Observational Emergence of a Fuzzy Controller Evolved by Genetic Algorithm

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Oservational Emergence of a zzy ontroller Evolved y Genetic Algorithm Seng-Ik Lee Dept of ompter Science, Yonsei University Seol 12-749, Soth Korea cypher@candyyonseiackr Sng-Bae ho Dept of ompter

1 Oservational Emergence of a zzy ontroller Evolved y Genetic Algorithm Seng-Ik Lee Dept of ompter Science, Yonsei University Seol , Soth Korea cypher@candyyonseiackr Sng-Bae ho Dept of ompter Science, Yonsei University Seol , Soth Korea scho@csaiyonseiackr Astract- Explaining emergence is a difficlt work sch that there are many argments on what it is or how it can e explained Nonetheless, it is freqently referred in many fields sch as ehavior ased rootics, artificial life, and complex systems withot any on formal definition In this paper, we develop a fzzy logic controller for a simlated moile root with genetic algorithm and analyze ehaviors of the controller from the perspective of the oservational emergence The analysis shows that the fzzy logic controller has acqired emergent ehaviors throgh the interactions of the nderlying fzzy rles 1 Introdction Khepera (see igre 1) was originally designed for research and teaching in the framework of a Swiss Research Priority Program It allows confrontation to the real world of algorithms developed in simlation for trajectory exection, ostacle avoidance, pre-processing of sensory information, and hypothesis test on ehavior processing Eight infrared proximity sensors are placed arond the root and each of them emeds an infrared emitter and a receiver 1 2 Top View Side View Bottom View 4 6 igre 1: Position of some parts of the root [1] ➀ LEDs ➁ Serial line (S) connector ➂ Reset tton ➃ mpers for the rnning mode selection ➄ Infra-Red proximity sensors ➅ Battery recharge connector ➆ ON-O attery switch ➇ Second reset tton zzy logic controllers (L) [2]-[1] have een widely sed for ehavior-ased roots like Khepera ecase they can easily transform lingistic information and expert knowledge into control signals While fzzy logic control has many advantages over traditional methods, it has also some drawacks at the design stage in that it is difficlt to determine the optimal parameters Ths, many researchers have applied evoltionary algorithms to the constrction of Ls in order to atomate the procedre of determining the parameters [6]-[9] Most of them, however, do not provide an in-depth analysis of the ehaviors otained y the Ls evolved Recently, the concept of emergence has een focsed as a reslt of researches in non-linear dynamics, artificial life, complex systems, and ehavior-ased rootics Emergence of a system, in a road way, is said to e the properties or ehaviors that cannot easily e predicted from its internal properties Examples of these phenomena are the flocking ehavior in simlated irds from a set of three simple steering ehaviors [11], some patterns in the game of life [12], and the highway pattern y the artificial Langton ant [1] In spite of the roadness of emergence phenomena, there is no nified agreement on what emergence is One of the first definition on emergence was made y Morgan who defined: emergence is the denomination of something new which cold not e predicted from the elements constitting the preceding condition or the prodct is not a mere sm of the separate elements [14] Beda proposed weak emergence in contrast to strong emergence [1] According to his definition, properties or ehaviors of a system are weakly emergent if and only if they can e derived from the dynamics which governs the time evoltion of the system s microstates, only y simlation Ronald proposed a three-step emergence test [16] The three steps are design, oservation, and srprise He drew an analogy with the concept of intelligence and the Tring test Baas [17] defined two emergence: Dedcile emergence if there is dedctional or comptational process or theory, and oservational emergence if it cannot e dedced In this paper, we constrct the L whose internal parameters are tned y GA to control the sensor-ased moile root, Khepera In order to do this, we represent the L parameters, the fzzy sets and rles of the L, in genetic codes We show that the evolved ehaviors are oservationally emergent ased on Baas notion of emergence 2 Oservational Emergence Emergence has played a major role in the description and discssion of natral and artificial life, and complex systems In an intitive point of view, it is sed as a name for creation of new strctres and properties as the old philosophical statement, the whole is more than the sm of its parts or more formal definition of emergence, we have sed Baas notion which will e explained as follows [17] The definition of emergence starts with a general notion

