Mobile Sensor Networks for Informative Forecasting Han-Lim Choi Postdoctoral Associate Dept. Aeronautics & Astronautics Massachusetts Institute of Technology.

Mobile Sensor Networks forMobile Sensor Networks forInformative ForecastingInformative Forecasting

Han-Lim Choi

Postdoctoral AssociateDept. Aeronautics & Astronautics

Massachusetts Institute of Technology

Nov. 10, 2009

Research Theme: Research Theme: Networked Information SystemsNetworked Information Systems

• Planning of Sensor Networks– Allocate sensing resources

to extract information– Information quantification in

large-scale systems– Balance between

information and energy

• 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.

[ChoiPhD] H.-L. Choi, “Adaptive sampling and forecasting with mobile sensor networks,” PhD Thesis, MIT.

M u l t i - F u n c t i o n / M u l t i - I n t U A V S e n s o r S u i t e S t u d yM u l t i - F u n c t i o n / M u l t i -M u l t i - F u n c t i o n / M u l t i - I n tI n t U A V S e n s o r S u i t e S t u d y U A V S e n s o r S u i t e S t u d y

N o r t h r o p G r u m m a n P r i v a t e / P r o p r i e t a r y L e v e l I


E l e c t r o n i c S y s t e m s





Han-Lim Choi (MIT), Nov. 10

IntroductionIntroduction• 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

3


IntroductionIntroduction• 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

4

© MIT EAPS

© UC Berkeley


Overall ArchitectureOverall 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

Focus on Planning – given model, make measurement plans

Planning

Models - Environment- Sensor- Uncertainty

Data

Performance Evaluation

EnvironmentSensors

Planning

5


Planning ChallengesPlanning 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

6

Han-Lim Choi (MIT), Nov. 10 7

Weather ForecastingWeather 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)– UAV path planning with considering realistic

weather conditions (e.g., icing, storm) [Rubio04, Frew09]

– 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

4 UAV sensors for better forecast over red squares in

3days


Planning for InformationPlanning 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

8


ApproachApproach• Bi-level decision framework

Better tractability and better accounting for multi-scale dynamics

• Mutual Information– Information-theoretic notion of uncertainty

reduction– Information reward for both abstractions

• Key Focus: Efficient quantification of Mutual Information

8

4o W

7

8o W

72

o W 6

6 oW

60 oW

32oN

36oN

40o N

44o N

48o N

Targeting Motion Planning

Objective Information-rich waypoints

Where to go

Informative SteeringHow to get there

Scale of motion

Long Short

Decision space

Discrete Continuous

Problem Class Combinatorial selection Optimal control

TargetingMotion

Planning


Targeting as Sensor SelectionTargeting as Sensor Selection

• 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

VZ1

Z2Zn

Z3ZS

V : Verification Variables

S : Search Space (N)

s : measurement candidate (n)

time


Forward ApproachForward Approach

• 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)

VZ1

Z2Zn

Z3ZS



V : Verification Variables (M)


Key Intuition for Alternative ApproachKey Intuition for Alternative Approach• Mutual Information

– Represents entropy reduction

– Commutative [Cover91]:

12

Area = Entropy


Backward ApproachBackward Approach

• 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

VZ1

Z2Zn

Z3ZS



V : Verification Variables (M)


Efficiency of BackwardEfficiency of Backward

• Backward approach is never slower than Forward approach

• Significant benefit for ensemble representations

Numerical experiments:

103

102

10

1

104

Ensemble

Covariance

• Probabilistic representations– Covariance vs. Ensemble– Ensemble: typical framework for

weather forecasting• Computation time comparison

– Asymptotic analysis– Numerical experiments

Asymptotic analysis in flops

[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.


Summary of TargetingSummary 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]

• Next: Given where to go, How to get there by maximizing information

[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.

Targeting

8

4o W

7

8o W

72

o W 6

6 oW

60 oW

32oN

36oN

40o N

44o N

48o N

TargetingMotion

Planning

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Continuous ExplorationContinuous Exploration

• 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:


Issues in Continuous PlanningIssues in Continuous Planning

• 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

17


• 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

18

Continuous Mutual InformationContinuous 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

– Difference in mutual information between and before and after knowing


Smoother FormSmoother 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.

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Information Potential FieldInformation 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 objectivesMinimize uncertainty in current state

Minimize uncertainty in V at T


SummarySummary• 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]

• 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

[ChoiACC09] H.-L. Choi and J. P. How, “On the roles of smoothing in planning informative paths,” American Control Conference, June 2009.


Future ResearchFuture 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

– 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.

22

Indoor aerial robots


Future ResearchFuture 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

• 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] 23








E l e c t r o n i c S y s t e m sCooperative UxV missions

Human-robot interactions

©UMBC eBiquity Research Group

Social network


Future ResearchFuture 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 electricity grid

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Air traffic management

Networked wind turbines Building emergency Underwater mixing


Educational SynergyEducational Synergy• Education Philosophy

– Encourage inter-disciplinary thinking– Engineering insights & Mathematical foundation

• why do we care about this • how can we solve it

• 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

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©RPI Center for Innovation in Undergraduate Education


AcknowledgmentAcknowledgment• 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)

26


ReferencesReferences• [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



Probabilistic RepresentationsProbabilistic 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 Square-Root Filter[Whitaker01])

– Preferred for estimation of large-scale nonlinear systems

Comparison of efficiency of backward approach in these two forms

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Motion Planning ResultsMotion Planning Results

• 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

Strategy Reward Type

Optimal minimizing

uncertainty in V at T

0.69 OCP

Gradient-ascent in potential field 0.62 Close

d

Minimize uncertainty

in X at 0.20 OCP

Minimize uncertainty in current X

0.14Close

d

Best Straight-line 0.43 NLP

Worst Straight 0.14 NLP

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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

Confidence

Mobile Sensor Networks for Informative Forecasting Han-Lim Choi Postdoctoral Associate Dept. Aeronautics & Astronautics Massachusetts Institute of Technology.

Documents

dayshanlim choi mit

weather system

weather forecastingexample

supplementary sensing

numerical model of environment

realistic weather conditions

uav path planning

model states