Predator-Prey Pgeon-Inspred Optmzaton for UAV Three-Dmensonal Path Plannng Bo Zhang 1 and Habn Duan 1,2,* 1 Scence and Technology on Arcraft Control Laboratory, School of Automaton Scence and Electrcal Engneerng, Behang Unversty, Bejng, 1191, P. R. Chna 2 Provncal Key Laboratory for Informaton Processng Technology, Soochow Unversty, Suzhou, 2156, P. R. Chna zhangbo216@163.com, hbduan@buaa.edu.cn Abstract. Pgeon-nspred optmzaton (PIO) s a new bo-nspred optmzaton algorthm. Ths algorthm searches for global optmum through two models: map and compass operator model s presented based on magnetc feld and sun, whle landmark operator model s desgned based on landmarks. In ths paper, a novel Predator-prey pgeon-nspred optmzaton (PPPIO) s proposed to solve the three-dmensonal path plannng problem of unmanned aeral vehcles (UAVs), whch s a key aspect of UAV autonomy. To enhance the global convergence of the PIO algorthm, the concept of predator-prey s adopted to mprove global best propertes and enhance the convergence speed. The comparatve smulaton results show that our proposed PPPIO algorthm s more effcent than the basc PIO and partcle swarm optmzaton (PSO) n solvng UAV three-dmensonal path plannng problems. Keywords: pgeon-nspred optmzaton (PIO), unmanned aeral vehcle (UAV), path plannng, predator-prey. 1 Introducton Three-dmensonal path planner s an essental element of the unmanned aeral vehcle (UAV) autonomous control module [1]. It allows the UAV to compute the best path from a start pont to an end pont autonomously [2, 3]. Whereas commercal arlnes fly constant prescrbed trajectores, UAVs n operatonal areas have to travel constantly changng trajectores that depend on the partcular terran and condtons prevalng at the tme of ther flght. Pgeon-nspred optmzaton (PIO), whch s a new swarm ntellgence optmzer based on the movement of pgeons, was frstly nvented by Duan n 214 [4]. Homng pgeons can easly fnd ther homes by usng three homng tools: magnetc feld, sun and landmarks. In the optmzaton, map and compass model s presented based on magnetc feld and sun, whle landmark operator model s presented based on landmarks. In ths paper, we propose a predator-prey pgeon-nspred optmzaton (PPPIO) method, ntegratng the concept of predator-prey nto PIO n order to mprove ts * Correspondng author. Y. Tan et al. (Eds.): ICSI 214, Part II, LNCS 8795, pp. 96 15, 214. Sprnger Internatonal Publshng Swtzerland 214
Predator-Prey Pgeon-Inspred Optmzaton for UAV Three-Dmensonal Path Plannng 97 capablty of fndng satsfactory solutons and ncreasng the dversty of the populaton. We also solve the UAV three-dmensonal path plannng problem by PPPIO. Smulaton results and comparsons verfed the feasblty and effectveness of our proposed algorthm. The rest of the paper s organzed as follows: Secton 2 provdes the representaton and the cost functon we developed to evaluate the qualty of canddate trajectores. Secton 3 descrbes the prncple of basc PIO algorthm. Secton 4 shows the mplementaton procedure of our proposed predator-prey PIO algorthm. Fnally, we compare the qualty of the trajectores produced by the PIO, partcle swarm optmzaton (PSO) and the PPPIO n Secton 5. 2 Problem Formulaton The frst step of three-dmensonal path plannng s to dscretze the world space nto a representaton that wll be meanngful to the path plannng algorthm. In ths work, we use a formula to ndcate the terran envronment. The mathematcal functon s of the form [5]: 2 2 2 2 zxy (, ) = sn( x/5+ 1) + sn( y/5) + cos( a x + y) + sn( b x + y) (1) where z ndcate the alttude of a certan pont, and a, b are constants expermentally defned. Our representaton of cylndrcal danger zones (or no-fly zones) to be n a separate matrx where each row represents the coordnates (x, y ) and the radus r of the th cylnder as shown n Eq. (2). Complex no-fly zone can be bult by partally juxtaposng multple cylnders x1 y1 r1 x2 y2 r2 danger zones = (2) xn yn rn The three-dmensonal trajectores generated by the algorthm are composed of lne segments and (x, y, z ) represents the coordnates of the th way pont. The trajectores are flown at constant speed. In the stuaton of UAV path plannng, the optmal path s complex and ncludes many dfferent characterstcs. To take nto account these desred characterstcs, a cost functon s used and the path plannng algorthm becomes a for a path that wll mnmze the cost functon. We defne our cost functon as follows [6]: Fcost = Clength + Calttude + Cdanger zones + Cpower + Ccollson + C (3) fuel In the cost functon, the term assocated wth the length of a path s defned as follows: Lp1p2 Clength = 1 ( ) (4) L traj length [,1] C (5)
