Value-of-Information Aware Active Task Assignment Aware Active Task Assignment ... Ì Value of EVs: ... Iterates between assignments of EV and TV until the best feasible

Value-of-Information Aware Active Task Assignment

Beipeng Mu, Girish Chowdhary and Jonathan P. How

Laboratory for Information and Decision SystemsDepartment of Aeronautics and Astronautics

Massachusetts Institute of Technology

September 9th, 2013

J.P. How (LIDS, MIT) VoI Task Assignment 09/09/13 1 / 14

Introduction

Motivation

▶Problem: Robustify mission planning to uncertainty caused byclassification errors in situational awareness∎ Uncertainty in target classification

(not just location)∎ Uncertainty impacts mission∎ Heterogeneous UV – explore & exploit∎ Velocity, fuel, time UV constraints

▶Contributions:∎ Evaluate information gathering by

improvement in mission score (VoI)∎ Develop algorithms that couple

exploration activities into taskingactivities

∎ CBBA to incorporate UV constraints∎ Test algorithm in hardware

Target Uncertainty


Introduction

Motivation







Target Uncertainty


Introduction

Motivation







Target Uncertainty


Introduction

Motivation







Target Uncertainty


Introduction

Motivation







Target Uncertainty


Introduction

Robust UV Planning

▶Assign tasking vehicles (TV): mathematical programming [1, 2]

maxN

∑i=1

f(Ci)xi s.t.N

∑i=1

xi ≤ n

∎ Ci: random variable indicating target i’s possible return at time k∎ xi ∈ {0,1}: whether a UV is assigned to do tasks at target i∎ f(C): score function provides quality measure of score distribution C

▶ If score deterministic & known, can use integer programming

▶With score uncertainty, can use various metrics:

∎ Expected score [3] f(C) = E(C)∎ Worst case score [4] f(C) =minC∎ Expected with offset [2] f(C) = µ(C) − σ(C)∎ Chance constraint [5–7]f(C) = c s.t. Prob(C < c) ≤ ε


Introduction

Robust UV Planning


maxN

∑i=1

f(Ci)xi s.t.N

∑i=1

xi ≤ n






Introduction

Robust UV Planning


maxN

∑i=1

f(Ci)xi s.t.N

∑i=1

xi ≤ n






Introduction

Uncertainty Reduction by Exploration

▶Given the importance of score uncertainty to the mission, can use UVto take observations ⇒ uncertainty reduced, performance improved∎ Standard sensor management procedure [8–12]∎ Exploration/exploitation here focused on classification rather than just

localization∎ Extends prior work to non-Gaussian uncertainty distributions

▶ Exploration Vehicles (EV) take observations

▶ EV assignment: maximize uncertaintyreduction based on expected posterior∎ Uncertainty measure: g(Ci)⇒ g(Ci∣zi)∎ zi unknown Ezi[g(Ci∣zi)] = ∫ g(Ci∣zi)dp(zi)∎ Could assign EV based on uncertainty reduction

maxN

∑i=1

(g(Ci) − g(Ci∣zi)) yi s.t.N

∑i=1

yi ≤m

∎ yi ∈ {0,1} denotes whether EV assigned to target i


Introduction

Uncertainty Reduction by Exploration

▶Given the importance of score uncertainty to the mission, can use UVto take observations ⇒ uncertainty reduced, performance improved∎ Standard sensor management procedure [8–12]∎ Exploration/exploitation here focused on classification rather than just

localization∎ Extends prior work to non-Gaussian uncertainty distributions

▶ Exploration Vehicles (EV) take observations

▶ EV assignment: maximize uncertaintyreduction based on expected posterior∎ Uncertainty measure: g(Ci)⇒ g(Ci∣zi)∎ zi unknown Ezi[g(Ci∣zi)] = ∫ g(Ci∣zi)dp(zi)∎ Could assign EV based on uncertainty reduction

maxN

∑i=1

(g(Ci) − g(Ci∣zi)) yi s.t.N

∑i=1

yi ≤m

∎ yi ∈ {0,1} denotes whether EV assigned to target i


Value of Information based Assignment

Assignment of Heterogeneous Vehicles

▶ Straightforward approach:∎ Assign Tasking Vehicle (TV) to maximize score∎ Assign Exploration Vehicle (EV) to maximize uncertainty reduction

