An Integrated Asset Allocation and Path Planning Method to to Search for a Moving Target in in a Dynamic Environment

Transcription

1 An Integrated Asset Allocaton and Path Plannng Method to to Search for a Movng Target n n a Dynamc Envronment Woosun An Mansha Mshra Chulwoo Park Prof. Krshna R. Pattpat Dept. of Electrcal and Computer Engneerng Unversty of Connectcut Tel./Fax: (860) /5585 E-mal: krshna@engr.uconn.edu June 3, 010

2 Outlne Ant-submarne Warfare (ASW) Search Problem ASW search ssues Search Plannng usng Hdden Markov Models (HMM) Asset/sensor capablty modeled usng emsson matrx Submarne trajectory modeled usng transton matrx Search Plannng Involves Two Phases Phase 1 : Search regon partton and asset allocaton Geographc parttonng va an evolutonary algorthm, coupled wth a Vorono tessellaton approach Assgnment of regons va Aucton algorthm Phase : Search path optmzaton Optmal search path va an evolutonary algorthm Smulaton Results Summary

3 ASW Allocaton and Search Issues ASW search ssues Search should be contguous Conflct avodance among search assets Dynamc asset assgnment and search paths Meteorologcal and Oceanographc effects on search assets and targets Multple objectves (e.g., maxmze probablty of detecton, mnmze rsk to hgh value assets (e.g., carrer), etc.)

4 MM-based Asset Allocaton / Search Plannng - 1 Hdden Markov Model (HMM) en state rvatons Ms Descrbe Dynamcs of Uncertan Tasks HMMs are useful for analyzng sequental data, where the true states of a task are hdden (e.g., enemy submarne s locaton) Enables us to nfer the true task state from uncertan observatons (ncludng ntellgence) M Model Parameters Pror probablty vector (Intellgence) State transton dynamcs (Transton matrx), e.g., envronment, submarne moton patterns Uncertan observatons (Emsson matrx), e.g., asset/sensor capablty to detect targets Imprecse measurements of state Dfferent nformaton sets and accuraces Pror probablty vector [ ] Px ( (1) S) Transton matrx A aj P(( x k1) j x() k ) Pd (emsson probablty) map Emsson matrx j B b P(() y k l (() x k, u () k j)) Current target locaton Neghbor cells Target moton, j: Cell ndex ASW asset observaton probablty

5 MM-based Asset Allocaton / Search Plannng - bmarne Trajectory Transton Matrx nston matrx A a j P (( x k 1) j x() k )) or each cell, choose the cell transton model relevant submarne trajectory hypothess rne trajectory hypothess 0 h Probablty w Probablty Submarne path model usng state transton matrx Actve Sonar Equaton SE ( SL TL TL TS) ( NL DI) DT SL: Source level, DI: Drectvty ndex SE: Sgnal excess, DT: Detecton threshold TS: Target strength, NL: Nose level TLST: Transmsson loss from source to target TLTR: Transmsson loss from target to recever Emsson Probablty Model Gven the envronmental parameters (wnd, shppng densty, wave heghts, etc), talored products (e.g., Wentz Curve, etc) are used to determne the nose level (NL) Pyk ( ( ) 1 xk ( ) 1) P Detecton D Pyk ( ( ) 0 xk ( ) 1) 1P Mssng D No target Pyk ( ( ) 0 xk ( ) 0) 1PF Pyk ( ( ) 1 xk ( ) 0) P False alarm F If non-observable yk ( ) 1: Detecton yk ( ) 0: Non-Detecton xk ( ) ST TR 1: f submarne = cell j = asset Null observaton Asset Current cell locaton Observable regon

6 HMM-based Search Problem sensors are assgned to N X M cells to search for a movng target (partally bservable restless bandt) modeled usng a HMM tegrated asset allocaton and path plannng Gven total search tme, defne the search regon and the search path for each asset Assgnment Search path State-dependent perodc re-assgnment bjectve functon maxmze detecton probablty of target

