Application of Evolutionary Artificial Potential Field in Robot Soccer System Prahlad Vadakkepat, Tong Heng Lee and Liu Xin Department of Electrical and Computer Engineering, National University of Singapore 10 Kent Ridge Crescent Singapore 119260 { elepv, eleleeth, engp054 1 } @nus.edu. sg

Abstract

tential field functions at the beginning to the Artificial PotentialField (APF) functions. Diverse path planning methodsbasedon APF have been developedrecently. Researchon APF problemscoversfrom building artificial potential functions to surpassingthe restrictionsof the workspace[4,9]. SomeAPFs are inspiredby physical processes.A new artificial potential field method for path planning of non-sphericalsingle-body robots is presentedin [3], which simulates steady-stateheat transfer with variable thermal conductivity. A tradeoff between the navigation performanceand the real time computation is to be resorted to in real time applications. Simple and effective functions are preferred in dynamic environmentswhere absolute accuracy is of lessimportance.

Evolutionary Artificial Potential Field (EAPF) functions areutilized for mobile robot navigationin a microrobot soccer(MiroSot) environment. In a micro-robot soccersystem the robots are monitored using an overheadCCD Camera,making it suitablefor real time application of the EAPF functions. The effectivenessof theEAPF functionsin real time mobile robot navigation are verified through experimentation.The EAPF functionsproposedaretestedin different scenariosrelatedto ball tracking andball kicking, while facing competition from other robots.

Recently the topic of Evolutionary Robotics (ER) has generatedmuch attentionas a tool for the creation and programmingof robot control systems[ 11.ER is an attempt to developrobots and their sensorimotorcontrol systemthrough an automatic design processinvolving artificial evolution[6]. The core techniqueof ER is Evolutionary Algorithm (EA), which is aimed at a coherent population-orientedmethodology of structural and parametricoptimization of a diversity of systems.The field of evolutionary computation has reacheda stage of somematurity. The methodsof evolutionarycomputation are among such technique. The stochasticalgorithms model the naturalphenomenalike, geneticinheritance and Darwinian strife for survival. EAs offer an important ability to copewith realistic goalsand design objectivesreflectedin the form of relevantfitnessfunctions. In ER, a new approachhasbeendeveloped,which emphasizeson co-evolution. From biological sciences it is learnedthat the animal brains and bodieshavedevelopedin parallel. By evolving the robot structureand control programin parallel it is hopedthat ER canbegin to solvemore complexproblems.

1. Introduction Autonomouspath planning plays an important role in mobile robot systems. Various methodshavebeendevelopedfor mobile robot path planning. The path planning problem can be statedas seekinga collision free path between two locations with certain optimization criteria. The two major directionsin collision free navigationare theArtificial Intelligence(AI) andthepotentialfield approaches.The AI direction focuseson global path planning with optimization algorithms. It involves complex computing,andcanbe resortedto when the information on theenvironmentis ambiguous.The potentialfield direction providesfreedomin selectingthe potential field functions and is simple in realization. This researchdirection has attractedgreat interest among researchers. Currently the robot vision systemsare capableto provide efficient image processingon the workspace in real time. As a result, the positions of objects in the workspacecan be identified easily, making it easierto calculatethe potential field.

Researchon APF with genetic algorithms is presented in [8]. Blendedwith EAs, a new potential field method-

Potentialfield functionshaveevolvedfrom physicalpo1

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ology named Evolutionary Artificial Potential Field (EAPF) has emerged[Z]. It is proposedfor real-time robot pathplanning. The artificial potentialfield method is combined with genetic algorithms to derive optimal potentialfield functions. The multi-objective evolutionary algorithm (MOEA) can be resortedto, to deal with the multiple objectives associatedwith mobile robot navigation. MOEA is a stochasticsearchtechniqueinspiredby the principles of natural selection and genetics. It has attractedsignificant attention from researchersin various fields due to its ability to searchfor a setof paretooptimal solutions. The resolution is not guaranteedto be the best, but it brings out fine control result in most time. Robot Soccer System is one of the standardproblems for the study on multi-agent systems,andcanbe usedas a commontest-benchfor multi-agentsystems[ 11, 121. The robot soccersystemis involved with diversefields like robotics, intelligent control, communication,computer technology,sensortechnology,image processing, mechatronics,artificial life, etc. In a robot soccer system, the active environment is placid andcontinuous,with fixed boundsandgoals.For such a known environment,APF approachesare convenient to be utilized for path navigation and collision avoidance.The robot soccersystemis usedto verify the usefulnessof the EAPF functions for real time applications. This paper is organized as follows. The EAPF functions and the fitness function are presentedin Section 2. Simulation and experimentalresultsare included in Section3. Conclusionand future researchdirection are provided in Section4.

