A Pesticide Spraying Mission Assignment Performed by Multi-Quadcopters and Its Simulation Platform Establishment*

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1 Poceedings of 6 IEEE Chinese Guidance, Navigation and Contol Confeence August -4, 6 Nanjing, China A Pesticide Spaying Mission Assignment Pefomed by Multi-Quadcoptes and Its Simulation Platfom Establishment* Luo Yao, Yan Jiang, Zhao Zhiyao, Yang Shuaishuai and Quan Quan Abstact his pape poposes a new mission assignment scheme aimed at the famland spaying poblem by using the plant-potection-quadcoptes. A mathematical model of the mission assignment poblem is established by simplifying some mino factos of the optimization poblem and a Sequential Quadatic Pogamming (SQP) method is used to obtain the optimal solution. hen, a simulation platfom is established and a seies of simulations ae caied out to veify the easonability and coectness of this mission assignment scheme. I. INRODUCION Quadcoptes [], [] ae well-suited to a wide ange of mission scenaios, such as seach and escue [3], [4], pacage delivey [5], bode patol [6], militay suveillance [5], [7] and agicultual poduction [8]. Fo agicultual poduction, the plant-potection-quadcoptes has been moe and moe widely used because of the shotage of ual labo foce and the demand fo high efficiency. With advancements in electonics and aifames, nowadays, the development diection of plant potection should be lage-scale and high-efficiency with multi-aicafts [9], []. Since the efom and opening up, Chinese govenment has eleased Agicultue, Rual aeas and Fames as the No. Cental Document fo 8 times to solve it. In paticula, since 4, the agicultual modenization is witten into the title of the No. Cental Document fo thee consecutive yeas. hese documents indicate that thee is an ugent need to push fowad the building of new socialist countyside, acceleate the tansfomation of the development mode of agicultue, acceleate agicultual modenization, and deepen ual efoms compehensively. In ecent yeas, many specific favoable policies elated to civil aviation industy and plant potection have been announced by the Ministy of Agicultue of China, Civil Aviation Administation of China and the State Council. hese policies indicate that civil aviation industy is an impotant stategic industy fo the social and economic development of China and *Reseach suppoted by National Natual Science Foundation of China unde gant #6473 and # Luo Yao is with School of Automation Science and Electical Engineeing, Beihang Univesity, Beijing, 9, China (phone: ; luo-yao@buaa.edu.cn). Yan Jiang is with School of Automation Science and Electical Engineeing, Beihang Univesity, Beijing, 9, China ( sy43533@buaa.edu.cn). Zhao Zhiyao is with School of Automation Science and Electical Engineeing, Beihang Univesity, Beijing, 9, China ( zzy_buaa@buaa.edu.cn). Yang Shuaishuai is with School of Reliability and Systems Engineeing, Beihang Univesity, Beijing, 9, China ( yss9389@buaa.edu.cn). Quan Quan is associate pofesso of School of Automation Science and Electical Engineeing, Beihang Univesity, Beijing, 9, China. ( qq_buaa@buaa.edu.cn). development of quadcoptes fo pevention and contol of pests and diseases in some appopiate egion deseves to be encouaged. In civil aviation industy and plant potection field, a poblem that has attacted paticula attention is how to cove and tavese an agicultual egion. Cuently, thee have been a lot of eseach on the coveage tavesal poblem in the field of both academic and engineeing. Refeence [] poposes a coopeative coveage algoithm aimed at the collaboative seach of an unnown gid envionment by using multiple mobile obots. he collaboative seach tass may be mine detection, floo cleaning, and othes ae essentially coveage tass, in which a obot must pass a senso o effecto ove evey point in its envionment and a single obot with only intinsic contact sensing can cove any finite ectilinea envionment. his algoithm is pefomed by incementally constucting a cellula decomposition of the envionment (C) and using only the stuctue of C to detemine the coveage path. Refeence [] uses eal-time heuistic seach methods to implement ant obots and pesents a simulation study with seveal eal-time heuistic seach methods to study thei popeties fo teain coveage. hus, by leaving maings in the teain, coodinating teams of simple agents can implement mobile coveage of the teain even if they do not communicate with each othe ecept via the maings, do not have any ind of memoy, do not now the teain, cannot maintain maps of the teain, no plan complete paths. In the aspect of eseach on multi Unmanned Aeial Vehicles (UAVs), efeence [3] poposes a method which begins with an abitay numbe of items of inteest (tagets) andomly distibuted ove a given geogaphic aea and the definition of a launch/ecovey point fo the UAVs. he combinatoial optimization poblem that finds the shotest path connecting each taget on an idealized suveillance mission is then solved using the method of simulated annealing. Refeence [4] consides that the aea coveage should involve two stages - aea decomposition into cells and path planning inside the cells and popose aea decomposition using sweeping method and develop a novel method of geneating lanes inside the cells such that the numbe of lanes is optimal and aea can be coveed consideing pesistence equiements into account. hen in the aspect of eseach on coveage flight path planning in a conve polygon aea, efeence [5] poves that the tuning motion is less efficient compaed to the flat flying theoetically fom the viewpoints of enegy, oute length and duation. A high pefomance vete-edge algoithm to obtain the width of a conve polygon is given based on the theoem which poves that only vete-edge pais need to be consideed in the computation of the width. If a UAV flies along the diection of paallel lines of suppot with the obtaining of width, the coveage path can get the least numbe of tuns /6/$3. 6 IEEE 98

