– Weather forecasting, Plume source tracking, Wildfire tracking,
Geoscientific investigation, Smart building
© MIT EAPS
© UC Berkeley
Han-Lim Choi (MIT), Nov. 10
4
Overall Architecture
• Dynamic Data-Driven Loop Closure
– Use model to make measurement plans ) Plan execution ) Use
collected data to update model/plans
– Integration of physical environment, (mobile) sensors,
numerical model of environment, planning & control algorithms
Sensors
Models
- Environment
- Sensor
- Uncertainty
Performance
Evaluation
Environment
Planning
Planning
Data
Focus on Planning – given model, make measurement plans
Han-Lim Choi (MIT), Nov. 10
5
Planning Challenges
• Environmental dynamics nonlinear and typically have
large state dimension
– E.g. weather system ~O(106)
• Multi-scale dynamics
– What is the right choice of time- and length-scale to make the
decisions of interest?
• Uncertainty in model states, parameters, and
observations
– Need to be able to quantify uncertainty propagation
through large-scale nonlinear dynamics
• Planning: Large-Scale Complex Optimization
Han-Lim Choi (MIT), Nov. 10
6
Weather Forecasting
• Example: Improve weather forecast by
developing supplementary sensing networks
with teams of Unmanned Aerial Vehicles
• Related work
– Targeting for crewed aircraft to localize
error-sensitive or error-reducing
regions [Lorenz98,Palmer98, Majumdar02, Daescu04]
• High cost, high risk, less adaptability
– NOAA’s Unmanned Aerial Vehicles Program
(announced ’08)
4 UAV sensors for better forecast
– UAV path planning with considering realistic
over red squares in 3days
[Rubio04,
Frew09]
weather conditions (e.g., icing, storm)
– Development of Micro Air Vehicles for weather sensing[Lawrence07]
• This work: higher level decision on where and when to take
measurement using network of mobile sensors
Han-Lim Choi (MIT), Nov. 10
7
Planning for Information
• Design mobile sensor networks to extract best possible information
– Objective: Reduce uncertainty in knowledge about some
environmental quantities of interest at some time of interest (called
verification variables and time)
– Quantification: Define information reward of sensing path to
represent uncertainty reduction
– Complications:
• Combinatorial decision making
• Constraints in mobility, communication, power
• More complicated if large state dimension and/or long verification horizon
– Most previous work in the context of tracking targets (small state)
• Goal: Efficient algorithms for allocation of mobile sensor networks
in a large-scale complex systems for maximum information
Han-Lim Choi (MIT), Nov. 10
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Approach
• Bi-level decision framework
 Better tractability and better accounting for multi-scale dynamics
Scale of motion
Long
Short
Decision space
Discrete
Continuous
Problem Class
Combinatorial selection
Optimal control
o
o
72 W
Informative Steering
How to get there
78oW
Information-rich waypoints
Where to go
84 oW
Objective
o
60 W
Motion Planning
66 W
Targeting
o
48 N
• Mutual Information
– Information-theoretic notion of uncertainty
reduction
– Information reward for both abstractions
• Key Focus: Efficient quantification of Mutual
Information
Han-Lim Choi (MIT), Nov. 10
o
44 N
Motion
Targeting
Planning
o
40 N
o
36 N
o
32 N
9
Targeting as Sensor Selection
s : measurement
candidate (n)
Z1
Z3
ZS
V
Z2
S : Search Space (N)
Zn
V : Verification
Variables
time
• Objective: Select n sensing points from search space that maximize
uncertainty reduction of verification variables (V )
–
–
: entropy of V (i.e., degree of randomness)
: conditional entropy of V after knowing
• Baseline formulation for problems with dynamics and constraints
Han-Lim Choi (MIT), Nov. 10
10
Forward Approach
s : measurement
candidate (n)
Z1
Z3
ZS
V
Z2
S : Search Space (N)
Zn
V : Verification
Variables (M)
• Explicitly compute conditional entropy for all possible measurement
candidate
–
: same for all candidates  minimize conditional entropy
– Gaussian  Entropy = log det of Covariance
• Issues: Computational complexity
– Combinatorial number of candidates
(75 million for N=100, n=5)
– Calculation of each conditional entropy takes non-trivial time
