Proceedings of the 00EEE on Robotics, Automation and Mechatronics , - December, 00 Comparing Harmonic Functions and Potential Fields in the Trajectory Control of Mobile Robots* dson Faria and os A. F Roro SCC Edson Pestes niaale Mar A. P. Iiar FFGS e-mai: (gedson7rafrance)@icmc.usp8br e-mal: preses@nf:ur.br e-mai iartiDfrgs.b -Potential Field is a reactive method that has been used for trajectory control of mobile robots. In this method the robot behaves like a particle moving under the inHuence of an artificial potential produced b the target and the obstacle. This method has loer computacional cot than others that utilie maps as a world model. However, one problem of this method is that  can generate regions of local minima. In these regons the driving force vanishe due to specifc obstacle and goal confguration and the robot gets trapped. The use of harmonic functions for the potential calculation can solve this problem. In the Haronic Function method the environment is represented by a grid, in which cells with an obstacle have their potential value set to  wherea cells that contain the target have their potential value set to O. A relaxation algorithmis then emploed to cruculate the harmonic potential among the obstacles and the target. In this work, these two technques have been applied in robot soccer environment to develop game strategies. Result obtained show that both techniques present better result hen compared to the standard strateg of FIRA Simulator. Further, a comparison of these tehniques i s preented for showing the advantages and disadvantages existing in each one of them. I. I The idea of robots playing socer was rst mentioned by roessor Aan acworth (niersity o itish olumbia, Canada) in a pape entitled "n Seeing Robots" preented at VI -92, 1992I. Robot soccer s an inteational initiative tued to researh and education, aming to promot eveopmens n rcial Intelligene and Robotcs 2. One of the main reasons why root soccer is adopted as a researh envonmet is hat the esec can be clearl defined and followed. esides, it is posibe toevauate various theories, agorithms, architetue and peormances adoptng this rolem [3]. ueto the necessiy to nagatein a dynamc environment avoding collisions, the attack and defense behaios ca e mlemented by usin path panning technique9 One of these techniues airl used n rbotics is the oo- architecture proposed by Arkin 4]. arios ehniques ha been appied to buid te attack, defense ad cooperation behaviors for robts. art al. 5] proposed theuse ofpotential eldstoplan the traectories of the robts inside the soccer evironmentC or thi, the archtectuepposed by Arkin 4] wasused,in which vector elds are recalculated at ach new instant of timeF • ʦ   pp  P A draback ofthis method s kon as  , n which the atacon potenti ihbis the repulion potentalE This techiue has been widly used nd many modifcatons [61, [7] have be prosd i literature o e its dawbas; n another approach, Gmes and Camos 81 used an enironment modl n whih the gol and the obscle are mked n a map. n the net se, values are propagated to the neghbor cells othe map to pot the shortest path to the goal which is re rom colsons< he disadantage o this method s to eep and updae the map ateach istant of te. The smller thegranlarty of the map, the more precise this ill be, but the inoved processng cos wil b uch her= ConnllyandGrupen [9]roposedteseof metrical ap to store the hamonic fuction o each positon of the ap> This approach wa recently etended by restes 10], niying planin aneprationehaviors.Themetrical mapust  updated step by step. owver the drection to be folwed is obtaied throuh direct acess to the cel ferring to the  of the robot. In the present paper two diernt path panning technques have ben proposd and mlemented o conrolling theobot soccer team? Th irst is a modcation o MorS archteture popsed by rkin 4 an the second i the techniqe proposedinl@ [12]adapedorobotsoccer. sing hese tehniques  is possil to bild strategie to contro each root from'robot soccer eam. n the straegies proposed here ro are abletootasssuhas avoidngcollisions blocin the adversaes and folow the bal. hi aper is organied s it followsA In he section  the potentia ed tecniue is briefy described. I n escton III, the technique caled harmonic fntion is resented. he detais of mplementation o both techniues are preseted in secton , wher the soccer stegies adoptd are dned. A comparison of esults otaned s presented in section V show the advantages anddisadvaages eiing in eacone othemin the socer robot contet. nally in sction , the conclusions an uggestions or futue work ae prestdB II. POTENTIALFIELDS he idea o imaginary orces acting on a robot  been suggestd by hatib [13.  this pth lanning method the robot - eprsented by a pont - behaeslie a artcle mvng uder the nluence of an articia potentia prodced by 0-7803-8645-/041$20.00 2004IEEE 762