In pactical engineeing, thee main plant-potection-quadcoptes poduction companies in China ae DJI, ZEROECH and XAIRCRAF, espectively. Figs.

he MG- plant-potection-quadcopte poduced by DJI etends the battey life up to moe than 3 times.

he Potecto-Z plant-potection-quadcopte poduced by ZEROECH has a tailoed APP fo agicultual applications and oute ecall capacity aimed at the oute planning of iegula famland [7].

automatic weathe station [8]. Fig. MG- poduced by DJI Fig. Potecto-Z poduced by ZEROECH veify the easonability and coectness of this mission assignment scheme. he est of the pape is as follows.

2 In pactical engineeing, thee main plant-potection-quadcoptes poduction companies in China ae DJI, ZEROECH and XAIRCRAF, espectively. Figs.-3 show the latest plant-potection-quadcoptes poduced by the thee companies duing the last two yeas which all have thei own beathoughs and advantages. he MG- plant-potection-quadcopte poduced by DJI etends the battey life up to moe than 3 times. Meanwhile, the amount of wo pe hou can each 4 to 6 aces and the opeating efficiency is 4 times moe than that by labou [6]. he Potecto-Z plant-potection-quadcopte poduced by ZEROECH has a tailoed APP fo agicultual applications and oute ecall capacity aimed at the oute planning of iegula famland [7]. he P plant-potection-quadcopte poduced by XAIRCRAF uses an intelligent spaying system which can adjust spay flow intelligently based on the gound station instuctions and weathe infomation fom the automatic weathe station [8]. Fig. MG- poduced by DJI Fig. Potecto-Z poduced by ZEROECH veify the easonability and coectness of this mission assignment scheme. he est of the pape is as follows. Section II fomulates the famland spaying poblem. In Section III, a mathematical model of the mission assignment poblem is established and the optimization method is poposed. he simulation platfom establishment and the esults analysis ae given in Section IV. Section V pesents the conclusion and possible futue eseach. II. PROBLEM FORMULAION he bacgound of the eseach in this pape is a pesticide spaying mission pefomed by multi-quadcoptes. Fig. pesents a schematic diagam of the mission. he length and width of the ectangula famland ae w and h, espectively; the point O is the oigin; the point Base is the place that quadcoptes tae off. As the famland is ectangula and the quadcoptes can spay pesticides coveing the famland with a cetain width w, the moving paths of the quadcoptes can be depicted by the dotted lines. In ode to mae the quadcoptes wo in ode, we mae the following pinciples: () Quadcoptes can move in the 3-dimensional-space. () he numbe of the quadcoptes is geate than and is abitay. (3) hee ae fou woing modes of the quadcoptes, including spay, Retun o Base (RB), Retun o Wo (RW), chage. Note that quadcoptes only spay pesticides duing the spay mode. (4) When the battey capacity of a quadcopte is low, the quadcopte will quicly etun to base to chage and etun to wo afte fully chaging the batteies. (5) he same egion of the famland is not pemitted to be epeatedly spayed by diffeent quadcoptes. w h Fig. 3 P poduced by XAIRCRAF he eseach of algoithm in theoy is mainly fo comple egion, howeve, the egion we concen in this eseach ae egula, such as a ectangula egion. hus, all the methods in efeences []-[5] need to be simplified. he poblem we study is a pactical engineeing poblem of which the pupose is to save time, meanwhile, the situation of low battey capacity should be consideed. hus, this pape poposes a new mission assignment scheme aimed at the famland spaying poblem by using the plant-potection-quadcoptes. A mathematical model of the mission assignment poblem is fistly established. hen, the optimal solution is obtained by using a SQP method. Fo claification, a simulation platfom is established and a seies of simulations ae caied out to Oy - w Fig. 4 A schematic diagam of the mission Note that each dotted line in the Fig. is a unit tas. hus, the total numbe of moving paths satisfies n = w / w. All n tass should be assigned to m quadcoptes befoe the quadcoptes stating to wo, and the mission assignment scheme is to divide the ectangula famland into m blocs and distibuted to the m quadcoptes. In ou eseach, on the pemise of finishing the whole mission, how to educe the mission time is the main poblem 98