2. The Artificial Potential Field In the traditional artificial potential filed methods,an obstacleis consideredas a point of highest potential, and a goal as a point of lowest potential [2]. The attractive force towards the goal (F,) and the repulsive force (F,.) from an obstacleare definedrespectivelyin Equations1 and 2. The potential field angle is defined in Equation 3. F, = -$ Q7

Fr= &

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(1)

(2)

Potentialfield angle = L (F, + c

F,.)

(3)

Where D,, is distancebetweenthe robot and the goal, D,, is distancebetween the robot and the obstacle;p and n arepositive parametersthat are to be optimized. When the attractive and repulsive forces balanceout, the robot is trapped. To avoid this, an escapeforce Fe (Equation4) is utilized [2].

F,(i) =

cos( LFii) - L C FJi’) - cos(c) / wzl

(4)

The potential field angle 6 acts as the control signal to the robot. 8= LF,-

LxF,

(5)

The multi-objective evolutionary algorithm is used to optimize the parameters(p, n, c and d) associatedwith the potential field function. Fitnessselectionis the preliminary problemin optimization. The influenceof cost terms in control policy and evolutionary program techniquesis presentedin [ 1,7]. In this paper,the following (penalty) valuesare minimized using EA. Cl = Penaltyvalueassociatedwith thedistancebetween the robot and goal. Cz = Penaltyvalue consideredon collision. Cs = Penaltyrelatedto the length of the path in configuration space. CJ = Penaltybasedon the robot turn-angle. The fitnessfunction is formulatedin two ways: As a linear combination of penalty functions and through prioritization. The robot is desired to arrive at the goal point (Kicking the ball - Cl) through a collision free path (Cz). Cr and C2 havehigher priority. The smoothness(CJ) of the path followed and path length (C’s)are of lesserpriority.

3. Experimental results on a robot soccer system The Micro-Robot Soccer System platform is used to test the navigation approach. The robots used in the setupare 7.5(cm) cubic in size, semi autonomous.The robots have driving mechanism,communication parts and, computationalparts for velocity control and for processingthe datareceivedfrom a host computer.All

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=\ \

? ,i /’ . 1

i

\

Figure 1. The Artificial

potential field.

(150,130)

..-..

-.

-.-...-..-.-.-...r-

-

--

-

-----------------

7

1

-

I Robot

_-.,

I

1

j

0

Figure 3. Robot motion.

The Potentialfield forcesare definedas:

Figure 2. Position Representation of Robots.

Fa

=

F,

=

IIPG i PRII @l,pR

the calculationsfor vision dataprocessingand position control of robots aredone on the host computer. In the robot systemconsidered,there are three robots per side,acting asattacker,defenderandgoalie. A CCD camera(vision system) grabs the positions of the ball (goal) and the other robots (obstacles).The play field is mappedonto a 2-D coordinatesystem.Positionsof the robots and ball are representedby respectiveX and Y coordinatesas illustrated in Figure 2. The home robot positions are presentedby the vector PR(ZR, YR), the opponentrobots by Poi(zOi, yOi) (i = 1,2,3), and of the ball as PG (zg , yg). Distancesof the robot from the goal point and obstacles arecalculatedwith Equations6 and 7: D,,

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= IlpG - PRII

(6)

Potentialfield angle =

_’ POiIl)n

L(E + x4-)

(8)

(9)

(10)

The escapeforce F, is definedas:

cos( LFii) - L C FJi)) - cos(c) F, =

D min

(11)

where,

D min LF,

= =

min(llPR - P&II) l-I/4

i = 1,2,3 (12) (13)

Oncetheescapestatusis reached,F, is executed3 times to ensurethat the robot leavesthe null-force area. The reasonfor such a design is that if the escapeforce becomeszero at the exact time interval when the robot is

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out of the escapearea,the robot cannotmoveeffectively enoughto leavethe null-force area.It may possibly fall into the escapestatusagainand may take longer time to move towards the real target. The experimentalresults are illustrated in Figure 3. The potential field angle (Equation 10) is the control input signal and the appropriatevelocitiesproportional to the turn-angleare transmitted(RF) to the robots. The actual motor velocities of the left and right wheels are determinedby the on-boardmicro-controller through a classicalPID controller with velocity feedback(Equations 14 to 20). Vleft = UC+ Vtl ’ @p

(14) Figure 4. Ball tracking with two stationarq robots.

Vright = v, - Ve - 0,

where K,,&

(15)

& E (0, l), and

v,

=

W 8,

Moving

Kc

(16)

=

1+ =PwLJtal) vp KpBp + Ki[, + Kdp

(17)

=

LFtotai

(18)

CP

=

KP

8F)

=

BC) - 8fl)

+ e,

siaiiulaly Robot 3

(19)

i - interval

(20)

Wherethe parametersIceand vCare relatedto the robot angle(0) androbot to goal distancerespectively.

