Letters. Evolving a Modular Neural Network-Based Behavioral Fusion Using Extended VFF and Environment Classification for Mobile Robot Navigation

Transcription

1 IEEE RANSACIONS ON EVOLUIONARY COMPUAION, VOL. 6, NO. 4, AUGUS Letters Evolvng a Modular Neural Network-Based Behavoral Fuson Usng Extended VFF and Envronment Classfcaton for Moble Robot Navgaton Kwang-Young Im, Se-Young Oh, and Seong-Joo Han Abstract A local navgaton algorthm for moble robots s proposed that combnes rule-based and neural network approaches. Frst, the extended vrtual force feld (EVFF), an extenson of the conventonal vrtual force feld (VFF), mplements a rule base under the potental feld concept. Second, the neural network performs fuson of the three prmtve behavors generated by EVFF. Fnally, evolutonary programmng s used to optmze the weghts of the neural network wth an arbtrary form of objectve functon. Furthermore, a multnetwork verson of the fuson neural network has been proposed that lends tself to not only an effcent archtecture but also a greatly enhanced generalzaton capablty. Heren, the global path envronment has been classfed nto a number of basc local path envronments to whch each module has been optmzed wth hgher resoluton and better generalzaton. hese technques have been verfed through computer smulaton under a collecton of complex and varyng envronments. Index erms Behavoral fuson, evolutonary learnng, moble robot navgaton, modular neural networks. Fg. 1. Conventonal VFF concept. number of basc local envronments [13] to whch each of the above behavor modules has been optmzed. hs modular approach [14], [15] lends tself to better generalzaton of the navgaton algorthm. I. INRODUCION he vrtual force feld (VFF) approach [1], [2] s one of the classcal heurstc approaches to local navgaton assumng no global maps of the navgaton envronment. hs s a knd of behavor-based control paradgm [3], [4] n whch the prmtve behavors, such as goal seekng and obstacle avodance, are mutually coordnated to execute a certan task. Heren, each behavor s defned as a stmulus-acton par [4]. On the other sde, evolutonary robotcs [5] [9] s ganng ncreased attenton, whch conssts of a coordnated collecton of smple modules exhbtng emergent ntellgent behavors. In ths paper, the VFF method s extended to nclude free-space behavor as the thrd component. Each of the three forces may be consdered as three basc behavors: 1) obstacle avodance; 2) goal-seekng; and 3) free-space attracton. here are two basc routes to generate overall behavor from these component behavors. Cooperatve fuson [4] takes a lnear combnaton of these behavors, whle compettve fuson selects only one of the behavors at a tme. Whle ths extended vrtual force feld (EVFF) method can solve the local mnmum problems of cooperatve fuson n most cases, t stll may run nto local mnma n specal envronments such as U-shaped objects or narrow channels along the path. o crcumvent ths, a neural network s used for behavoral fuson [10] [12] and further, ts weghts are traned utlzng evolutonary programmng (EP) [6] so that any desred cost functon may be optmzed. Fnally, the global envronment s classfed nto a Manuscrpt receved July 25, 2000; revsed July 23, 2001 and January 2, hs work was supported n part by the Bran Scence and Engneerng Research Program of the Korean Mnstry of Scence and echnology and n part by the Mnstry of Educaton of Korea toward the Electrcal and Computer Engneerng Dvson at Pohang Unversty of Scence and echnology under Program BK21. K.-Y. Im s wth the Insttute of Intellgent System, Samsung Electroncs Ltd., Paldal-Ku, Suwon, Korea (e-mal: neospace@samsung.co.kr). S.-Y. Oh and S.-J. Han are wth the Department of Electrcal Engneerng, Pohang Unversty of Scence and echnology, Pohang, South Korea (e-mal: syoh@postech.ac.kr; hansl@postech.ac.kr). Publsher Item Identfer /EVC II. EXENDED VIRUAL FORCE FIELD MEHOD he VFF method n Fg. 1, a varant of the potental-feld method [1], [2], determnes moble robot s speed accordng to the vector sum of two component forces: 1) goal seekng and 2) obstacle avodance. he magntude of the repulsve force F vr s nversely proportonal to the square of the dstance between the robot and the obstacle. A slght modfcaton s made n our own defnton so that the repulsve force decreases as the dstance ncreases where d F r = F vr [(cos )e x +(sn )e y ] (1) Fvr =6tanh 2 3 (1 