3 this pape concened. Let be total time to complete the tas of the th quadcopte. hen, the poblem can be witten as min(ma ). Obviously, diffeent mission assignment scheme may esult in diffeent mission time. hus, the poblem of ou eseach is tansfomed into the optimization poblem of mission assignment scheme. III. ESABLISHMEN OF HE MAHEMAICAL MODEL AND HE OPIMIZAION MEHOD A. Establishment of the mathematical model Befoe we establish the mathematical model, some useful paametes ae defined as shown in ABLE. Symbol n ABLE I. MODEL PARAMEERS Desciption Numbe of tass assigned to the th n Chaging times of the th quadcopte chage Chaging time of the th quadcopte d V q b w quadcopte Round-tip distance fo chaging of the th Speed of the quadcoptes quadcopte Flight time of the quadcoptes afte fully chaging w = nw assignment scheme will mae n have diffeent values, and the value of p4 is also diffeent. hus, in ode to simplify the model, it is consideed that the value of p 3 and p 4 ae appoimately the distance between the cente of the tass assigned to the th quadcopte and the base p 5. Assumption. he speed V q is viewed as constant wheneve the quadcoptes ae flying. Rema. Assumption confines that the quadcopte flies with a same speed unde diffeent woing modes. his assumption is without loss of geneality. Assumption 3. Battey capacity and chage time is identical fo all quadcoptes. Rema 3. All the quadcoptes ae in a same type, meanwhile, the pefomances of batteies equipped on the quadcoptes ae simila. By ignoing the subtle diffeence between chage and dischage among individuals, we can conside that the battey capacity and chage time is identical fo all quadcoptes. Based on these assumptions, a mathematical model of the mission assignment poblem is established as follows: s.t. min n +, nq, + ma nh + w( n ) + ( n + ) d = + n () q, Chage Vq q, q, q b () nh + w( n ) + ( n + ) d ( n + ) V (3) nh + w( n ) + ( n + ) d > n V (4) q, q, q b y O Fig. 5 Flight outes of quadcoptes As shown in Fig., the whole paths that a quadcopte moves ae depicted. hee ae fou inds of paths, including egula spaying path p (each p equals to h ), switching path between two unit tass p (each p equals to w ) RB path fo chaging p 3 (equals to RW path), RB path afte all tass finished p 4. Fo peciseness, some assumptions ae made fist. Assumption. he distance d is viewed as constant fo the quadcoptes flying bac and foth between the base and the famland. Rema. As the quadcopte position is diffeent each time the th quadcopte etun to chage, the value of p 3 is diffeent fo each time, too. Meanwhile, diffeent mission h d = w ( n + n / n/) + ( h /) (5) n = ni (6) i= m n = n (7) = Equation () is the optimization goal, which is to minimize the maimum woing time of the quadcoptes. It guaantees that all quadcoptes have to complete the spaying mission and RB at about the same time. If the numbe of tass assigned to the th quadcopte and chaging times of the th quadcopte ae n and n, then the total p, p, distance of flying bac and foth between the base and the famland, flight outes, chaging time and each sustainable flight length afte fully chaging of the th quadcopte ae nh, w ( n ), ( n + ) d, nh + w( n ) + ( n + ) d q,, n Chage and V q b, espectively. Constaint () epesents the time fo the quadcoptes to complete thei assigned tass, which equals to the value that the flight outes of the quadcoptes divided by the speed of the 98

