A Genetic-Algorithm-Based Approach to UAV Path Planning Problem

Transcription

1 A Genetc-Algorm-Based Approach to UAV Pa Plannng Problem XIAO-GUAG GAO 1 XIAO-WEI FU 2 and DA-QIG CHE School of Electronc and Informaton orwestern Polytechncal Unversty X An CHIA 3 Dept of Info Systems & IT London Sou Bank Unversty London SE1 0AA UK Abstract: - Ths paper presents a genetc-algorm-based approach to e problem of UAV pa plannng n dynamc envronments. Varable- chromosomes and er genes have been used for encodng e problem. We model e vehcle pa as a sequence of speed and headng transtons occurrng at dscrete tmes and s model specfcally contans e vehcle dynamc constrants n e generaton of tral solutons. Smulaton studes have shown at e proposed algorm s effectve n fndng a near-optmal -free pa n a dynamcally changng envronment and e algorm can guarantee at all canddate solutons le wn a feasble and reachable pa space. Key-Words: - UAV Pa plannng Genetc algorm Dynamc envronments Varable- chromosomes 1 Introducton Flght pa plannng s part of Unnhabted Ar Vehcle (UAV) msson plannng and has receved consderable research attenton [1] [2] [3]. In essence flght pa plannng s ultmately responsble for e generaton of a traectory n space whch when followed maxmzes e lkelhood of e UAV completng ts assgned tasks. However most prevous approaches have er drawbacks. In [2] for example e plannng result needs to be optmzed furer to make t flyable to UAV. In s paper we propose an algorm at can overcome s drawback and can plan flght pa effectvely. In s paper a Genetc Algorm (GA) has been developed and used for e UAV pa plannng n a dynamc envronment. Frstly an ntal set of pa genotype strngs wll be generated randomly and e elements of e set are varable- chromosomes. We model e vehcle pa as a sequence of speed and headng transtons occurrng at dscrete tmes and s model specfcally contans e vehcle dynamc constrants n e generaton of tral solutons. Subsequently a new set of pa genotype strngs wll be generated by genetc operatng some of whch wll replace e prevous strngs based on ftness selecton. Ths process s repeated untl some predefned stoppng crtera are met. 2 Genetc Algorm Genetc algorm s a probablstc search algorm whch s motvated by e prncples of evoluton by natural selecton and can be used for searchng effectvely for optmal structures from a number of canddate patterns []. An mplementaton of a genetc algorm begns w a populaton of chromosomes (typcally randomly selected). One en evaluates ese structures and allocates reproductve opportuntes n such a way at chromosomes at potentally provde a better soluton to e target problem are gven more chances to reproduce emselves an ose at potentally lead to poorer solutons. The goodness of a soluton s typcally defned w respect to e current populaton []. 3 UAV Pa Plannng Pa plannng s ultmately responsble for e generaton of a traectory n space whch when followed maxmzes e lkelhood of e UAV completng ts assgned tasks. Wout loss of