0 d) (2) F r = F r (3) angle between the th sensor and the obstacle; dstance to the obstacle for the th sensor; e x; e y unt vector along x; y axes. Next, the goal attractve force s F a = Fca[(cos g)e x + (sn g)e y] (4) g = tan 01 yg 0 y xg 0 x Fca force constant; g robot-to-goal orentaton; x g ; y g goal coordnates. hen, the resultant force vector F becomes (5) F = Fa + Fr: (6) However, usng only attractve and repulsve forces makes the robot vulnerable to becomng trapped n local mnma. he motvaton behnd the EVFF method s to avod three local traps by addng the free force F f as the thrd vrtual force component. hs pont s llustrated n Fg. 2. he free-space force n Fg. 2 allows the robot to escape X/02$ IEEE

2 414 IEEE RANSACIONS ON EVOLUIONARY COMPUAION, VOL. 6, NO. 4, AUGUS 2002 Fg. 4. Proposed archtecture. III. NEURAL-NEWORK-BASED BEHAVIORAL FUSION WIH EVOLUIONARY PROGRAMMING WEIGH OPIMIZAION As mentoned, EVFF stll suffers from the local traps n dffcult stuatons. herefore, each of the three force components s multpled by proper gans before beng added as follows: Fg. 2. Fg. 3. Conventonal VFF versus EVFF. Defnton of the free-space force. F = 1 F a + 1 F r + F f (8) where 0 < < 1 and 0 < < 1. Fg. 4 shows the overall archtecture. he eght sensor readngs and goal orentaton are nput to the EVFF block, whch then computes the three vrtual force components and combnes them through proper gans nto the resultant force, from whch the steerng and velocty commands are derved. he coeffcents, provde the weghts for the attractve and repulsve force components and are obtaned as output of a sngle layer perceptron [11] feedng on the sensory data and the goal drecton relatve to the robot. he weghts of ths sngle-layer percepton are optmzed through EP [6] snce the cost functon s hghly complex and not dfferentable wth respect to the weghts. he cost functon used n ths research wll be explaned next. A. Optmal Gan Learnng hrough Evolutonary Programmng he objectve n gan tunng va a neural network s to determne the optmal values for and, whch we acheve obstacle avodance and goal seekng wthout beng trapped at local mnma, and do ths n the shortest possble tme. Of course, some of these ndvdual objectves may be n conflct and some sutable weghts representng ther relatve mportance must be selected. After fxng the start and goal postons n a rather complex envronment, EP s executed regardng the current neural weghts as an ndvdual, usng the cost functon calculated over the robot s trajectory [5], [6]. EP for neural weght learnng uses the followng self-adaptve mutaton rule [6]: x 0j = xj + N(0; j ) 0j = j 1 exp( 1 N (0; 1) N j (0; 1)) (9) local mnma. F f s computed from ultrasonc sensor readngs and goal orentaton. Frst, the group of eght sensors used n our experment s parttoned nto sx overlappng subgroups of three sensors for each, as shown n Fg. 3. he basc dea behnd sensor groupng s that the free drecton s toward the sensor group wth maxmum average dstance to the obstacle. he averagng s needed to fnd as wde an open space as possble and further to make t robust to sensor nose. hen, the subgroup wth the maxmum average dstance to the obstacle becomes the drecton of the free space. In case of multple maxma, the subgroup lyng n closest drecton to the goal s chosen. hus, the resultant force n EVFF becomes F = Fa + Fr + F f : (7) where x j s jth component of th ndvdual and j s jth standard devaton of th ndvdual. he nput to the neural network conssts of [S(t); S(t02); S(t04)], where S(t) are the 24 sensor readngs at tme t. he reason for usng the sensor hstory data s to look at the local navgaton hstory n order to derve better commands. Hstory of the ultrasonc readngs s used as nput to the neural network to reflect the local path (not just a pont n the path) followed by the robot. hs hstory data consttute the dynamc state of the robot and provde contextual nformaton. hs hstory nformaton allows a dfferent control command to be offered at a gven tme, even for the same value of current sensor readngs dependng on what the past readngs were. hs way, more optmal path plannng s possble. Next, we come to the queston of how far nto the

