Multiscale Adaptive Sensor Systems

Transcription

1 Multiscale Adaptive Sensor Systems Silvia Ferrari Sibley School of Mechanical and Aerospace Engineering Cornell University ONR Maritime Sensing D&I Review Naval Surface Warfare Center, Carderock 9-11 August 2016

2 Introduction and Motivation Sensor planning: control reconfigurable sensors for collaborative gather information in contested communication environments { Tracking endangered species target control Sensor Model output [1] { Security surveillance task { Search and Rescue [3] [2] [1] [2] [3] 2

3 Information-driven sensor planning Literature Review { Information value comparison [Polcari 13, Kastella 97,... ] { Cell decomposition [Cai 09, Paull 10, Ferrari 09, 12,... ] { Probability road maps and trees [Zhang 09, Lu 10, 12, 14,... ] { Graphical model [Krause 06, 10, 12, Singh 09, Guestrin 05, Meliou 07, Srinivas 12, Le Ny 09,... ] { Advantage: a. Represent information value of measurements for improving the target model b. Can be calculated before measurements are obtained { Disadvantage: a. Can only be applied when target models are known b. Assumptions too restricted: stationary target; discrete and finite control space; unbounded sensor field of view; 3 unconstrained sensor dynamics,...

4 Problem Formulation

5 Assumptions sensor 5

6 Problem Formulation 6

7 Example

8 Information Sufficiency Motivation: Develop planning and control algorithms for collaborative networks with intermittent communications Existing decentralized optimization methods assume constant communications (network is a connected graph) or detailed prior information (perfect models) Consider networks in which some or all nodes (agents) may be disconnected some of the time, and there is no or little prior information (high uncertainty) Agents aim to construct probabilistic model from data Disconnected agents can determine when their own local information is insufficient, and it is time to reestablish communications Model a spatial phenomenon: T( F) Max temperature over a 2D ROI Time invariant Observable at a set of target locations: 8

9 Applications Robot Navigation Traffic Planning Animal Tracking Env. Monitor 1: 2: 3: 4: PRISM Climate Group, Oregon State University, created March

10 Model and Information Value Estimation of spatial phenomenon: estimation Measurements: f(x) ~ Gaussian process Gaussian process: f(x) ~ GP(µ(x), ψ(x 1,x 2 )); µ(x) = E[f(x)] ψ(x 1, x 2 ) = E[( f(x 1 ) µ(x 1 ) )( f(x 2 ) µ(x 2 ) )] Planning objective: at time k choose locations and measurements {y k,z k } to maximize, where, X T = [x 1 x r ], x i T, i = 1,, r ; Y k = [y 1 y k ]; Z k = [z 1 z k ] Since z k is unknown, optimize expected discrimination gain (EDG):

11 Methodology

12 Sensor Planning Framework 12

13 GP Regression Training output Test output Training input Test input 13

14 GP Regression Example Example: Fig. Ground truth Fig. GP regression result 14

15 GP Target Kinematics Model : Target trajectory : Target initial position v x (m/s) 10 8 y (m) x (m) y (m) v y (m/s) x (m) y (m) x (m) { Equivalently: single multi-output GP with diagonal covariance matrix function 15

16 GP Information Value f (x) y x 16

17 GP-EKLD where 17

18 DPGP-EKLD 18

19 DPGP Particle Filter { Time update { Measurement update Target FOV Gaussian distribution Sample of target state 19

20 DPGP-EKLD Approximation Gaussian distribution 20

21 Methodology Part III: Sensor Planning Algorithms Model Update Targets Sensor System Measurements Target Model Control Input Estimated Target States Optimal Planner Objectives Information Value

22 Optimize DPGP-EKLD DPGP-EKLD optimization without sensor dynamics constraints DPGP-EKLD approximation: FOV Sweep line algorithm: segment tree 22

23 Incorporate Sensor Dynamics DPGP-EKLD optimization with sensor dynamics constraints Linear sensor dynamics with constraints: Lower bound: Reward for observing j th target that follows i th VF: FOV 0 Multiple objective optimization -1 2 y (m) x (m)

24 Lexicographic Algorithm Objectives can be ordered by relative importance reorder Remaining iterations: Additional constraints: 24