2 generalty e pa plannng problem consdered n s paper can be descrbed as follows. Gven: A UAV ntally at locaton ( x0 y 0) ; A target to be reached located at ( xt y T) ; o o A set of s located at ( x y ) = {12... o } respectvely to be avoded; To fnd: A traectory for e UAV ( x y ) = { ( xk y k) } defned at tmes k = { } whch arrves at e target. Ths s equvalent to optmzng a cost functon J( x y ) subect to a set of constrants gx ( y ) = 0. Usually e cost functon J( x y ) s a weghted scalar functon whch must reflect all e forces at conspre to deral e ntensons of e UAV. In s paper e cost functon conssts of several components ncludng cost cost and pa cost. 3.1 Dstance cost J The cost s defned as e from e termnal pont on a pa for e UAV to ts goal locaton. The termnaton tme at e goal locaton t s a free parameter as n s paper we use varable- chromosome to present flght pa. The computaton of J s straghtforward. We defne e J as e Eucldean between e fnal pont on a gven traectory and e target locaton: J = Rx r ( [ t ] T r [ t ]) (1) 3.2 Obstacle cost J For e purposes of s research t s assumed at s n e envronment can be approprately approxmated by crcle (Ths s for a 2-dmensonal case). Thus each s defned by ts tme-varyng center poston and dameter of e crcle. We model UAV as a dsk of radus R UAV and consder ts moton along a partcular pa segment from tme t k to t k + 1 as shown n Fgure 1. So e J s computed by collson detecton. x[k] R UAV R 0 x[ k +1] Fg. 1. cost calculatng An approprate collson detecton scheme would model e moton of bo e UAV and s usng boundng rectangles to capture er movement over each sample nterval. Collson detecton would en nvolve checkng for e ntersecton of each possble par of rectangles and calculatng e ntersecton areas between e UAV pa boundng rectangle and boundng rectangles at each sample nterval. The cost J s equal to e sum of all ntersecton areas. 3.3 Pa Leng cost J The pa cost s used for e planner to fnd out shorter pas. The frst and most obvous choce s to try and lmt e number of ponts n e pa. More specfcally one can try to mnmze e J whch can be expressed as: 1 J = u ( t t ) (2) k k + 1 k k = 0 Where uk s e UAV velocty from tme t k to t k + 1. s e number of e sample ntervals. Proposed GA for UAV Pa Plannng Ths secton dscusses e proposed pa plannng algorm ncludng genetc representaton chromosome decodng e choce of ftness functon and GA operators..1 Genetc Representaton In e presented algorm a chromosome conssts of dfferent sequences of postve ntegers t k

3 at represent a sequence of speed and headng transtons takng place at dscrete tmes { t k k= } respectvely. The possble transtons assumed to be trggered at e start of each nterval tk s us one of e followng. Table 1. Genetc representaton Parameter Genetc representaton u ϕ where u and ϕ denote ncrement n velocty and headng of e UAV respectvely. ote at e orderng of e transtons n Table 1 s arbtrary and e transtons mean at all turns can be done at e maxmum turn rate ϕ& max and all acceleratons/deceleratons can be done at e maxmum value a max. Ths corresponds to an aggressve maneuverng of e UAV. Thus e ndvdual of a populaton can be expressed as a sequence of transtons at reflect e nature of changes n e moton state to be ntated at tme nstant k : r P = [ I2... Il ] (3) where I k ndcates e type of change to be ntated at samplng nterval k and ranges from 1 to 9 n our case..2 Chromosome Decodng Gven a sequence of transtons n speed and headng as dscussed above t s en necessary to generate a correspondng expected traectory for e flght. Ths traectory s typcally requred for evaluaton of e performance of a tral soluton. In e case of 2-dmensonal space gven a constant acceleraton and turn rate as defned by e transton rules n Table 1 e moton of e UAV over an nterval s descrbed by e equatons: uk [ + 1] = uk [ ] + u ϕ[ k+ 1] = ϕ[ k] + ϕ xk [ + 1] = xk [ ] + uk [ + 1]cos( ϕ[ k+ 1]) () yk [ + 1] = yk [ ] + uk [ + 1]sn( ϕ[ k+ 1]) where u s UAV velocty w u mn u u max ϕ s e UAV headng w ϕ ϕmax u and ϕ are e nputs and ( x y ) are nertal UAV poston coordnates. The ratonale for usng e knematcs model s based on e assumpton at ere exst nner and outer loop navgaton control laws whch enable e UAV to track a traectory as long as changes n speed and headng are wn e UAV s moton lmts..3 Ftness Functon The ftness functon nterprets a chromosome n terms of physcal representaton and evaluates ts ftness based on desred trats of e soluton. And e ftness functon must accurately measure e qualty of e chromosomes n e populaton. The ftness functon n e UAV pa plannng problem evaluates e cost of a gven pa. Therefore e ftness functon s defned as follows: 1 f = (5) n ω J ( x y ) = 1 where ( x y ) represents e traectory f s e ftness value of e traectory J ( x y ) represents e cost component of e r n traectory ω R s a weght vector relatng to each component of e cost and n s e total number of e components n s paper n =3. The components of e cost nclude J J and J. The ftness functon of GA s generally an obectve functon at needs to be optmzed. The ftness functon (5) has a lower value f e ftness characterstcs of a chromosome are better an oers. In addton e ftness functon ntroduces a crteron for e selecton of chromosomes.. Genetc Operators..1 Selecton The selecton (reproducton) operator s ntended to mprove e average qualty of e populaton by gvng e hgh-qualty chromosomes a better chance to get coped nto e next generaton. Proportonate selecton s used n our paper...2 Crossover The mechansm of e crossover s e same as at of e conventonal one-pont crossover []. Fg. 2 shows an example of e crossover procedure.

