Complete Coverage Path Planning of Mobile Robot Based on Dynamic Programming Algorithm Peng Zhou, Zhong-min Wang, Zhen-nan Li, Yang Li

Transcription

1 2nd Interntionl Conference on Electronic & Mechnicl Engineering nd Informtion Technology (EMEIT-212) Complete Coverge Pth Plnning of Mobile Robot Bsed on Dynmic Progrmming Algorithm Peng Zhou, Zhong-min Wng, Zhen-nn Li, Yng Li Institute of Mechtronics Engineering, Tinjin University of Technology nd Eduction Tinjin 3222, Chin Keywords: Mobile robot, Complete coverge pth plnning, Boustrophedon unit decomposition, Dynmic progrmming lgorithm. Abstrct. A complete coverge pth plnning lgorithm, which combines locl spce coverge with globl plnning, is proposed. At first, environmentl model of mobile robot in spce with obstcles is built by Boustrophedon unit decomposition method, nd mobile robot relizes coverge in reciprocting wy in locl spce. Secondly, it tkes locl spce dividing, sub-spce connecting sequence nd sub-spce wlking route into ccount, then completely connected distnce mtrix tht represents the connecting reltionship of the coverge spce re defined. Thirdly, dynmic progrmming lgorithm is used to optimize this mtrix nd shortest globl coverge sequence is cquired. Simultion exmple proves the effectiveness of the proposed lgorithm. Introduction Coverge pth plnning methods to the mobile robot re different from Point-to-Point (PTP) pth plnning method [1].It hs been pplied in clening robot, mowing robot nd other fields. The coverge pth plnning is roughly divided into two types: rndom coverge plnning nd complete coverge plnning. Complete coverge pth plnning method use some performnce evlution function to control the mobile robot coverge movement to mke sure the optiml performnces. Types of coverge pth plnning performnce evlution re coverge efficiencies, percentge of coverge re, coverge overlp rte nd energy loss, etc [1,2]. Currently, the coverge lgorithm which is commonly used is templte model method nd cell decomposition method [3]. Becuse the templte lgorithm lcks overll plnning of the whole environment, so it hs low efficiency, besides, the mobile robot cn not be hndled nd esily get into the ded circultion [4]. Templte-bsed complete coverge pth plnning model requires pre-defined environment model nd templte memory. Cell decomposition method divides working spce of mobile robot into series spces of non-collision, finite, non-obstcle ccording to distributions of obstcles nd their occupying spces [5]. In this pper, complete coverge pth plnning lgorithm re studied. At first, complete coverge pth plnning problem, which combines locl spce coverge with globl plnning, re discussed. Secondly, complete coverge pth plnning lgorithm is put forwrd bsed on the combintion of cell decomposition method nd templte model method in sttic environment, nd the simultion results show the effectiveness of the lgorithm. Coverge Pth Plnning Bsed on Dynmic Progrmming Algorithm Dynmic Progrmming Algorithm The principles of dynmic progrmming lgorithm re prtition ides nd solving the problems of redundncy. The ides of dynmic progrmming lgorithm re decomposing plnning problem into severl smller nd similr sub-problems nd storge solutions of sub-problems to void the repeted clcultion of sub-problems. This lgorithm is strtegy to solve optiml problems. As long s the problems cn be divided into smller sub-problems nd the optiml solutions of the originl problems include sub-problem optiml solution, the dynmic progrmming lgorithm cn be considered [6]. Published by Atlntis Press, Pris, Frnce. the uthors 1837

2 2nd Interntionl Conference on Electronic & Mechnicl Engineering nd Informtion Technology (EMEIT-212) Complete Coverge Pth Plnning of Mobile Robot Geometric method is chrcterized by simple nd high efficient. It is esy for plnning nd mintennce of the mp. Geometric method is reltively intuitive, so it is convenient to construct environmentl mp, especilly for the structured indoor environment. In this pper, environmentl mp is shown in Fig.1 by using Boustrophedon unit decomposition method; it includes points, lines, nd combintions of points nd lines which represent the chrcteristics of the environment. The prmeters re used to indicte the specific loction of the vrious fetures in the environment. Fig.1 Environmentl mp bsed on Boustrophedon unit decomposition Boustrophedon unit decomposition method uses virtul line which is prllel to the edges of the rectngulr obstcles from left edge to right edge, shown in Fig.1. In Fig.1, coverge res re generted through the judgment which connects to scnning line. The scnning line strts scnning from the left side of the Fig.1. After environmentl mp is decomposed with Boustrophedon method, the mp is mde up by some obstcles re nd some coverge re. By Boustrophedon unit decomposition method, the environmentl mp cn be decomposed into some coverge res nd obstcles res, shown in Fig.1. Becuse ech coverge spce hs fetures of two prllel edges nd they hve public edges of the djcent re, so through judging ech certin public edge to judge whether to n re, nd it judges whether reching to nother public edge to judge whether coverge out of n re. In the re through the reciprocting movement, it relizes the coverge. On the bsis of the coverge of single re, it needs to determine coverge sequence of the re to rech full environment coverge, which is importnt to use dynmic progrmming lgorithm to solve the coverge pth plnning problems. Fig.2 is the result of Fig. 1 by Boustrophedon unit decomposition method. Normlly, it is not esy to crry out coverge lgorithm ccording to the connection reltions in Fig.2. Especilly, the dynmic progrmming lgorithm requires the visited re joining in the visited forbidden tble. In this pper, the spce distnces re defined by using the connected reltionship, distnce reltionship nd obstcles mong ech re in Fig.1. The existing spce connection reltionship is further dded, which forms fully connected grph. By definition of Hmilton pth, the structure of Fig.2 stisfies conditions of Hmilton chnnel, so there existing pth which psses ech re once nd only once ccess. Fig.2 Structure chrt bsed on Boustrophedon unit decomposition Published by Atlntis Press, Pris, Frnce. the uthors 1838