3 IEEE RANSACIONS ON EVOLUIONARY COMPUAION, VOL. 6, NO. 4, AUGUS past to look for past hstory. Use of [S(t); S(t0 1); S(t02)] may not be effectve snce there may be lttle change n sensor values for such a short tme span. Our research determned the choce of [S(t); S(t 0 2); S(t 0 4)] emprcally. hese values were selected after expermentng wth two to fve moments n tme of the sensory values. Hence, ths s not an optmal combnaton and t may be possble to fnd a better combnaton of past hstores. B. Defnton of Cost Functons he defnton of cost s a very mportant problem n any optmzaton [5], [6]. he most mportant concern s to complete the msson wthout becomng trapped at local mnma. hs comprses the frst term of the cost, represented by lm. Next, t must do so wthout collson. co stands for collson occurrence and defnes a penalty functon that degrades performance n the event of a collson wth an obstacle. hrd, n order to reduce the chance of collson, t s better to maxmze the mnmum obstacle clearance (oc) for safety margn. Fourth, the steerng angle change (sc) must also be mnmzed for smoother moton. Last, t s better to run wth mnmum path length (pathlen). From these consderatons, the cost functon s Cost = Q 1 1 lm + Q2 1 co + Q3 1 oc + Q4 1 sc + Q5 1 pathlen = lm + co +201 oc(t)+81 sc(t) + pathlen (10) 0; f the robot does not get trapped at local mnmum lm = (11) ; f the robot gets trapped at local mnmum co = oc(t) = 0; f the robot does not collde wth obstacles ; f the robot colldes wth obstacles 0; f Mn S >k2, 1 0 Mn k2 S ; f k1 < Mn S <k2, (12) (13) 500; f Mn S <k1. sc(t) = j(t) 0 (t 0 1)j; (t) = steerng angle (14) pathlen = t 1l(t); 1l(t) = (1x(t)) 2 +(1y(t)) 2 : (15) he relatve weghts Q1Q5 have been chosen subjectvely after many navgaton experments n varous envronments. he assgned weghts of the cost functon reflect the relatve penalty for each cost component. he weghts Q1, Q2 for [lm and co] were chosen very hgh to heavly dscourage the occurrence of a local trap or collson. hs hgh value was normalzed to 1.0 whle the remanng weghts Q3Q5 may be properly selected accordng to a subjectve judgment upon the mportance of obstacle clearance, path smoothness, and total tour length for a good navgator. IV. MULINEWORK FUSION ARCHIECURE he EP-optmzed EVFF enables the robot to move from start to goal n a gven envronment. However, f the envronment changes greatly Fg. 5. wo sensory stuatons. U-shaped object wth = = 1. Narrow channel wth = =1. (c) U-shaped object wth = small and = large. (d) Narrow channel wth = large and = small. and/or the startng locaton changes, then the orgnal gans must be further optmzed for a new stuaton. herefore, the navgaton envronment may be segmented nto a local regon wthn whch optmzaton s performed n a fne-gran mode [14], [15]. After ths local optmzaton process, the navgator wll recognze each stuaton n real tme as belongng to one of the pretraned small regons and then read out the proper network weghts [8], [12]. hs wll ncrease the algorthm s robustness as well as ts generalzaton capacty. he mportant ssue to ths end s how to classfy the local stuatons encountered durng navgaton. A. Modular Network Usng Manual Envronment Classfcaton he exact form of the force equaton used n VFF has a large nfluence upon the navgaton performance. It may even be better to change the form of the equaton as a functon of the envronment. herefore, we formulated the basc force equaton as a summaton of the three force components and then adjusted the relatve contrbuton of each component by controllng, whch s the gan term for the repulsve force. hs gan term s generated by a neural network lookng at the local envronment as ts nput. Snce the cost functon representng the robot performance s dscrete and nonlnear as a functon of the neural network weghts and the dynamc model of the robot, EP has to be used to tran these weghts. In ths secton, two classes of stuatons are consdered n whch the performance s qute senstve to the gan. he sensor nformaton alone s not unque to the stuaton classfcaton. Consder two stuatons n Fg. 5 and wthout controllable values of,. he sensory patterns at the entrances of a U-shape obstacle and a narrow corrdor are dentcal as shown n Fg. 5. However, n front of a U-shape local mnmum, the robot needs to be dscouraged from enterng t by ncreasng and, therefore, the repulsve force. In contrast, n front of a narrow corrdor, the robot needs to be encouraged to pass through by decreasng or the repulsve force. In order for the robot to move n a desred drecton, the attractve force and repulsve force must have a substantal