(Covariance update, determinant calculation)
Han-Lim Choi (MIT), Nov. 10
11
Key Intuition for Alternative Approach
• Mutual Information
– Represents entropy reduction
– Commutative [Cover91]:
Area = Entropy
Han-Lim Choi (MIT), Nov. 10
12
Backward Approach
s : measurement
candidate (n)
Z1
Z3
ZS
V
Z2
S : Search Space (N)
Zn
V : Verification
Variables (M)
• Look at entropy reduction of measurement candidate
– Motivated by
[Williams05]
but identified new insights:
• Single covariance update to compute conditional
covariance of entire search space
– Calculation of
: submatrix extraction
– Still combinatorial number of determinant calculation
Han-Lim Choi (MIT), Nov. 10
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Efficiency of Backward
• Probabilistic representations
– Covariance vs. Ensemble
– Ensemble: typical framework for
weather forecasting
• Computation time comparison
– Asymptotic analysis
– Numerical experiments
Numerical experiments:
104
103
Ensemble
102
Asymptotic analysis in flops
10
Covariance
1
• Backward approach is never slower than Forward approach
• Significant benefit for ensemble representations
[ChoiACC07] H.-L. Choi, J. P. How, and J. A. Hansen, “Ensemble-based adaptive targeting of mobile sensor
networks,” American Control Conference, 2007.
[ChoiTCST09] H.-L. Choi, and J. P. How, “Efficient targeting of sensor networks for large-scale systems,”
IEEE Transactions on Control Systems Technology, submitted.
Han-Lim Choi (MIT), Nov. 10
14
Summary of Targeting
• Commutative mutual information  backward
– Provable efficiency over forward approach by reducing the
number of covariance updates
– Significant computational saving for ensemble-based large-scale
targeting
• Constrained problem can be embedded in the backward
framework [ChoiGNC07]
o
72 W
78oW
o
60 W
o
66 W
84 oW
[ChoiGNC07] H.-L. Choi and J. P. How, “A mult-UAV targeting algorithm for ensemble forecast improvement,”
AIAA Guidance, Navigation, and Control Conference, Aug. 2007.
o
48 N
o
44 N
• Next: Given where to go, How to get there
by maximizing information
Motion
Targeting
Planning
o
40 N
o
36 N
Targeting
o
32 N
Han-Lim Choi (MIT), Nov. 10
15
Continuous Exploration
During 0 to t
θ
At T
Forecast
Verification
Sensing path
• Linear environmental dynamics:
– State variables Xt : environmental variables at grid points
– Short time-scale/local behavior of original nonlinear dynamics
– Additive Gaussian process noise
• Linear measurement:
– Off-grid measurement = linear combination of state variables
• Vehicle Motion:
Han-Lim Choi (MIT), Nov. 10
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Issues in Continuous Planning
During 0 to t
θ
At T
Forecast
Verification
Sensing path
• Continuous abstraction
– Better models environmental sensing
– Better scalability than increasing resolution of discrete targeting
• Issues
– Less-established theory on computation of mutual information
– Simple extension of previous work is computationally inefficient
Han-Lim Choi (MIT), Nov. 10
17
Continuous Mutual Information
• Straightforward way:
– Explicitly calculate entropy of verification variables at T
– Need to integrate matrix differential equations for long time
interval
to propagate effect of measurement into the future
 Computational inefficiency in optimal planning
• Mutual Information by conditional independence
– Once the state is known at the current time, no additional
information can be obtained from the past in order to predict
some future quantity
– Difference in mutual information between
before and after knowing
Han-Lim Choi (MIT), Nov. 10
and
18
Smoother Form
• Smoother form mutual information
–
–
–
: inverse covariance of state (Lyapunov)
: inverse covariance of state conditioned on V (Lyapunov-like)
: covariance of state conditioned on measurement (Riccati)
• In planning, integration of matrix differential equation during
 Computation time reduction by factor of
• On-the-fly track of information accumulation at arbitrary time t
 Expression of rate of information accumulation [Choi08cdc & Choi09auto]
[ChoiCDC08] H.-L. Choi and J. P. How, “Continuous motion planning for information forecast,” IEEE Conference
on Decision and Control, Dec. 2008.