4 2 3 I 7 I 6 I 5 I 2 I 1 I 2 I 7 I 6 I 5 Fg. 2. Example of e crossover procedure..3 Mutaton The populaton undergoes mutaton by an actual change or flppng of one of e genes of e canddate chromosomes ereby keepng away from local optma. * /* C : Input chromosome C : Output chromosome*/ sm = choose _ rand( C);// Randomly choose a node as a mutaton pont C[ sm] = Random(19);// Randomly change e value of e node C* = C; Fg. 3. Pseudo-code of e mutaton [5].. Inserton and Deleton The nserton and deleton operators mplement varable- chromosomes. The nserton operator nserts a gene nto e canddate chromosome. Fg. shows an example of e nserton procedure. The deleton operator deletes a gene from e canddate chromosome. Fg. 5 shows an example of e deleton procedure I 2 I 1 postons as shown n Fgure 6. A target s located at T T ( x y ) = (1-1). In s example e 2 s movng. Fgures 6(a)-(c) show e plannng result by e presented genetc algorm where an assumpton has been made at e movement of e movng s are predctable by assessng ts poston at any pont n tme. (a) Fg.. Example of e nserton procedure 2 3 I3 I Fg. 5. Example of e deleton procedure 5 Expermental Results In s secton some results of pa plannng experments n dynamc envronments are presented usng e proposed algorm. The UAV s assumed ntally at ( x0 y 0) = (0-1) w speed u [0] = 2 and headng ϕ [0] = 0. Speed changes are lmted to 1 w e UAV speed constraned to be an nteger n e range [1 3]. 0 Changes n headng are lmted to ± 30. The envronment rough whch e UAV must navgate o contans ree s ( = 3 ) located at e (b)

5 [5] Chang Wook Ahn R. S. Ramakrshna. A Genetc Algorm for Shortest Pa Routng Problem and e Szng of Populatons. Transactons on Evolutonary Computaton Vol. 6 o pp (c) Fg. 6. Pa plannng n dynamc envronment 6 Concluson Ths paper presented a genetc algorm for solvng e UAV pa plannng problem. The algorm can search e soluton space n a very effectve manner. Smulaton studes show at e algorm s effectve n fndng near-optmal s-free pas n a dynamcally changng envronment. Acknowledgements Ths research work was supported by e atonal ature Scence Foundaton of Chna (grant o ) and e Research Fund for e Doctoral Program of Hgher Educaton (grant o ). References: [1] Bran J. Capozz. Evoluton-based Pa Plannng and Management for Autonomous Vehcles. PhD ess Unversty of Washngton [2] Bortoff S. Pa plannng for UAVs. Proceedng of Amercan Control Conference Chcago USA 2000 pp [3] X. Fu X. Gao and D. Chen. A Bayesan Optmzaton Algorm for e UAV Pa Plannng Problem. Proc. of Internatonal Conference on Intellgent Informaton Processng Oct Beng pp [] Darrell Whtley. A Genetc Algorm Tutoral.