dfference n magntude despte ther drectons beng the same. Notce that the free-space force s dentcal. herefore, n case of local trap n Fg. 5,, the coeffcent multplyng the attractve force, must be small whle, the coeffcent multplyng the repulsve force, must be as large as possble. On the contrary, n the case of a narrow path n Fg. 5, must be large whle must be small. he results n Fg. 5(c) and (d) are obtaned usng these controllable values of, for better performance. A pragmatc alternatve wll be to localze the optmzed EVFF to each stuaton and adopt a module selecton network, whch wll classfy the stuaton at hand as shown n Fg. 6. hs sngle-layer network wll look at the goal drecton g as well as the sensor values n order to dstngush the two dfferent cases n

4 416 IEEE RANSACIONS ON EVOLUIONARY COMPUAION, VOL. 6, NO. 4, AUGUS 2002 Fg. 6. Smple module selecton network, whch s traned by manual classfcaton of the envronment. Fg. 5. After each module has been optmzed for ts doman of expertse of the sensory stuatons, they wll be combned wth the module selecton network so that the archtecture can cope wth a multtude of envronments. B. Modular Network Usng Automatc Envronment Classfcaton by Clusterng A sngle network cannot be traned to be a good controller for all the varous envronments. hs s why we proposed a modular neural network. In ths approach, an envronment represented by the sensory patterns s classfed nto fve prototype local envronments for each of whch a neural network s to be traned. he detals of the fve envronments are explaned n Secton V-C. he tranng data for clusterng was obtaned by navgatng a robot through a varety of obstacle envronments. Although we do not clam these fve prototypes are complete, relegaton to the closest prototype seems to work well for navgaton purposes even for other envronments not ncluded n the cluster set. In ths secton, the varous sensng patterns encountered along the way are classfed or clustered nto many local envronments, whch nclude the local mnmum and narrow passage stuatons dealt wth prevously. hen, each behavor module s traned only for the correspondng local envronment and a dfferent permutaton of these local envronments can generate a great varety of navgaton paths. hus, ths modular approach can adapt better to dfferent envronments than the monolthc case. he nput to the clusterng neural network s a quantzed verson of each sensor readng so that some of the detals wll be fltered out to group smlar envronments. Sensor values are quantzed before they are nput to the envronment classfcaton network n order to facltate clusterng by reducng the amount of varaton of the raw sensor patterns and also to allow a well-defned boundary between clusters. he level of quantzaton was determned heurstcally (tral and error) and has a great nfluence upon the navgaton performance. he envronment classfcaton network used n ths research s a smple adaptve-resonance-theory-lke network mplementng the follow-the-leader clusterng [13]. hs s a smple clusterng method where you start wth an ntal cluster whch s just the frst selected tranng pattern. When the second pattern enters, two thngs may happen. If ts dstance to the frst cluster center exceeds a threshold, then a new cluster center s created. Otherwse, t s assgned as a new member to an exstng cluster. After tranng, the classfcaton network looks at the sensory nput representng the current local envronment and determnes the closest prototype envronment. he ndex of ths prototype then enables the output of the correspondng neural network module to act as the two gan terms and, for the goal-attractve and obstacle-repulsve components, respectvely, of the EVFF computaton module. hs overall scheme s llustrated n Fg. 7. Fg. 7. Multnetwork archtecture where each module s localzed for the nput stuaton. Fg. 8. Evoluton of the robot s cost functon. V. SIMULAION RESULS he followng are the basc assumptons underlyng the seres of experments. 1) he moble robot can only move forward. 2) No sensor nose s assumed for smulaton. 3) Only statc obstacles are consdered. 4) he locatons of the goal and the robot are assumed to be known all the tme. 5) here s no pror nformaton regardng the envronmental map. 6) he sze of the navgaton envronment s confned to pxels. A. Evolutonary Programmng Optmzaton of Varable-Gan Extended Vrtual Force Feld he varable-gan EVFF s more useful n that t can adjust ts behavor gans, to meet varous objectves of nterest namely, local trap crcumventon whle avodng obstacles. he use of EP s deal for ths dffcult optmzaton problem. he populaton sze was 30, whle the tournament sze for selecton was 20. he ntal range for x was 01 x 1, for all, and (0) = 0:06667 (=dynamc range of x/populaton sze). Fg. 8 shows not only the total cost, but also the