4 quadcoptes, and then plus the total chaging time of the quadcoptes. Constaints (3) and (4) epesent the length of the flight outes of the quadcoptes should be less than ( n + ) times the sustainable flight length afte fully chaging but moe than n times the sustainable flight length afte fully chaging, because the quadcoptes ae full of electicity at the vey beginning. Constaint (5) epesents the appoimate distance of flying bac and foth between the base and the famland of the quadcoptes, and the definition of n which pesents the sum of tass assigned to the fist ( ) quadcoptes is given in the constaint (6). Constaint (7) epesents the sum of the numbe of the tass assigned to m quadcoptes is n. B. Optimization Method SQP has aguably become the most successful method fo solving nonlinealy constained optimization poblems, since it shows its advantages when solving poblems with significant nonlineaities in the constaints by solving quadatic sub poblems [9], []. Fo claify, we simplify equations ()-(7) as follows: min f ( ) (8) Gi = i =,, mg (9) G i = m +,, 6m () i whee = [ q, d, n, n q ] is the paamete vecto; q = [ q,,, q,m ] ; d = [ d,, d m ] ; n = [ n,, n m ] ; nq = [ nq,,, nq,m ]. he function f ( ) is the objective function, which can be obtained by simplifying equation (). he vecto G = [ g( ), g( ),, g m ( )] is the functional vecto, and m g is the bounday value of the equality and inequality constaints. Constaints (9) and () epesent the equality constaints and inequality constaints, espectively. Both f ( ) and g( ) can be nonlinea functions. Using the SQP method to solve the optimization poblem in this pape mainly has the following fou steps. g z is the full vaiable seach diection, which pesents a vecto of to +. he paameteα pesents a scala step paamete which can be obtained by the appopiate linea seach pocedue. he vecto + can be geneated by setting = +α z in the fouth step. A sequence of + can be geneated by epeating the above fou steps, and the local convegence popeties of the SQP appoach will be well * * undestood when the optimum solution (, λ ) satisfies the second-ode sufficiency conditions. If the stating point is sufficiently close to *, and the Lagange multiplie estimates { λ} emain sufficiently close to λ *, then the sequence conveges to * which is the esult of the optimization we want at a second-ode ate. IV. SIMULAION PLAFORM ESABLISHMEN AND RESULS ANALYSIS A. Simulation Platfom Establishment In ode to veify the easonability and coectness of the optimal mission assignment scheme, a simulation platfom is established using Matlab and a seies of simulations ae caied out. his simulation platfom mainly includes fou modules: paamete initialization, mission assignment, quadcopte contol and plotting. Fig.3 is a bloc diagam showing how this simulation platfom wos. As shown in Fig.3, the values of m, h, w and w ae enteed by the use, but othe paametes such as the base, the cuent point, the cuent velocity, the destination point, the last point, the way point, the cuent way point, the maimum electic quantity, the chaging ate, the consuming ate, the contol paamete, the contol pecision, the contol model and the quadcopte states ae initialized by the paamete initialization module. he mission assignment module implements the optimal mission assignment scheme, the way point geneation and the path planning on the basis of nown paametes. he quadcopte contol module implements the coopeative contol of the quadcoptes, the quadcopte attitude contol and the quadcopte state detemination. he plotting module implements moving path plotting in the Mission display aea in Fig.3 based on the mission assignment scheme and the geneated way point fom the mission assignment module.,h,h+ H, z, α + Fig. 6 Pocedues of using the SQP method to solve the optimization poblem Note that H is the Hessian mati of the Lagange function and the initial and H ae abitay. he vecto Fig. 7 A bloc diagam of the simulation platfom 983