[ChoiAuto09] H.-L. Choi and J. P. How, “Continuous trajectory planning of mobile sensors for informative
forecasting,” Automatica, submitted.
Han-Lim Choi (MIT), Nov. 10
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Information Potential Field
• Distribution of information based on rate of information
accumulation
– Instantaneous information increment when taking measurement
at location (x,y) at time t
• Variation by design objectives
Minimize uncertainty in V at T
Han-Lim Choi (MIT), Nov. 10
Minimize uncertainty in current state
20
Summary
• Conditional Independence  Smoother Form
– Computational efficiency by reducing interval of integration of
matrix differential equations
– On-the-fly access to information accumulation  Legitimate
information potential field
– More insights in broader class of planning problem [ChoiACC09]
[ChoiACC09] H.-L. Choi and J. P. How, “On the roles of smoothing in planning informative paths,”
American Control Conference, June 2009.
• Key Contributions:
– Efficient quantification of information reward: Backward and
Smoother
– Information-theoretic planning of mobile sensor networks in the
context of weather forecasting
 Guideline for tractable design of measurement systems for
multi-scale complex nonlinear systems
Han-Lim Choi (MIT), Nov. 10
21
Future Research
• Long-term goal: Innovations in Robotics and Control towards
Ubiquitous Intelligent & Sustainable Living Environment
• Information-driven decision making (for cyber-physical systems)
– Sensor/actuator networks for large-scale systems
• Richer class of uncertainties and constraints
– Enrich notions of information
• How to define information in constrained space
• How to incorporate notions like risk & safety
Indoor aerial robots
– Navigation and control of autonomous robots
– Uncertainty quantification & Design of experiments for complex systems
– Funding sources
• NSF cyber-physical systems, NSF cyber-enabled discovery & innovation
– Related on-going work
• Planning for mobile sensor networks with model uncertainty
• Sensor management under limited communication budget [ChoiACC08]
[ChoiACC08] H.-L. Choi, J. P. How, and P. I. Barton, “An outer-approximation algorithm for generalized
maximum entropy sampling,” American Control Conference, June 2008.
Han-Lim Choi (MIT), Nov. 10
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Future Research
• Networked (semi)-autonomous vehicles
– Distributed decision making
• Robustness in dynamic, uncertain environments
• Multi-agent learning & information fusion
– Interaction of humans and autonomy
– Fundamental theories of networks
Cooperative UxV missions
• Information flow in heterogeneous networks
– Funding sources
• AFOSR, ONR, ARO, NSF Network science &
engineering
– Related on-going work
• Distributed task allocation algorithm for network of
agents robust to inconsistent situational
awareness
• Its extensions to handle: complex missions
[Choi10acc, Ponda10acc], uncertainty [Bertuccelli09gnc,
Redding10acc], human-autonomy interaction [Ponda10info]
• Distributed decisions for sensor networks [Choi07gnc]
Human-robot interactions
©UMBC eBiquity
Research Group
Social network
Han-Lim Choi (MIT), Nov. 10
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Future Research
• New Applications (in Aerospace, Energy, Environment)
–
–
–
–
Geosciences, Weather, Climate
Air traffic management
Smart building, Water resource
Smart grid, Sustainable energy
• Collaborations