5 IEEE RANSACIONS ON EVOLUIONARY COMPUAION, VOL. 6, NO. 4, AUGUS (c) (d) (e) (f) Fg. 9. Navgaton performance durng evoluton. Pont 1. Pont 2. (c) Pont 3. (d) Pont 4. (e) Pont 5. (f) Pont 6. ndvdual objectves such as obstacle clearance (oc), average steerng change sc, and the path length (pathlen), whch have been combned wth the relatve weghts of 20, 8, and 1 to yeld the total cost. As shown, after 30 generatons and 357 control steps per traversal, oc, sc, and pathlen became (27 pxels), (5 per step), and 1.82 (2 pxels per step), respectvely. he reason that the path length does not change much compared to the other ones s that ts weght s very small,.e., a short path length was preferred only after the assumpton of no collson and smooth moton n ths experment. Fg. 9 shows the actual paths taken at sx desgnated ponts of Fg. 8 and demonstrates that the robot evolves tself nto a short smooth path wth good obstacle clearance. B. Enhanced Generalzaton Usng a wo Module Fuson Network Archtecture A rather dffcult envronment consstng of the U-shaped obstacle or the very narrow channels explaned n Fg. 5 (Secton IV) has been used to demonstrate the generalzaton capablty of the multnetwork archtecture. Fg. 10 shows the result usng only Module 1, whch has been traned only n envronments wth many narrow channels to pass through, but wth no U-shapes. It demonstrates that the robot could collde nto the obstacle snce the repulsve gan has evolved nto a small value. However, the reverse stuaton s depcted n Fg. 10 usng Module 2. Although there s no collson, the clearance s not

6 418 IEEE RANSACIONS ON EVOLUIONARY COMPUAION, VOL. 6, NO. 4, AUGUS 2002 Fg. 12. Comparson of varous costs. Fg. 10. Executed path usng only one module. Module 1. Module 2. Fg. 13. Quantzaton of the ultrasonc sensor values. (c) (d) (e) Fg. 14. Fve cluster prototypes found by leader clusterng. Wde corrdor. U-shape. (c) Narrow corrdor. (d) Rght wall. (e) Left wall. Fg. 11. Executed path usng modules (1 +2). very good. Fnally, Fg. 11 shows the modular scheme n whch s ncreased for the U-shape but decreased for the narrow channels n order to acheve the low overall cost. Fg. 12 shows the ndvdual costs of the three methods descrbed above. It shows the cost of module 1 s very hgh due to collson. Obvously, Module (1 + 2) can recognze and adapt to dfferent stuatons by selectng gans that have been optmzed for each stuaton n order to reduce the overall cost. he same strategy parameters of EP were used as n Secton V-A. Some statstcs on the experments follow. After 30 generatons of evoluton, a reasonably optmal path has been found. At the ntal generaton, 30% of the ndvduals ether became locally trapped or collded wth an obstacle. 50% dd not reach the goal wthn a specfed tme lmt. As evoluton proceeds, these portons changed to less than 10% and 30%, respectvely. he remanng 60% reached the goal n tme, wth some of these beng the optmal trajectory. It took about four hours of evoluton on a PC usng a smulated robot and ths would have taken longer to apply evoluton to a real robot. C. Multnetwork Archtecture Usng Envronment Classfcaton By Clusterng Secton V-B showed the advantages of usng modular networks for behavoral fuson n order to adapt to dfferent stuatons. In ths secton, automatc clusterng of wdely varyng envronments s performed so that the modular approach can acheve better generalzaton over wdely varyng envronments. he nput to the classfcaton network conssts of the quantzed sensory patterns as shown n Fg. 13 where, MSR stands for maxmum sensng range. Fg. 14 shows the fve prototypes for clusters representng fve local envronments rangng from a wde corrdor, U-shape, (c) narrow corrdor, (d) rght wall, and (e) left wall. Fve neural network modules were traned usng EP under these fve sensory stuatons and then a proper sequence of these modules were called n to match the local envronments encountered to navgate from the start to the goal postons, as shown n Fg. 15.