2 : i K T T M M P P X of strctres as primitive ojects or entities A strctre may e of an astract or physical natre, eg, systems, organizations, organisms, machines, concepts, etc rthermore, assme that we have some kind of oservational mechanism (or family of sch) in order to evalate, oserve, and descrie the strctre This cold e an internal mechanism of the system as well as an external one To give a general procedre for how to constrct a new strctre from a family of old ones, let s start ot with a family of strctres, (some index set, finite or infinite) (1) Then we apply or oservational mechanisms,, to otain properties of the strctres, (2) Next we pt the s to a family of interactions,, sing the properties registered nder the oservation Hence we get a new kind of strctre as follows! " # $%& () where stands for the reslt of the constrction process Here, is a second-order strctre as opposed to the s which are first-order strctres The interactions may e cased y the strctres themselves or imposed y external factors At each level of constrction new properties or new ehaviors may emerge, giving room for new interactions, and hence each level is necessary in order to get the last level s properties Therefore, the ' th order strctre is defined as follows )(*+ (-, /21 (-, 4 (-, (-,# (-,# (4) where ' means the ' th order and (-,# means th strctre of '7698 th order rom this, we can introdce the definition of emergence as follows is an emergent property of )=<?> : ) t :A@ D41 B,# for all () B,# Emergence is dedcile or comptale if there is a dedctional or comptational process or theory E sch : that )B,# can e determined y E from 41 B,# B,#, and oservational if : is an emergent property t cannot e dedced as in dedcile Evolved zzy ontroller As we se fzzy logic as the control mechanism of or moile root, the first order strctres and interactions are determined in terms of fzzy logic The asic strctre of a fzzy logic controller consists of three conceptal components: fzzification of the inpt-otpt variales, a rle ase which contains a set of fzzy rles, and a reasoning mechanism which performs the inference procedre on the rles and given facts to derive a reasonale otpt rom the fact that the control in fzzy logic controller is performed throgh the interactions (fzzy inference and defzzification) of fzzy rles, we determine the first order strctres and interactions as follows irst order strctres the th fzzy rle irst order interactions G the inference and defzzification 1 irst Order Strctres : zzy Rles To constrct the first order strctres, fzzy rles, we first need to define fzzy sets on oth inpts from sensors and otpts to the motors of the moile root Or L ses the sensory information of eight proximity sensors as inpts and controls the speed of the two motors on Khepera The inpt lingistic variale H and otpt lingistic variale I are expressed y lingistic vales (V,,, V) and (BH, B,, H) respectively The lingistic terms have the following meanings: Inpt Variale V : Very ar : ar : lose V : Very lose are all in a trian- The memership fnctions of E glar form defined y eqation (6) trianglelk NMO QP +RSM Otpt Variale BH : Backward High B : Backward : orward H : orward High RS and KU6 V6 6&K 6W#X where the parameters ZMO QP with M\[ [+P determine the K coordinates of the three corners of the nderlying trianglar memership fnction To redce the comptational complexity, some restrictions are applied to each memership fnction (see igre 2) The th rle can e represented as a fzzy relation defined y eqation (7) S] ^E a ` E \` E cd` E e ` E f\` E gd` E h (7) where i denotes fzzy relation This fzzy relation can e implemented with each corresponding memership fnction defined y eqations (8) and (9) j#kml n oh H H H c H e H f H g H h I!p j#q n ^H srrsr# j#q t ^H h j2l n oi N (8) j#kml oh H H H c H e H f H g H h I!p j q n ^H srrsr# j q t ^H h j l QY (6) oi N (9)

3 ` ` z { z E ` E di y vi v V BH di 1 vi 1 di 2 vi 2 di vi x di 4 U d di (a) vi 4 B vi di 6 w vi 6 di 7 vi 7 di 8 vi 8 v V di 9 12 H vi 9-1 U v +1 () igre 2: The memership fnctions of inpt (a) and otpt () variales 2 Interactions Here, we define the interactions of the first order strctres (fzzy rles) The fzzy rles can interact with each other y fzzy reasoning and defzzifiation } Let E and E e the fzzy sets defined on H in the } } niverse of discorse ~% and and e the fzzy sets defined on I and I in the niverse of discorse ~) respectively } To control the actions of moile root, and } shold e inferred from E and The th rle can e transformed into a fzzy relation ased on Mamdani s fzzy implication fnction [18] Based on Zadeh s compositional rle of inference [19], and are expressed as } } ` } ` } rsrr rsrr rsrr rsrr G h G h G h G h mƒ mƒ mƒ mƒ (-, } (-, } (-, } (-, } a` rrsr rrsr h i h i (1) (11) where ƒ denotes the maximm-minimm composition The reslting and are expressed as in the following eqations j l n (-, n Œ j q } ˆ Š n oh # j q n oh ŽO n t Œ j q ˆ Š t ^H h # j q t ^H h ŽO j l t (-, } Similarly, j l L rrsr h j l š Lœ ž Ÿ ^ L žn o j l is defined as (-, } n LI rsrr h j2l šz Lœ sž ŸL o L žn o rsrr n LI LI (12) (1) where denotes the minimm operation and is the maxima of the memership fnctions of E } Defzzification refers to the way I and I are extracted from a fzzy set as representative vales Among many defzzification methods [18], [2]-[21], the center of gravity method is sed ecase it is widely sed and also appropriate for or system to control the moile root I A n j n oi I H I n j n LI H I (14) Evoltion I A j oi I H I j LI H I (1) A genetic algorithm (GA) is a search techniqe ased on the mechanics of natral selection and natral genetics [22] This comines srvival of the fittest among string strctres with a strctred yet randomized information exchange to form a search algorithm with some of the innovative flair of hman search In every generation, a new set of strings is created sing its and pieces of the fittest of the old an occasional new part is tried for good measre While randomized, genetic algorithms are no simple random walk They efficiently exploit historical information to speclate on new search points with expected improved performance At first, a poplation of individals that encode candidate soltions to given prolem is initialized at random Each individal in the poplation is evalated in the prolem at hand and changed y genetic operations sch as crossover and mtation to reprodce a new poplation This process goes on ntil a satisfactory individal appears in the poplation There are two parameters that shold e determined to rn GA: how to encode the L parameters in gene code and how to estimate the fitness vale of each individal or the L parameters, eight inpt variales, two otpt variales,