3 2nd Interntionl Conference on Electronic & Mechnicl Engineering nd Informtion Technology (EMEIT-212) Modeling of Environmentl Mp for Coverge Pth Plnning As shown in Fig.1, the connected distnce between spce 3 nd spce 4 res is not convenient to solve, so distnce is defined to show the ctul distnce. Although the defined distnce nd the ctul distnce hs certin gp, but the trend of the distnce vlue is consistent. The definition of distnce minly considers the liner distnce between two res, connected reltionship nd obstcles sitution mong the spces. The distnce of djcent res is defined, by djusting to determine better vlue through computtion. D = bdjn is used to describe distnces of non-djcent spces. Among them, b is vrible coefficient, it cn be djusted through simultion to get better vlue. D is liner distnce mtrix between two res in environmentl mp. According to Boustrophedon unit decomposition method, recent vertex distnces between two res re defined s the liner distnce between two res. Seen from Fig.2, between spce 1nd spce 2 there exists connected pth. For reltions of not one time connected spce, it cn get n times connecting reltion of two spces through clculting mtrix A n times power. For i, j, k three spces, if spcei nd j re connected, nd spce j nd k re connected, then spcei nd re k re connected, lso. According to connecting reltion in Fig.2, it cn be connected through four times t most between ny two res in the environment, so connecting reltionship mtrix J cn be cquired s follows. The closed vertexes between two coverge sub-spce re Ax (, y) nd B( x, y ). Judging the number of obstcles is the judgment i j i j number of the obstcles through AB vector. Obstcles number mtrix N mong coverge sub-spce in environmentl mp in Fig.1 is shown s follows. Distnce mtrix D represents ctul distnce between coverge sub-spce, its element dij is shortest vertex distnce between sub-spcei nd j. For the djcent spces, the distnce vlue is. For non-djcent spces, the distnce is cquired ccording to spce coordinte in environmentl mp D in Fig.1 is mesured s Eq.1. Through multipliction of the sme position elements in the obstcles mtrix, distnce mtrix nd connected mtrix, non-connected re distnce multiplied by coefficientb, getting redefined comprehensive distnce mtrix D. Spce comprehensive distnce mtrix D in Fig.1 re described in Eq J = N= D= (1) Published by Atlntis Press, Pris, Frnce. the uthors 1839

4 2nd Interntionl Conference on Electronic & Mechnicl Engineering nd Informtion Technology (EMEIT-212) 3b b 3 3b 165.6b 165.6b 3b 152.4b 3b 4b 56.6b 4b 7b D = 12b 5b 1b 12b 24b 3b 22b 15b 6b 36b 22b 695b 135.9b 128b 134.4b 22b 322.4b 9b 7b 4b 26b 18b 12b 453b 125b 196.8b 36b 152.4b 3b 4b 6.8b 216.6b 216.6b 12b 283.2b 228b 127.5b 36b 453b 1b 24b 6b 128b 322.4b 18b 125b 4b 3b 36b 134.4b 9b 12b 196.8b 6.8b 216.6b 216.6b 12b 283.2b 228b 127.5b 67b 3b 67.2b 1.5b 12b 8b 7.8b 3b 5b 15b 67b 4b 4b 2b 331.2b 3b 4b 53.8b 2b 67.2b 7.8b 4b 72.8b 3b 1.5b 3b 53.8b 2b 12b 5b 2b 2b 72.8b 8b 15b 331.2b 3b 2b 7b 56.6b 12b 5b 22b 12b 22b 15b 695b 135.9b 7b 22b 4b 26b (2) Simultion Experiments To the environmentl mp in Fig.1, where I, II, III, IV re four obstcles. Simultion system is developed by VB softwre. During computtion prmeter =.1 nd b=1 re selected. The optimiztion sequence of coverge spce in Fig.1 is: , simultion results re shown in Fig.3. Fig.3 Simultion results Conclusion According to spce reltions nd spce connected grph in the coverge environmentl mp, the connected grph is supplement for fully connected grph. According to the connecting informtion, this pper defines distnce mtrix of the environmentl mp nd its connection weights mong structures. Spce coverge sequences were optimized by dynmic progrmming lgorithm ccording to this distnce mtrix. Simultion results show tht this method gurntees mobile robot coverge ll rechble working spce, nd pth repetition rte is smll. Acknowledgements This work is supported by the Tinjin Science nd Technology Key Reserch Progrm (1ZCKFSF15), the Reserch nd Development Projects of Tinjin University of Technology nd Eduction (YY96, KJY116). Published by Atlntis Press, Pris, Frnce. the uthors 184

5 2nd Interntionl Conference on Electronic & Mechnicl Engineering nd Informtion Technology (EMEIT-212) References [1] K. S. Li, H. H. Zhng, R. Y. Fei: Robot Vol. 23 (21), p [2] L. Li, T. Ye, M. Tn: Robot Vol. 24 (22), p [3] E. U. Acr, H. Choset: Proceedings of the 21 IEEE/RSJ on Intelligent Robots nd System, Mui, p [4] X. M. Zheng, K. Sven: 27 IEEE/RSJ Interntionl Conference on Intelligent Robots nd Systems, Sn Diego, p [5] C. B. Zhng, X. S. Wng: Chin Mechnicl Engineering Vol. 19 (28), p [6] D. E. Jckson, M. Holcombe, F. L. W. Rtnieks: Nture Vol. 719 (24), p Published by Atlntis Press, Pris, Frnce. the uthors 1841