98 B. Zhang and H. Duan L p1p2 s the length of the straght lne connectng the startng pont P 1 and where the end pont P 2 and L traj s the actual length of the trajectory. The term assocated wth the alttude of the path s defned as follows: Atraj Zmn Calttude = (6) Zmax Zmn Calttude [,1] (7) where Z max s the upper lmt of the elevaton n our search space, Z mn s the lower lmt and A traj s the average alttude of the actual trajectory. Z max and Z mn are respectvely set to be slghtly above the hghest and lowest pont of the terran. The term assocated wth the volaton of the danger zones s defned as follows: C danger zones = L nsde d.z. n d = 1 danger zones [,1] (8) C (9) where n s the total number of danger zones, L nsde d.z. s the total length of the subsectons of the trajectory whch go through danger zones and d s the dameter of the danger zone. The term assocated wth a requred power hgher than the avalable power of the UAV s defned as follows:, Lnot feasble = Cpower = L (1) not feasble P +, Lnot feasble > L traj Cpower [ P, P+ 1] (11) where L not feasble s the sum of the lengths of the lne segments formng the trajectory whch requre more power than the avalable power of the UAV, L traj s the total length of the trajectory and P s the penalty constant. Ths constant must be hgher than the cost of the worst feasble trajectory whch would have, based on our cost functon, a cost of 3. By addng ths penalty P, we separate nonfeasble solutons from the feasble ones. The term assocated wth ground collsons s defned as follows:, Lunder terran = Ccollson = L (12) under terran P +, Lunder terran > L traj
Predator-Prey Pgeon-Inspred Optmzaton for UAV Three-Dmensonal Path Plannng 99 Ccollson [ P, P+ 1] (13) where L under terran s the total length of the subsectons of the trajectory whch travels below the ground level and L traj s the total length of the trajectory. The term assocated wth an nsuffcent quantty of fuel avalable s defned as follows:, Ftraj Fnt Cfuel = F (14) P1P2 P + 1, Ftraj > F nt F traj Cfuel [ P, P+ 1] (15) where F P1P2 s the quantty of fuel requred to fly the magnary straght segment connecton the startng pont P 1 to the end pont P 2, F traj s the actual amount of fuel needed to fly the trajectory, F nt s the ntal quantty of fuel on board the UAV. The search engne wll be adopted to fnd a soluton, whch can mnmze the cost functon durng the optmzaton phase of our path planner algorthm. Ths can also be explaned as to fnd a trajectory that best satsfes all the qualtes represented by ths cost functon. Our cost functon demonstrates a specfc scenaro where the optmal path mnmzes the dstance travelled, the average alttude (to ncrease the stealthness of the UAV) and avods danger zones, whle respectng the UAV performance characterstcs. Ths cost functon s hghly complex and demonstrates the power of our path plannng algorthm. However, ths cost functon could easly be modfed and appled to a dfferent scenaro. 3 Prncple of Basc PIO PIO s a novel swam ntellgence optmzer for solvng global optmzaton problems. It s based on natural pgeon behavor. Studes show that the speces seem to have a system n whch sgnals from magnette partcles are carred from the nose to the bran by the trgemnal nerve [4, 7]. Evdence that the sun s also nvolved n pgeon navgaton has been nterpreted, ether partly or entrely, n terms of the pgeon s ablty to dstngush dfferences n alttude between the Sun at the home base and at the pont of release [8]. Recent researches on pgeons behavors also show that the pgeon can follow some landmarks, such as man roads, ralways and rvers rather than head for ther destnaton drectly. The mgraton of pgeons s summarzed as two mathematcal models. One s map and compass operator, and the other s landmark operator. 3.1 Map and Compass Operator In PIO model, vrtual pgeons are used. In the map and compass operator, the rules are defned wth the poston X and the velocty V of pgeon, and the postons and