4 8 ª gets higher fitness vale On the other hand, the root that collides against the wall or has many rles and fzzy sets gets lower fitness vale inary encoded vale 11 igre : Encoding of memership fnction and maximally ten rles are encoded Sixty its are reqired to encode all the fzzy sets defined on all the inpt-otpt variales ecase only two of the for fzzy sets of a variale need to e encoded and only six its are reqired to encode two fzzy sets (see igre ) d d1 d2 d d4 d d6 d7 v v1 ª ª ª ª ª ª ª ª ª ª ª ª variale toggle flag rle toggle flag 1 conditional part 2 conseqent part igre 4: Encoding of a rle Each rle has eight inpt variales, H s H h, and two otpt variales, I and I Three its represent each inpt variale Two of them (white cells in igre 4) are sed for coding one of the for fzzy sets, V (), (1), (1), and V (11) The last one is a toggle it The variale having the toggle it 1 participates in the conditional part in the fzzy rle In otpt variales, the two its of each variale are sed for coding one of the for fzzy sets, BH (), B (1), (1), H (11) There are no toggle flags ecase all the otpt variales shold appear in conseqent part inally, the last it in igre 4 designates whether this rle participates in fzzy inference process or not Therefore, igre 4 can e decoded as follows: oh 9 m±g² ³ ^H m±g² ³ ^H g *µ m±g² ³ ^H h -µ ¹»º¼ LI +½ #±G² ³ oi Ó Ø Í Ó Ô Ø To se GA for the evoltion of individals representing L for the moile root, a fitness fnction is defined y eqation (16) ps ¾ ²B ÁÀ ÂOÃÄ Å}Æ ÇÅ ÈÉÈDÊDËNÊDÅG² ËQmÌÍ À?Å4ÎBÊÉ²ÁÏ ³ÐÊË ÑÒ±}² ÇÃZ#Ì ²B ÁÀ ÂOÃÄ Å}Æ ÄN ÁÈDÃsËÒ#ÌÕÔ ²B ÁÀ ÂOÃÄ ÅGÆmÆL ÁÖsÖ ËNÃÑÒËQmÌ ÇÒÙÁÃZÇÒÚ ÛOÅGÊD²ÑQËQ (16) where ¾W 6ÝÜ YGÝ 68 YÁ ±G² ³ *Þ}YGY 68 Here, only moving distance and check points have positive effects on the fnction Therefore, the root that moves long distance or passes throgh many check points 2 4 Emergence Analysis Experiments have een performed on a SUN SparcStation 1 machine At the eginning of evoltion, two hndred individals are initialized at random rossover and mtation operations are applied with the proaility of and, respectively Then each individal is decoded into an L, which controls the Khepera moile root in a simlation environment like igre Each individal is evalated for five thosands times of sensor sampling In early generations, the igre : The environment sed for evolving the root fitness has radically increased with some oscillation After the 67th generation, the est fitness does not increase significantly On the contrary, average fitness steadily and continosly increases as generation passes Althogh we have sed an elite preserving strategy in the selection process [22], the est fitness vale oscillates ecase the sensor information is noisy to make the simlation more realistic rom the 64th generation, individals with extremely high fitness vale start to show p and disappear Among the individals, the first individal that reaches the goal position has appeared from the 67th to 7th generations The fzzy rles of the est individal are shown in Tale 1 or the demonstration of oservational emergence, we once again state the parameter settings of emergence irst order strctres the th fzzy rle irst order interactions the fzzy inference and defzzification the ehavioral properties of strctre Second order strctre 9 = the evolved fzzy logic controller 41 Trning Arond Trning arond from a dead end is an important ehavior that the root shold acqire rom the simlation, we find that