One is to divide all tass equally without optimization, and the othe is to use the optimal mission assignment scheme to assign the tass.

5 B. Results Analysis he values of m, h, w and w ae given as 3, 6 metes, 3 metes and metes, espectively, and so n is 3. In ode to veify the easonability and coectness of the optimal mission assignment scheme, two inds of simulations have been caied out. One is to divide all tass equally without optimization, and the othe is to use the optimal mission assignment scheme to assign the tass. hen, the time fo each quadcopte to complete its mission is ecoded. Fig.4 is the path diagams showing the time fo the fist quadcopte to complete its mission when the tass ae divided equally without optimization, and Fig.5 is the path diagams showing the time fo the fist quadcopte to complete its mission when use the optimal mission assignment scheme to assign the tass. Fig. 8 he time fo the fist quadcopte to complete its mission when the tass ae divided equally Fig. 5 he time fo the fist quadcopte to complete its mission when the optimal mission assignment method is used to assign the tass By compaing the above simulation path diagams, it is nown that the total time to complete the spaying tas is diffeent. When the sub tass ae divided equally, the numbe of sub tass assigned to each quadcopte is and the time fo thee quadcoptes to complete its mission ae 787.6, and 985 simulation time intevals, espectively. When use the optimal mission assignment scheme is used to assign the tass, the numbe of sub tass assigned to thee quadcopte ae 9, and 9, and the time fo thee quadcoptes to complete its mission ae 844.5, and 87.6 simulation time intevals, espectively. Fom the above compaison esults, we can now that the mission eecution will be moe efficient and the mission time of each quadcopte will be close to each othe by using the optimal mission assignment scheme. In ode to mae the simulation esults moe pesuasive, moe simulations ae caied out, including ) the same numbe of the quadcoptes with the diffeent size of the famland, and ) the diffeent numbe of the quadcoptes with the diffeent size of the famland. he esults of the simulations ae shown in ABLEs &. he paamete s is the aveage allocation scheme; s is the optimal mission assignment scheme; t is the completion time of the aveage allocation scheme; t is the completion time of the optimal mission assignment scheme; Δ t is the time saving by the optimal mission assignment scheme. he simulation time inteval is used as the unit of t, t and Δ t. 984