Moving Robot 2

To improve the performanceof the robots, the statusof robots are divided into severalcategoriesand different valuesare assignedto the parametersp and n of the repulsive function Equation2. In the experiments,the robot could reach the goal, but the path was not assatisfactoryasin 121,as the path has departedfrom the ideal trail slightly. Therearea couple of reasonsfor this mismatch: The processingtime required to calculatethe potential field anglein real time, the mapping of the potential field angle to the wheel velocities and the effectivenessof the velocity control. Furthermore, therobotsmoveat a fasterrate in comparison with the frame updaterate. When the robot moves too fast, its motion is expectedto deviate. Oneof the main problemsin EAPF is that therobot cannot passbetweentwo obstacles,even the spacein between the two is enoughfor the robot to move through. This happensas the direction of the sum of the two repulsiveforcespoint away from the openingbetweenthe two close obstacles[lo]. This problem will also affect the smoothmotion of the robot.

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Figure 5. Ball kicking while competing with another.

0 Slationary Robol2

Figunz 6. Ball tracking while in competition.

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[41 Ahmad A. Masoud, “Integrating DirecMovmg ball

tional Constraints in Motion Planning Using Nonlinear, Anisotropic, Harmonic Potential Fields”, Proceeding of the 1998 IEEE ISIC/CIRA/ISAS Joint Conference,Gaithersburg, MD, Sep 14-17, 1998

PI SukhanLee; JavierBautista,“Motion Control For Micro-Robots Playing Soccer Games”; Proceedingsof the 1998 IEEE, Int. Conferenceon Robotics& Automation Leuven,Belgium May 1998

Moving Robot 2

Robol 1

Figure 7. Ball kicking while competing with three other robots.

[61 Stefano Nolfi, “Evolutionary Robotics: Exploiting the full power of self-organization” Self-LearningRobotsII: Bio-robotics (Digest No. 1998/248),IEE , 1998Page(s):3/l -3/7 r71 Rana,A.S.; Zalzala, A.M.S., “An evolution-

ary algorithm for collision free motion planning of multi-arm robots’*, Genetic Algorithms in Engineering Systems: Innovations and Applications First International Conferenceon Page123 - 130, 1995

4. Conclusion In this paper, the application of the evolutionary artificial potential field (EAPF) method in a micro-robot soccerenvironmentis presented.The EAPF functions proposedwere testedin different scenariosin ball tracking and kicking, while facing competition from other robots. For more accuratesolutions, it is required to optimize the parametersassociatedwith the EAPF functions in real-time. Further researchis neededto impart cooperative behaviorsand learning capabilities to the mobile robots

@I Dozier, G.; Homaifar, A.; Bryson, S.; Moore, L. ” Artificial potential field based robot navigation,dynamicconstrainedoptimization and simple genetichill-climbing,” Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence.,1998Page(s):189 -194 [91 Toshio T.; Pietro G. Morasso; Makoto

Kaneko,” Trajectory Generationfor Manipulators Basedon Artificial PotentialField Approachwith Adjustable TemporalBehavior”, Intelligent Robotsand Systems‘96, IROS 96, Proceedingsof the 1996 lEEE/RSJ Intemational Conference on , Volume: 2 , 1996 Page(s):438 -443 vol.2

References VI Timothy E. Revello; Robert McCartney, “A Cost Term In An Evolutionary Robotics Fitness Function,” Congress on Evolutionary Computation.Proceedingsof, volume1.1, 2000, page 125- 132 . PI Vadakkepat, P.; K. C. Tan; Wang M.-L., “Evolutionary artificial potential fields and their applicationin real time robot path planning,: Congresson Evolutionary Computation, Proceedingsof the, 2000. Volume: 1, Page(s):256 -263 vol.1 . 131 Yunfeng Wang; Gregory S. Chirikjian,” A

New Potential Field Method for Robot Path Planning,”Proceedingsof the 2000IEEE Int. Conferenceon Robotics & Automation, San Francisco,CA April 2000

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m

YorarnKoren; HohannBorenstein,”Potential Field MethodsandTheir InherentLimitations for Mobile Robot Navigation,” Proceedingof the 1991IEEE, Int. Conferenceon Robotics andAutomation,Sacramento,CA-April 1991

WI J.-H. Kim and P. Vadakkepat,“Multi-Agent Systems: A Survey from the Robot-Soccer Perspective,”Intelligent Automation and Soft Computing,Vol. 6, No. 1, P.3-18,200O. WI H.S Sim, M.J Jung; H.S Kim; J.-H. Kim andP. Vadakkepat,“A Hybrid Control Structure for Vision BasedSoccerRobot System,” Intelligent Automation and Soft Computing, Vol. 6, No. 1, P.89-101,200O.

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