1 B. Zhang and H. Duan veloctes n a D-dmenson search space are updated n each teraton. The new poston X and velocty V of pgeon at the t-th teraton can be calculated wth the follows [3]: Rt V( t) = V( t 1) e + rand ( X X ( t 1)) (16) g X () t = X ( t 1) + V () t (17) where R s the map and compass factor, rand s a random number, and X g s the current global best poston, and whch can be obtaned by comparng all the postons among all the pgeons. 3.2 Landmark Operator In the landmark operator, half of the number of pgeons s decreased by N p n every generaton. However, the pgeons are stll far from the destnaton, and they are unfamlar the landmarks. Let Xc () t be the center of some pgeons poston at the t-th teraton, and suppose every pgeon can fly straght to the destnaton. The poston updatng rule for pgeon at t-th teraton can be gven by: X c () t N P NP ( t 1) () t 2 X () t ftness X () t = NP = (18) ( ) ( ()) ftness X t (19) X () t = X ( t 1) + rand ( X () t X ( t 1)) (2) c where ftness s the qualty of the pgeon ndvdual. For the mnmum optmzaton 1 problems, we can choose ftness ( X () t ) = for maxmum f ( X () t ) + ε ftness X () t = f X () t. optmzaton problems, we can choose ( ) ( ) 4 PPPIO for Three-Dmensonal Path Plannng 4.1 Predator-Prey Concept Predatory behavor s one of the most common phenomena n nature, and many optmzaton algorthms are nspred by the predator-prey strategy from ecology [9]. In nature, predators hunt prey to guarantee ther own survval, whle the preys need to be able to run away from predators. On the other hand, predators help to control the prey populaton whle creatng pressure n the prey populaton. In ths model, an ndvdual n predator populaton or prey populaton represents a soluton, each prey n the populaton can expand or get klled by predators based on ts ftness value, and
Predator-Prey Pgeon-Inspred Optmzaton for UAV Three-Dmensonal Path Plannng 11 a predator always tres to kll preys wth least ftness n ts neghborhood, whch represents removng bad solutons n the populaton. In ths paper, the concept of predator-prey s used to ncrease the dversty of the populaton, and the predators are modeled based on the worst solutons whch are demonstrated as follows: Ppredator = Pworst + ρ(1 t / tmax ) (21) where P predator s the predator (a possble soluton), P worst s the worst soluton n the populaton, t s the current teraton, whle t max s the maxmum number of teratons and ρ s the huntng rate. To model the nteractons between predator and prey, the solutons to mantan a dstance of the prey from the predator s showed as follows: Pk+1 = Pk + ρe Pk+1 = Pk ρe d d, d>, d< where d s the dstance between the soluton and the predator, and k s the current teraton. (22) 4.2 Parallelzaton of the Map and Compass Operatons and the Landmark Operatons In the basc model of PIO algorthm, the landmark operaton s used after several teratons of map and compass operaton. For example, when the number of generatons N s larger than the maxmum number of generatons of the map and c N compass operaton c max1. The map and compass operator wll stop and t the landmark operaton wll be start. Durng my experment, we found t s easy to fall nto a local best soluton before the number of generatons got to N c max1. Furthermore, half of the number of pgeons s decreased by N n every generaton on the landmark operator. The populaton of pgeons s decreased too rapdly accordng to formula (18), whch would reach to zero after a small amount of teratons. The landmark operator would make only a small mpact on the pgeons poston by ths way. So we make a small modfcaton on the basc PIO algorthm. The map and compass operaton and the compass operaton are used parallelly at each teraton. A parameter ω s used to defne the mpacton of the landmark ncrease wth a smoothly path. And a constant parameter c s used to defne the number of pgeons that are n the landmark operator. Our new formula of landmark operator s as follows: Pmax p N ( t) = c N c (,1) (23) P X () t c = NP ( ) ( ()) X () t ftness X () t ftness X t (24)
12 B. Zhang and H. Duan ω = s + (1 s) t/ N s (,1) (25) c max X () t = X ( t 1) + ω rand ( X () t X ( t 1)) (26) c where s s a constant expermentally defned. 