5 Rle 1 Rle 2 Rle Rle 4 Rle Rle 6 Rle 7 Tale 1: Evolved fzzy rles I (H ) and (H f V) and (H h V) BH) and (I B) I (H e V) H) and (I ) I (H V) and (H ) and (H e ) and (H h V) BH) and (I B) I (H ) and (H c ) and (H g V) ) and (I H) I (H e V) BH) and (I ) I (H V) and (H e ) and (H g V) ) and (I H) I (H V) and (H e ) and (H f ) BH) and (I ) the three first order strctres, f, and h in Tale 2 are interacting in trning arond sitation (a) Speed according to the activation of rle 2 Tale 2:, f, and h (=Rle 2) : I (H e V) H) and (I ) f (=Rle ) : I (H e V) BH) and (I ) h (=Rle 7) : I (H V) and (H e ) and (H f BH) and (I ) ) igre 6 shows the s of the three strctres As yo can see, shows that the root stops after some moves from the start position (see also igre 7) f and h show that the root does not move at all On the other hand, igre 8 shows of the fzzy controller composed of three strctres,, f, and h interacting with each other Dring the steps from 1 to 61 in igre 8, the root ses all the three first order strctres igre 9 () éê, éë, and é ç sensor vales (a) ß)à á â ã ä å æ () ß)à áâã ä ç æ (c) ß)à áâã ä è æ igre 6: of three strctres from step 1 to 61 shows another view of when the root trns arond: igre 9 (a) shows the sensing vales of the related sensors from step 1 to step 1 igre 9 () shows the activation levels of related rles, 2,, and 7, and igre 9 (c) shows the speed changes of the two motors dring this process As can e seen in igre 9, the interactions of the three (c) Activation of rle 2 igre 7: Analysis of

ò ì ñ í í í ø û ö ü @ Vales 12 1 ï8 ñ 6 4 õ2 ô ô 1 2 ó 4 6 ð7 ï8 d d4 d î9 1 Activation 1 8 6 4 2 1 2 ù ú4 6 ý7 Rle 2 Rle Rle 7 þ8 ÿ9 1 Speed 1 - -1 1 2 4 6 Left Motor Right Motor 7 8 9 1 (a) é ê, é

the different from the ( ) of first order This implies that : t :A@ for all with : (17) Trn Arond Therefore, we can conclde that the is the emergent ehavior y the definition in eqation () 42 Smooth

6 ò ì ñ í í í ø û ö Vales 12 1 ï8 ñ 6 4 õ2 ô ô 1 2 ó 4 6 ð7 ï8 d d4 d î9 1 Activation ù ú4 6 ý7 Rle 2 Rle Rle 7 þ8 ÿ9 1 Speed Left Motor Right Motor (a) é ê, é ë, and é ç sensor vales () Activation of related rles (c) wise speed change of the root igre 9: Analysis of (a) step 1 () step 1 igre 8: (c) step 41 (d) step 61 first order strctres,, f, and h, make the different from the ( ) of first order This implies that : t :A@ for all with : (17) Trn Arond Therefore, we can conclde that the is the emergent ehavior y the definition in eqation () 42 Smooth ornering At a corner, the root shold trn the corner to the left or right as safely and smoothly as possile rom the simlation, we find that the two first order strctres and h shown in Tale 2 are interacting in conrer sitations igre 1 shows the two strctres, and h As yo can (a) ß)à áâã å æ ä () ß)à áâã è æ ä igre 1: of three strctres from step 1 to 9 see, shows that the root trns the corner with difficlty, and also there are some mps at the corner (see also igre 11) h shows that the root rather moves ackward On the other hand, igre 12 shows of the fzzy controller composed of two strctres and h interacting with each other Dring the steps from 1 to 9 in igre 12, the root ses all the two first order strctres igre 1 shows another view of when the root trns the corner: igre 1 (a) shows the activation levels of related rles, 2 and 7, and igre 1 () shows the speed changes of the two motors dring this process As can e seen in igre 1, the interactions of the two first order strctres, and h, make the different from the ) of first order This implies that : t : for all with : (18) Smooth ornering Therefore, we can conclde that the is the emergent ehavior y the definition in eqation () onclsion In this paper, we have analyzed the L of a moile root evolved y a GA with Baas definition of emergence The L finally constrcted y evoltion consists of jst seven rles with one to three inpt variales and even more only three of them are sed to get to the goal position, althogh, theoretically, there can e rles ecase there are eight inpt variales and two otpt variales in a rle and for fzzy sets per variale and a toggle flag with every inpt variale The root has otained proper rles for several ehaviors like smooth cornering and trning arond to navigate in the complex environment These rles form what Baas calls first order strctres We have shown that these first strctres and their interactions give rise to the emergent ehaviors or oservational emergence of second order strctres As frther research, the third or higher order strctres are to e researched ased on the second order strctres shown as the root s ehaviors in this paper This can e researched in several ways One of them is to stdy the grop ehaviors of mltiple root agents each of which consists of second order strctres