– Center for automation technologies and systems
– Multi-scale science and engineering
– Scientific computation research center
Networked wind turbines
Han-Lim Choi (MIT), Nov. 10
Networked electricity grid
Air traffic management
Building emergency
Underwater mixing
24
Educational Synergy
• Education Philosophy
– Encourage inter-disciplinary thinking
– Engineering insights & Mathematical foundation
• why do we care about this
• how can we solve it
©RPI Center for Innovation in
Undergraduate Education
• Educational impacts
– Graduate research
– Undergraduate research
• Modeling/analysis/optimization of a variety of systems
• Hands-on experiments with multi-robot testbeds
– Existing curriculum
• Enrich description of system dynamics
– Curriculum development
• Senior: Introduction to high-level control & autonomy
• Graduate: Decision making under uncertainty
Han-Lim Choi (MIT), Nov. 10
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Acknowledgment
• NSF Dynamic Data Driven Application System
• AFOSR, ONR, Boeing
• Collaborators:
–
–
–
–
–
–
–
Prof. Jonathan P. How (MIT Aero/Astro)
Prof. Nicholas Roy (MIT Aero/Astro)
Dr. James A. Hansen (Naval Research Laboratory)
Prof. Paul I. Barton (MIT ChemE)
Prof. Emilio Frazzoli (MIT Aero/Astro)
Sooho Park, Daniel Gombos (MIT DDDAS)
Luca Bertuccelli, Luc Brunet, Cameron Fraser, Sameera Ponda,
Andrew Whitten, Josh Redding (MIT ACL)
Han-Lim Choi (MIT), Nov. 10
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References
•
[Lorenz98] E. Lorenz and K. Emanuel, “Optimal sites for supplementary weather observations: simulation with a small model,”
Journal of the Atmospheric Sciences, 55(3), pp. 399-414.
• [Parmer98] T. Palmer, R. Celaro, J. Barkmeijer, and R. Buizza, “Singular vectors, metrics, and adaptive observations,” Journal
of the Atmospheric Sciences, 55(4), pp. 633-653.
• [Majumdar02] S. Majumdar, C. Bishop, B. Etherton, and Z. Toth, “Adaptive sampling with the ensemble transform Kalman
filter. Part II: Filed programming implementation,” Monthly Weather Review, 130(3), pp. 1356-1369.
• [Daescu04] D. Daescu and I. Navon, “Adaptive observations in the context of 4D-var data assimilation,” Meteorology and
Atmospheric Physics, 85(111), pp. 205-226.
• [Williams05] J. Williams, J. Fisher III, and A. Willsky, “An approximate dynamic programming approach to a communication
constrained sensor management,” Int’l conf. of Information Fusion, 2005.
• [Cover91] T. Cover and J. Thomas, Elements of Information Theory. Wiley Series In Telecommunications, 1991.
• [Rubio04] J.C. Rubio, J. Vagners, R. Rysdyk, “Adaptive path planning for autonomous UAV oceanic search missions,” AIAA
Intelligent Systems Technical Conference, 2004.
• [Frew09] J. Elston, E. W. Frew, “Unmanned Aircraft Guidance for Penetration of Pre-Tornadic Storms,” AIAA Journal of
Guidance, Control, and Dynamics, 2009.
• [ChoiACC10] H.-L. Choi, A.K. Whitten, and J.P. How, "Decentralized task allocation for heterogeneous teams with coordination
constraints," American Control Conference, Baltimore, MD, USA, July 2010, submitted.
• [PondaInfo10] S. Ponda, H.-L. Choi, and J.P. How, "Predictive planning for heterogeneous teams with human agents," AIAA
Infotech@Aerospace, Atlanta, GA, USA, Apr. 2010, submitted.
• [PondaACC10] S. Ponda, J. Redding, H.-L. Choi, J.P. How, B. Bethke, M. A. Vavrina, and J. Vian, "Distributed task planning for
complex missions with communication constraints,"American Control Conference, Baltimore, MD, USA, July 2010, submitted.