4.3 Proposed Predator-Prey PIO (PPPIO) Based Path Planner In order to overcome the dsadvantages of the classcal PIO algorthm, such as the tendency to converge to local best solutons, PPPIO, whch ntegrates PIO wth the concept of predator-prey, was proposed n our work. After the mutaton of each generaton, the predator-prey behavor s been conducted n order to choose better solutons nto next generaton. In ths way, our proposed algorthm takes the advantage of the predator-prey concept to make the ndvduals of sub generatons dstrbuted ergodcally n the defned space and t can avod from the premature of the ndvduals, as well as to ncrease the speed of fndng the optmal soluton. The mplementaton procedure of our proposed PIO approach to UAV path plannng can be descrbed as follows: Step 1: Accordng to the envronmental modelng n Secton 2, ntalze the detaled nformaton about the path plannng task. Step 2: Intalze the PIO parameters, such as soluton space dmenson D, the populaton sze N p, map and compass factor R, the number of teraton N c. Step 3: Set each pgeon wth a randomzed velocty and path. Compare the ftness of each pgeons, and fnd the current best path. Step 4: Operate map and compass operator. Frstly, we update the velocty and path of every pgeon by usng Eqs. (16) and (17). Step 5: Rank all pgeons accordng ther ftness values. Some of pgeons whose ftness are low wll follow those pgeons wth hgh ftness accordng to Eq. (23). We then fnd the center of all pgeons accordng to Eq. (24), and ths center s the desrable destnaton. All pgeons wll fly to the destnaton by adjustng ther flyng drecton accordng to Eq. (26). Next, store the best soluton parameters and the best cost value. Step 6: Model the predators based on the worst soluton as Eq. (15) demonstrates. Then, use Eq. (16) to provde the other solutons to mantan a dstance between the predator and the prey. Step 7: If Nc > N, stop the teraton, and output the results. If not, go to step 6. c max 5 Comparatve Expermental Results In order to evaluate the performance of our proposed PPPIO algorthm n ths work, seres of experments are conducted n Matlab212a programng envronment. Coordnates of a startng pont are set as (1, 16, ), and the target pont as (55, 1, ). The ntal parameters of PIO algorthm were set as: NP =15. The comparatve
Predator-Prey Pgeon-Inspred Optmzaton for UAV Three-Dmensonal Path Plannng results of PPPIO wth PIO and PSO are showed as follows:.6 PSO PPPIO PIO.55.5.45.4.35.3.25.2.15.1 2 4 6 8 1 12 14 16 18 2 Fg. 1. Comparatve evolutonary curves of PPPIO, PIO and PSO 1 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 Fg. 2. Comparatve path plannng results of PPPIO, PIO and PSO 7 13
14 B. Zhang and H. Duan 1 4 2 8 6 4 2 1 2 3 4 5 6 7 Fg. 3. Comparatve path plannng results of PPPIO, PIO and PSO on 3D verson 6 Conclusons Ths paper proposed a novel PPPIO algorthm for solvng the UAV three-dmensonal path plannng problem n complex envronments. The concept of predator-prey s adopted to mprove the performance of the basc PIO algorthm. Seres of comparatve smulaton results were gven to show that our proposed PPPIO algorthm s more effcent than basc PIO and PSO n solvng UAV threedmensonal path plannng problems. Acknowledgements. Ths work was partally supported by Natonal Key Basc Research Program of Chna(973 Project) under grant #214CB4641, Natural Scence Foundaton of Chna (NSFC) under grant # 613334 and #6127354, Natonal Magnetc Confnement Fuson Research Program of Chna under grant # 212GB126, and Aeronautcal Foundaton of Chna under grant #213585142. References 1. Chen, H., Wang, X.M., L, Y.: A Survey of Autonomous Control for UAV. In: Internatonal Conference on Artfcal Intellgence and Computatonal Intellgence, vol. 2, pp. 267 271 (29) 2. Duan, H.B., L, P.: Bo-nspred Computaton n Unmanned Aeral Vehcles. Sprnger, Hedelberg (214)
Predator-Prey Pgeon-Inspred Optmzaton for UAV Three-Dmensonal Path Plannng 15 3. Duan, H.B., Luo, Q.N., Ma, G.J., Sh, Y.H.: Hybrd Partcle Swarm Optmzaton and Genetc Algorthm for Mult-UAVs Formaton Reconfguraton. IEEE Computatonal Intellgence Magazne 8(3), 16 27 (213) 4. Duan, H.B., Qao, P.X.: Pgeon-Inspred Optmzaton: A New Swarm Intellgence Optmzer for Ar Robot Path Plannng. Internatonal Journal of Intellgent Computng and Cybernetcs 7(1), 24 37 (214) 5. Ioanns, K.N., Athna, N.B.: Coordnated UAV Path Plannng Usng Dfferental Evoluton. In: IEEE Internatonal Symposum on, Medterrean Conference on Control and Automaton, vol. 7, pp. 77 111. Sprnger, Hedelberg (25) 6. Vncent, R., Mohammed, T., Glles, L.: Comparson of Parallel Genetc Algorthm and Partcle Swarm Optmzaton for Real-Tme UAV Path Plannng. IEEE Transactons on Industral Informatcs 9(1), 132 141 (213) 7. Mora, C.V., Davson, M., Wld, J.M., Mchael, M.W.: Magnetorecepton and Its Trgemnal Medaton n the Homng Pgeon. Nature 432, 58 511 (24) 8. Whten, A.: Operant Study of Sun Alttude and Pgeon Navgaton. Nature 237, 45 46 (1972) 9. Zhu, W.R., Duan, H.B.: Chaotc Predator-Prey Bogeography-Based Optmzaton Approach for UCAV Path Plannng. Aerospace Scence and Technology 32(1), 153 161 (214)