25 Nominal Network Performance Let Σ denote the covariance matrix and Ψ(x, y) denote the cross-covariance matrix, then the GP average generalization error (AGE), 2 T ε ( k) = Ex Σ( x) Ψ( x, Yk ) Σ( Yk ) + δ I Ψ ( x, Yk ) represent a measure of GP performance. From the latest GP, the posterior covariance, and the network nominal AGE can be estimated from an assumed probability distribution for future measurement locations, and an assumed probability of detection p (b) t 1 [ ] 1 (a) average generalization error, ε(k) p t = 3/4 p t = 1 experimental ε(k) theoretical ε(k) p t = 1/25 p t = 1/ time step, k

26 AGE Communications

27 Communication Control Robot _ i Environment Random Policy Sensor (i) x n Buffer Sender (a) (a) Local GP Receiver Nominal GP Communication Control Approximate nominal average generalization error (AGE) from latest GP 18

28 Communication Control Robot _ i Environment Random Policy Sensor (i) x n Buffer Sender (a) (a) Local GP Receiver Nominal GP Communication Control Approximate nominal average generalization error (AGE) from latest GP Local GP (GPL) computation GPL is updated using local measurements (obtained by robot i) Actual AGE is calculated from the local covariance function. 18

29 Communication Control Robot _ i Environment Random Policy Sensor (i) x n Buffer Sender (a) (a) Local GP Receiver Nominal GP Communication Control Approximate nominal average generalization error (AGE) from latest GP Local GP (GPL) computation Communication time: at the n th time step, the i th robot communicates if max i n k = n ε ( k) ε ( k) > γ 0 i nominal where, is predefined performance threshold. γ 18

30 Communication Control Robot _ i Environment Random Policy Sensor (i) x n Buffer Sender (a) (a) Local GP Receiver Nominal GP Communication Control Approximate nominal average generalization error (AGE) from latest GP Local GP (GPL) computation Communication time Information sharing: all new measurements are communicated and used to update the robot GP 18

31 Communication Control Robot _ i Random Policy (a) Environment Sensor (i) x n Buffer Sender Actual AGE (robot i) Nominal AGE Receiver Robot _ j Environment Local GP Nominal GP Random Policy Sensor ( j) x n Communication Control Buffer (a) Sender average generalization error, ε(k) Current time step, k Local GP Receiver Nominal GP Communication Control 19

32 Communication Control Robot _ i Random Policy (a) Environment Sensor (i) x n Buffer Sender Actual AGE (robot i) Nominal AGE Receiver Robot _ j Environment Local GP Nominal GP Random Policy Sensor ( j) x n Communication Control Buffer (a) Sender average generalization error, ε(k) Current time step, k Local GP Receiver Nominal GP Communication Control 19

33 Communication Control Robot _ i Random Policy (a) Environment Sensor (i) x n Buffer Sender Actual AGE (robot i) Nominal AGE Receiver Robot _ j Environment Local GP Nominal GP Random Policy Sensor ( j) x n Communication Control Buffer (a) Sender average generalization error, ε(k) Current time step, k Local GP Receiver Nominal GP Communication Control 19

34 Communication Control Robot _ i Random Policy (a) Environment Sensor (i) x n Buffer Sender Actual AGE (robot i) Nominal AGE Receiver Robot _ j Environment Local GP Nominal GP Random Policy Sensor ( j) x n Communication Control Buffer (a) Sender average generalization error, ε(k) Current time step, k Local GP Receiver Nominal GP Communication Control 19

35 Simulation Results Modeling of a spatial phenomenon, g(x), by four robots with disjoint workspaces: W 1 W 2 y (Km) W 3 W 4 x (Km) 20

36 Conclusions Conclusion { Developed novel information theoretic functions for GP models of distributed spatio-temporal processes { Developed information-theoretic sensor planning algorithms for distributed networks with bounded fields of view { Developed AGE method for monitoring information sufficiency and schedule communications Future work { Extend information theoretic functions to partially observable targets { Extend information theoretic functions to decentralized control { Develop multiscale adaptive planners to uncertain environments 36

37 Thank you!