• [ReddingACC10] J. Redding, H.-L. Choi, and J.P. How, "An intelligent cooperative control architecture,"American Control
Conference, Baltimore, MD, USA, July 2010, submitted.
• [ChoiTRO09] H.-L. Choi, L. Brunet, and J.P. How, "Consensus-based decentralized auctions for robust task allocation," IEEE
Trans. on Robotics, , Vol. 25, No. 4, pp. 912 - 926, 2009
• [ChoiAuto09] H.-L. Choi and J.P. How, "Continuous trajectory planning of mobile sensors for informative
forecasting,"Automatica, submitted
• [ChoiTCST09] H.-L. Choi and J.P. How, "Information-theoretic targeting of sensor networks for large-scale systems," IEEE
Trans. on Control Systems Technology, submitted
• [ChoiACC09] H.-L. Choi and J.P. How, "On the roles of smoothing in informative path planning," American Control Conference,
St.Loius, MO, USA, June 2009, submitted.
• [ChoiCDC08] H.-L. Choi and J.P. How, "Continuous motion planning for information forecast," IEEE Conference on Decision
and Control, Cancun, Mexico, Dec. 2008.
• [ChoiACC07] H.-L. Choi, J.P. How, and J.A. Hansen, "Ensemble-based adaptive targeting of mobile sensor networks,"
American Control Conference 2007, New York City, NY, USA, July 2007.
• [ChoiGNC07] H.-L. Choi and J.P. How, "A multi-UAV targeting algorithm for ensemble forecast improvement," AIAA Guidance,
Navigation, and Control Conference 2007, Hilton Head, SC, USA, Aug. 2007, AIAA-2007-6753.
• [ChoiACC08] H.-L. Choi, J.P. How, and P.I. Barton "An outer-approximation algorithm for generalized maximum entropy
sampling," American Control Conference 2008, Seattle, WA, USA, June 2008
Han-Lim Choi (MIT), Nov. 10
Han-Lim Choi (MIT), Nov. 10
Probabilistic Representations
• Covariance Form
– Mean and covariance
– Conditional distribution: Update covariance (Kalman Filter[Grewel01])
• Ensemble Form
– Monte-Carlo samples (a total of LE )
– Covariance is approximated as sample covariance
– Conditional distribution: Update each sample (Ensemble SquareRoot Filter[Whitaker01])
– Preferred for estimation of large-scale nonlinear systems
 Comparison of efficiency of backward approach in these
two forms
Han-Lim Choi (MIT), Nov. 10
29
Motion Planning Results
Strategy
Reward
Optimal minimizing
0.69
uncertainty in V at T
Gradient-ascent in
0.62
potential field
Minimize uncertainty
0.20
in X at
Minimize uncertainty
0.14
in current X
Best Straight-line
0.43
Worst Straight
0.14
Type
OCP
Closed
OCP
Closed
NLP
NLP
• Goal: 6-hr sensing trajectory to reduce uncertainty over
in 3 days
• Optimal Control Problem solution by NLP reformulation (<2mins per
initial guess)
• Reasonable performance of gradient-ascent
• Potential performance degradation in decisions based on short-term
perspectives
Han-Lim Choi (MIT), Nov. 10
32
Probability of Correct Decision (PCD)
• PCD = Prob [ Correctly distinguish the best candidate from a total of q
candidates] = PCD (RNR, q)
– Expressed as CDF of (q-1)-dimensional multivariate normal distribution
• ε-PCD = Prob [ Better than (1- ε)-optimal solution obtained ]
≈ PCD (RNR, 1/ε)
– Useful for large-scale targeting with very large q
• Useful quantification:
– Required RNR to achieve given level
of optimality with a certain surety
• RNR=16.5 for 90% optimality with
90% confidence
– Achievable level of Optimality for
given RNR with a certain surety
• 75% optimality guaranteed for
RNR=6 with 90% confidence
Han-Lim Choi (MIT), Nov. 10
Confidence