Assignments of Tasking/Exploration Vehicles in a decoupled way

TVs and EVs areassigned to differenttargets

Exploration by EVdoes not necessarilyhelp TV obtain higherscore

▶Decoupled Assignment – Information gathered possibly has novalue in terms of mission return [2]



Value of Information based Exploration

▶Real question: What is the value of information gathered?∎ Information gathered will change score distribution of a task

Ezi [f(Ci∣zi)] = ∫ f(Ci∣zi)dp(zi)

▶How to tie information gathering to missions (TV activities)?∎ Exploration adds value only when a TV is also assigned to the target

▶Value of Information based Task Assignment

maxN

∑i=1

Ezif(Ci∣zi)xiyi + f(Ci)xi(1 − yi)

s.t. xi, yi ∈ {0,1}, ∑xi ≤ n, ∑ yi ≤m∎ Recover value of information gathering/exploration activities∎ Note complexity with products of xiyi



Value of Information based Exploration

▶Real question: What is the value of information gathered?∎ Information gathered will change score distribution of a task

Ezi [f(Ci∣zi)] = ∫ f(Ci∣zi)dp(zi)

▶How to tie information gathering to missions (TV activities)?∎ Exploration adds value only when a TV is also assigned to the target

▶Value of Information based Task Assignment

maxN

∑i=1

Ezif(Ci∣zi)xiyi + f(Ci)xi(1 − yi)

s.t. xi, yi ∈ {0,1}, ∑xi ≤ n, ∑ yi ≤m∎ Recover value of information gathering/exploration activities∎ Note complexity with products of xiyi



VoI based Active Task Assignment

Assignments of Tasking/Exploration Vehicles in a coupled way

▶Assignments of EVs are coupled into assignments of TVs∎ EVs and TVs are paired up∎Value of EVs: help TVs to reduce uncertainty and thus get higher score



Consensus-Based Bundle Algorithm (CBBA)

▶ System dynamics and constraints∎ Various features

e.g. Location, speed∎ Cooperation put extra constraints

EV finish exploration before TV starts task∎ Integer programming ⇒ combinational number of candidate solutions

▶ CBBA∎ Given agents and tasks features, give agent-task assignment pairs

▶ Feature∎ Incorporates system dynamics∎ Decentralized∎ Polynomial in number of targets and vehicles



VoI based Coupled Planning using CBBA

Algorithm 1 VoI Based Coupled Distributed Planning

1: initialize candidate solution queue Q2: while UTV requirement not satisfied do3: P = nextBestCandidate(Q)4: Q = {Q, sub-candidates(P) }5: call CBBA to assign UTVs6: AT = CBBA(P, agents, tasks)7: call CBBA to assign UEVs8: AE = CBBA(AT , agents, tasks)9: check whether UTV requirement

10: checkMatch(AT ,AE)11: end while12: return AT , AE

▶ Iterates between assignments of EV and TV until the best feasiblesolution is found.

▶More details in posterJ.P. How (LIDS, MIT) VoI Task Assignment 09/09/13 9 / 14

Numerical Result

Simulation Result

▶NEV = 3 and NTV = 5

▶Targets have uncertainties with categorical distribution

▶ Constraint failure chance: ∀i, f(Ci) = ci s.t. p(Ci < ci) ≤ ε

100 200 300 400 500 600 700 8000

5

10

15

20

25

30

35

40

45

Score

Fre

qu

ency

UTV onlyDecoupledCoupled

Histogram of score

▶ Expected score, decoupled > TV only

▶ Expected score, coupled > decoupled

40 50 60 70 80 90 100 1100

5

10

15

20

25

30

Running Time

Fre

qu

ency


Histogram of expected execution time

▶ No significant impact on execution time


Numerical Result

Simulation Result

▶During execution, when exploration gives new measurements, replanto obtain better assignments