(a) step 1 () step 28 (c) step 68 (d) step 9 igre 12:

rle 2 rle 7 Activation 6 4 2 1 2 4 6 7 8 9 () éê, éë, and é ç

7 (a) step 1 () step 28 (c) step 68 (d) step 9 igre 12: ornering (a) Speed according to the activation of rle rle 2 rle 7 Activation () éê, éë, and é ç sensor vales (a) Activation of related rles 1 Left Motor Right Motor Speed ! (c) Activation of rle 2 igre 11: Analysis of () wise speed change of the root igre 1: Analysis of

8 Biliography [1] K-Team, Khepera Simlator Version 2 User Manal, 1999 [2] LA Zadeh, zzy sets, Information and ontrol, vol 8, pp 8-, 196 [] SR ang, T Sn and E Miztani, Nero-zzy and Soft ompting, Prentice-Hall, 1997 [4] P King and EH Mamdani, The application of fzzy control system to indstrial process, Atomatica, vol 1, pp 2-242, 1977 [] HR Beom and HS ho, A sensor-ased navigation for a moile root sing fzzy logic and reinforcement learning, IEEE Transactions on Systems, Man, and yernetics, vol 2, no, pp , 199 [6] TL Seng, MB Khalid and R Ysof, Tning of a nero-fzzy controller y genetic algorithm, IEEE Transactions on Systems, Man, and yernetics-part : yernetics, vol 29, no 2, pp , 1999 [7] MH Lim, S Rahardja and BW Gwee, A GA paradigm for learning fzzy rles, zzy Sets and Systems, vol 82, pp , 1996 [8] S-B ho and SI Lee, Moile root learning y evoltion of fzzy controller, ornal of Intelligent and zzy Systems, vol 6, pp 91-97, 1997 [16] EMA Ronald, M Sipper and MS apcarrere, Design, oservation, srprise! A test of emergence, Artificial Life, vol, pp 22-29, 1999 [17] NA Baas, Emergence, hierarchies, and hyperstrctres, Artificial Life, pp 1-7, 1992 [18] EH Mamdani and S Assilian, An experiment in lingistic synthesis with a fzzy logic controller, International ornal of Man-Machine Stdies, vol 7, no 1, pp 1-1, 197 [19] LA Zadeh, Otline of a new approach to the analysis of complex systems and decision processes, IEEE Transactions on Systems, Man, and yernetics, vol, no 1, pp 28-44, 197 [2] N Pflger, Yen and R Langari, A defzzification strategy for a fzzy logic controller employing prohiitive information in command formlation, Proceedings of IEEE International onference on zzy Systems, pp , 1992 [21] RR Yager and DP ilev, A simple adaptive defzzification method, IEEE Transactions on zzy Systems, vol 1, no 1, pp 69-78, 199 [22] DE Golderg, Genetic Algorithms in Search, Optimization " Machine Learning, Addison Wesley, 1989 [9] K Izmi, K Watanae, T Miyazaki, zzy ehaviorased control for a miniatre moile root, Proceedings of Knowledge-Based Electronic Systems, vol, pp 48-49, 1998 [1] Lee, zzy logic in control systems : zzy logic controller, part 2, IEEE Transactions on Systems, Man, and yernetics, vol 2, no 2, pp 419-4, 199 [11] W Reynolds, locks, herds, and schools: A distrited ehavioral model, ompter Graphics, vol 21, pp 2-4, 1987 [12] ER Berlekamp, H onway and RK Gy, Winning ways for yor mathematical plays, Academic Press, vol 2, pp 817-8, 1982 [1] I Stewart, The ltimate in anty-particles, Scientific American, vol 271, pp 14-17, 1994 [14] L Morgan, Emergent Evoltion, Williams and Norgate, 192 [1] MA Beda, Weak emergence, Philosophical Perspectives: Mind, asation, and World, vol 11, pp 7-99, 1997

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