7 ( K/ T) 1 T m 1 Mathematcal Problem Formulaton h max ( k k 1) b ( k) ( k) v0 t1 1 ja( Tv1) hdj h jlr j where k Tvt, v 0,...,( K / T) 1, t 1,..., T m s.t. A( Tv1) A, A A, j, v 0,...,( K / T) 1 ja ( Tv1) j ( vt 1) 1,, v 0,...,( K / T ) 1, (b) j ( vt t) ( vt t 1) 0,, t,..., T 1, v 0,...,( K / T) 1, (c) j ja C A C A j ( Tv1) j ( Tv1) ( Tv1) C j ( vt ) 1,, v 1,...,( K / T ) 1 (d) j Asset should travel to all regons of A wthout crossng over A, n (e) ( k) {0,1}, 1,..., m, j 1,..., MN, k 1,..., K (f) j n (a) Constrant (a) ensures that the assets are assgned to mutually exclusve search areas (.e., no two assets are assgned to the same regon) Constrant (e) ensures contguty of search actvtes. Constrants (b), (c) and (d) ensure that the searcher s move s constraned only to the neghborng cells from the current cell wthn the assgned regon

8 Soluton Approach / Phase 1 Vorono tessellaton Phase 1: Asset allocaton Employs an evolutonary algorthm, coupled wth the Vorono tessellaton approach, for search regon parttonng Each ndvdual n the populaton sequence of centers of Vorono cells Vorono tessellaton s used for ensurng contguty and to obtan a near-optmal soluton Partton the search space nto cells based on some metrc (e.g., Eucldean dstance) Solve the assgnment problem of allocatng assets to Vorono cells va the aucton algorthm

9 utaton process for next generaton of search path Soluton Approach / Phase Phase : Search path Solve the optmal search path selecton problem va an evolutonary algorthm Each ndvdual n the populaton Search path sequence. ssover process for next generaton of search path Crossover If parents A and B are selected for crossover and f they share any common genes, the chld can be produced by exchangng the segments of parent A wth that of parent B Mutaton A gene s randomly selected and mutated by dsplacng t from the orgnal locaton (e.g., left, rght, up or down) Addtonal genes are ntroduced to mantan a contguous search path Some genes are removed to satsfy the total search effort constrant

10 Sngle Searcher, Sngle Target Problem - 1 One searcher and one target problem Target and searcher move among the 9 cells Searcher s move s constraned to 5 move optons (.e., no move, up, down, left, rght) or 4 neghborng cells (.e., up, down, left, rght) The total search tme allotted to each asset s K=10 tme unts Submarne moton pattern s modeled va a transton matrx The target starts n cell 9 Detecton s certan f the target s n the cell currently beng searched Pyk ( ( ) detecton submarne locaton cell jasset locaton) q j 1 V( ( k), ) maxmum obtanable probablty of detecton wth K k tme perods n cell V( ( k1), ) mn{ q ( k) (1 q ( k)) V( ( k), j)} jc j j j j Dynamc programmng recurson Detecton Non-Detecton

11 Sngle Searcher, Sngle Target Problem - Results When the searcher ntates search n cell 1, the optmal detecton probabltes are the same n both the cases (4 or 5 move optons) If the search s ntated n other cells, the detecton probablty dffers n both the cases As the sensor capabltes deterorate (e.g., due to weather), the target detecton probablty decreases

12 Three Searchers, Sngle Target Problem nterference Model Suppose assets are conductng the search actvty n non-overlappng partton regons Assumpton: the assets do not observe any valuable nformaton wthn the nterference regon Observaton probablty wthn the nterference regon s gven as: D : D D Set of observable cells for asset j Interference regon yk ( ) Non-observable Asset Allocaton / Search Plannng Example Objectve: Gven an area of 0x0 search cells, allocate three assets of equal search capablty to maxmze the detecton probablty Each asset s allotted K=0 tme unts Searcher s move s constraned only to the neghborng cells (.e.,,,, ) Nomnal value for SE s used for emsson probablty setup Anmaton shows the asset allocaton and nformaton state for tme unts k=1 to 0 Illustratve Search Regon Partton

13 Probablty Map of Target Locaton x x k= Current target locaton Target trajectory Asset locaton Observable regon (3x3 cells) x k= x

14 Summary Problem: Movng target search problem usng a HMM framework Formulaton and model of search path problem usng a hdden Markov Model Modelng Approach: Hdden Markov Models Asset/sensor capablty modeled usng emsson matrx Submarne trajectory modeled usng transton matrx -Phase Soluton Approach Phase 1 : Search regon partton and asset allocaton Phase : Search path optmzaton Applcaton One searcher - one target Multple searchers - one target Future Work Multple searchers - multple targets Intellgent targets