▶Decoupled between coupledand TV only

▶ Less targets ⇒ higher chanceEVs pair up with TVs ⇒ score ofdecoupled ∼ coupled

▶More targets ⇒ less chance EVspair up with TVs ⇒ score ofdecoupled ∼ TV only

0 10 20 30 40 50 60 70 80 90 1000

100

200

300

400

500

600

700

800

900

1000

Number of Tasks

Sco

re


Compares statistics vs. # of targets


Numerical Result

Experiments – Detail in Poster

Robot system in the MIT Aerospace Control Laboratory [13]J.P. How (LIDS, MIT) VoI Task Assignment 09/09/13 12 / 14

Numerical Result

Conclusion and Future Work

▶Conclusion∎ Developed an approach to compute the value of information for

multiagent systems by explicitly coupling the exploration to improvementsin the mission performance

Coupled exploration into mission assignmentsImplemented VoI based coupled planning algorithm in a distributedframework using CBBATested proposed approaches in hardware

▶ Future Work∎ Sub-team size optimization∎ Dynamics in targets

e.g. moving targets where uncertainty of targets may change with time∎ Extend to more general sensing problems

e.g. information gathering in nonparametric models.


Numerical Result References

References I

[1] J. Bellingham, M. Tillerson, A. Richards, and J. How. Multi-task allocation and path planning for cooperating UAVs.In Proceedings of Conference of Cooperative Control and Optimization, Nov. 2001.

[2] Luca F. Bertuccelli. Robust Planning for Heterogeneous UAVs in Uncertain Environments. Master’s thesis,Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, Cambridge MA, June 2004.

[3] J.R. Birge and F. Louveaux. Introduction to Stochastic Programming. Springer Series in Operations Research andFinancial Enginee. Springer, 2011.

[4] Pavlo Krokhmal, Robert Murphey, Panos Pardalos, Stanislav Uryasev, and Grigory Zrazhevski. Robust decisionmaking: Addressing uncertainties. In in Distributions”, In: S. Butenko et al. (Eds.) ”Cooperative Control: Models,Applications and Algorithms, pages 165–185. Kluwer Academic Publishers, 2003.

[5] A. Nemirovski and A. Shapiro. Convex approximations of chance constrained programs. SIAM Journal onOptimization, 17(4):969–996, 2007.

[6] E. Delage and S. Mannor. Percentile optimization for markov decision processes with parameter uncertainty.Operations research, 58(1):203–213, 2010.

[7] L. Blackmore and M. Ono. Convex chance constrained predictive control without sampling. AIAA Proceedings.[np].10-13 Aug, 2009.

[8] Loredana Arienzo. An information-theoretic approach for energy-efficient collaborative tracking in wireless sensornetworks. EURASIP J. Wirel. Commun. Netw., 2010:13:1–13:14, January 2010.

[9] Hanbiao Wang, Kung Yao, and Deborah Estrin. Information-theoretic approaches for sensor selection and placementin sensor networks for target localization and tracking. Communications and Networks, Journal of, 7(4):438 –449, dec.2005.

[10] Feng Zhao, Jaewon Shin, and J. Reich. Information-driven dynamic sensor collaboration. Signal Processing Magazine,IEEE, 19(2):61 –72, mar 2002.

[11] C. Kreucher, M. Morelande, K. Kastella, and A.O. Hero. Particle filtering for multitarget detection and tracking. InIEEE Aerospace Conference, pages 2101 –2116, march 2005.

[12] A. Logothetis, A. Isaksson, and R.J. Evans. An information theoretic approach to observer path design forbearings-only tracking. In Decision and Control, 1997., Proceedings of the 36th IEEE Conference on, volume 4, pages3132 –3137 vol.4, dec 1997.

[13] J. P. How, B. Bethke, A. Frank, D. Dale, and J. Vian. Real-time indoor autonomous vehicle test environment. IEEEControl Systems Magazine, 28(2):51–64, April 2008.


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Value-of-Information Aware Active Task Assignment Aware Active Task Assignment ... Ì Value of EVs: ... Iterates between assignments of EV and TV until the best feasible