7 IEEE RANSACIONS ON EVOLUIONARY COMPUAION, VOL. 6, NO. 4, AUGUS VII. SUMMARY AND CONCLUSION A new algorthm for safe and fast navgaton to a gven goal has been proposed n a completely unknown envronment. An EVFF scheme wth a neural network generated gans and an EP optmzaton of the weghts to satsfy a cost constrant lends tself to a very flexble structure that can cope wth varous envronments wth good generalzaton. However, the local weghts optmzed around a local stuaton may not be always sutable for global navgaton. herefore, the navgaton envronment has been classfed nto a certan number of classes and local optmzaton wthn the class has been attempted. he outcome s a modular EVFF approach n whch many local EVFFs are defned and optmzed locally. A module selecton network looks at the current stuaton and determnes the most sutable module to carry out the local task at a gven tme and the sequence of these selected modules performs global navgaton. hs way, the algorthm can adapt to a great varety of envronments wth a unfed archtecture. All these have been verfed va smulaton. Future work stll remans. he proposed algorthm needs to be recombed out to cover the dynamc obstacle envronment. In case of a drastc change of envronment, reoptmzaton may be needed. hus, an onlne optmzaton algorthm has been nvestgated. Map buldng s the next step so that the knowledge can be accumulated along the way. Fnally, the goal has to be specfed va ts absolute poston assumng accurate dead reckonng but eventually vson-based homng would be more desrable. REFERENCES Fg. 15. Navgaton performance of the multnetwork archtecture under two dfferng global envronments contanng U-shape and narrow passage. Narrow channel. VI. DISCUSSION Local navgaton, by defnton, cannot generate an optmal trajectory generally because no map nformaton s avalable. he robot only knows where t s and where the goal s. However, even local navgaton may generate a near-optmal trajectory f several local neural networks are traned to be local experts optmzed for a group of local envronments. he neural network wll generate, wth ts weghts optmzed to meet an objectve functon (defned n the paper). In summary, the proposed local navgaton algorthm represents a reasonably optmal trajectory wthout any pror map nformaton. Many researchers utlze EP to desgn and tran neural networks or fuzzy logc systems. hs s due to the dffculty of modelng the moble robot dynamcs under varous envronments. However, backpropagaton learnng s helpless wthout an exact model of the robot snce the robot performance depends on t. Furthermore, the optmalty of a global path, obtaned by a concatenaton of the local paths to be decded upon at each nstant of tme, can only be determned after the completon of navgaton. hs s why supervsed learnng cannot be used for ths applcaton. Fnally, EP allows the use of any cost functon whch sometmes cannot be expressed mathematcally n terms of the unknown parameters. [1] J. Borensten, Real-tme obstacle avodance for fast moble robots, IEEE rans. Syst. Man Cybern., vol. 19, pp , Sept./Oct [2] J. Borensten and Y. Koren, he vector feld hstogram Fast obstacle avodance for moble robots, IEEE J. Robot. Automat., vol. 7, pp , June [3] R. A. Brooks, A robust layered control system for a moble robot, IEEE J. Robot. Automat., vol. RA-2, pp , Mar [4] R. C. Arkn, Behavor-Based Robotcs. Cambrdge, MA: MI Press, [5]. Gom, Evolutonary Robotcs: From Intellgent Robots to Artfcal Lfe ER97. ON, Canada: AAI Books, [6]. Bäck, D. Fogel, and Z. Mchalewcz, Eds., Handbook of Evolutonary Computaton. London, U.K.: Oxford Unv. Press, [7] J.-M. Yang, J.-. Horng, and C.-Y. Kao, A new evolutonary approach to developng neural autonomous agents, n Proc. IEEE Int. Conf. Robotcs and Automaton, 1998, pp [8] A. Berlanga, P. Isas, A. Sanchs, and J. M. Molna, Neural network robot controller traned wth evoluton strateges, n Proc. Congr. Evolutonary Computaton, 1999, pp [9] R. Odagr, W. Yu,. Asa, O. Yamakawat, and K. Murase, Measurng the complexty of the real envronment wth evolutonary robot: Evoluton of a real moble robot Khepera to have a mnmal structure, n Proc. IEEE World Congr. Computatonal Intellgence, 1998, pp [10] J. an and N. Fukumura, Learnng goal-drected sensory-based navgaton of a moble robot, Neural Netw., vol. 7, no. 3, pp , [11] S. Haykn, Neural Networks: A Comprehensve Foundaton. New York: Macmllan, [12] A. M. S. Zalzala and A. S. Morrs, Neural Networks for Robotc Control. Herts, U.K.: Ells Horwood, [13] J.. ou and R. C. Gonzalez, Pattern Recognton Prncples. Readng, MA: Addsson-Wesley, [14] S. Yamaguch and H. Itakura, A modular neural network for control of moble robots, n Proc. Int. Conf. Neural Informaton Processng, vol. 2, 1999, pp [15] A. Ram and R. C. Arkn, Case-based reactve navgaton: A method for on-lne selecton and adaptaton of reactve robotc control parameters, IEEE rans. Syst. Man Cybern., vol. 27, pp , June 1997.