6 ABLE II. RESULS OF HE DIFFEREN NUMBER OF HE QUADCOPERS WIH HE DIFFEREN SIZE OF HE FARMLAND m n s s t t 3 3 :: 9:: ::: 8:: :::: 7::4:: ::::: 6::3:3:: ABLE III. RESULS OF HE SAME NUMBER OF HE QUADCOPERS WIH HE DIFFEREN SIZE OF HE FARMLAND m n s s t t 3 3 :: 9:: :3:3 :8: :7:6 5:: As can be obseved fom ABLEs &, the effect of saving time by using the optimal mission assignment scheme is significant whethe when the numbe of the quadcoptes is the same but the size of the famland is diffeent o when the numbe of the quadcoptes is the diffeent and the size of the famland is diffeent. V. CONCLUSION his pape poposes a new mission assignment scheme aimed at the famland spaying poblem. A simulation platfom is established and a seies of simulations ae caied out to veify the easonability and coectness of this scheme. his scheme mainly solves the mission assignment poblem when use the plant-potection-quadcoptes to spay pesticides on a ectangula field, and its pupose is to minimize the time to complete the spaying mission. he esults of this pape pove that, by using the optimal mission assignment scheme, the mission eecution will be moe efficient and the mission time of each quadcopte will be close to each othe. Although this scheme has some ideal simulation esults in this pape, thee ae still some aspects need to be impoved. Fistly, most of the actual famland is not ectangula and this scheme only suitable fo the ectangula famland. hus, this scheme needs to be impoved to apply to the iegula famland. Secondly, a quadcopte may suddenly be damaged and unable to wo in pactice. hus, this scheme should also conside quadcopte failues in futue eseach. Δt Δt [4] M. Goodich, B. Mose and D. Gehadt, Suppoting wildeness seach and escue using a camea-equipped mini UAV, Jounal of Field Robotics, vol. 5, no. -, pp. 89-, 8. [5] A. Agha-Mohammadi, N. Ue and J. How, Health awae stochastic planning fo pesistent pacage delivey missions using quadotos, in IEEE/RSJ Intenational Confeence on Intelligent Robots and Systems (IROS), Chicago, 4, pp [6] A. Giad, A. Howell and J. Hedic, Bode patol and suveillance missions using multiple unmanned ai vehicles, in 43d IEEE Confeence on Decision and Contol (CDC), Bahamas, 4, pp [7] B. Bethe, J. How and J. Vian, Multi-UAV pesistent suveillance with communication constaints and health management, in AIAA Guidance, Navigation, and Contol Confeence (GNCC), Chicago, 9, pp. -3. [8] Y. Huang, W. Hoffman and Y. Lan, Development of a low-volume spaye fo an unmanned helicopte, Jounal of Agicultual Science, vol. 7, no., pp , 5. [9] I. Schmal, G. David, B. Dingus and C. Reinholtz, Development and application of an autonomous unmanned aeial vehicle fo pecise aeobiological sampling above agicultual fields, Jounal of Field Robotics, vol. 5, no. 3, pp , 8. [] C. Zhang and J. Kovacs, he application of small unmanned aeial systems fo pecision agicultue: a eview, Pecision Agicultue, vol. 3, no. 6, pp ,. [] Z. Butle, A. Rizzi and R. Hollis, Coopeative coveage of ectilinea envionments, in Poceedings of IEEE Intenational Confeence on Robotics and Automation, San Fancisco,, pp [] S. Koenig and Y. Liu, eain coveage with ant obots: a simulation study, in Poceedings of the 5th Intenational Confeence on Autonomous Agents, Canada,, pp [3] M. Hutchison. A method fo estimating ange equiements of tactical econnaissance UAVs, in st Unmanned Aeospace Vehicles, Systems, echnologies, and Opeations Confeence and Woshop, Potsmouth, VA,, pp. -5. [4] J. Aaujo, P. Sujit and J. Sousa. Multiple UAV aea decomposition and coveage, in IEEE Symposium on Computational Intelligence fo Secuity and Defense Applications (CISDA), Singapoe, 3, pp [5] H. Chen, X. Wang, Y. Jiao and Y. Li, An algoithm of coveage flight path planning fo UAVs in conve polygon aeas, Acta Aeonautica et Astonautica Sinica, vol. 3, no. 9, pp. 8-88,. (in Chinese) [6] [7] [8] [9] P. Boggs and J. olle, Sequential quadatic pogamming, Acta Numeica, vol. 4, pp. -5, 995. [] J. Nocedal and S. Wight, Numeical Optimization. New Yo: Spinge Science & Business Media, 6, ch. 8. REFERENCES [] A. Ailon and S. Aogeti, Closed-fom nonlinea tacing contolles fo quadotos with model and input geneato uncetainties, Automatica, vol. 54, pp , 5. [] H. Liu, X. Wang and Y. Zhong, Quatenion-based obust attitude contol fo uncetain obotic quadotos, IEEE ansactions on Industial Infomatics, vol., no., pp , 5. [3]. omi, K. Schmid and P. Lutz P, owad a fully autonomous UAV: Reseach platfom fo indoo and outdoo uban seach and escue, IEEE Robotics & Automation Magazine, vol. 9, no. 3, pp ,. 985

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