Mobile Sensor Networks for Informative Forecasting Han-Lim Choi Postdoctoral Associate Dept....
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Transcript of Mobile Sensor Networks for Informative Forecasting Han-Lim Choi Postdoctoral Associate Dept....
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
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
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
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
Han-Lim Choi (MIT), Nov. 10
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
Han-Lim Choi (MIT), Nov. 10
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
Han-Lim Choi (MIT), Nov. 10
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
Han-Lim Choi (MIT), Nov. 10
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
Han-Lim Choi (MIT), Nov. 10 9
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
Han-Lim Choi (MIT), Nov. 10 10
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
Han-Lim Choi (MIT), Nov. 10 11
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
S : Search Space (N)
s : measurement candidate (n)
V : Verification Variables (M)
Han-Lim Choi (MIT), Nov. 10
Key Intuition for Alternative ApproachKey Intuition for Alternative Approach• Mutual Information
– Represents entropy reduction
– Commutative [Cover91]:
12
Area = Entropy
Han-Lim Choi (MIT), Nov. 10 13
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
S : Search Space (N)
s : measurement candidate (n)
V : Verification Variables (M)
Han-Lim Choi (MIT), Nov. 10 14
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.
Han-Lim Choi (MIT), Nov. 10
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
15
Han-Lim Choi (MIT), Nov. 10 16
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:
Han-Lim Choi (MIT), Nov. 10
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
Han-Lim Choi (MIT), Nov. 10
• 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
Han-Lim Choi (MIT), Nov. 10
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.
19
Han-Lim Choi (MIT), Nov. 10 20
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
Han-Lim Choi (MIT), Nov. 10 21
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.
Han-Lim Choi (MIT), Nov. 10
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
Han-Lim Choi (MIT), Nov. 10
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
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
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
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
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 sCooperative UxV missions
Human-robot interactions
©UMBC eBiquity Research Group
Social network
Han-Lim Choi (MIT), Nov. 10
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
24
Air traffic management
Networked wind turbines Building emergency Underwater mixing
Han-Lim Choi (MIT), Nov. 10
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
25
©RPI Center for Innovation in Undergraduate Education
Han-Lim Choi (MIT), Nov. 10
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
Han-Lim Choi (MIT), Nov. 10
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
Han-Lim Choi (MIT), Nov. 10
Han-Lim Choi (MIT), Nov. 10
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
29
Han-Lim Choi (MIT), Nov. 10
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
32
Han-Lim Choi (MIT), Nov. 10
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