Multi-Objectivity for Brain-Behavior Evolution of a Physically-Embodied Organism

Transcription

1 in Artificial Life VIII, Standis, Abbass, Bedau (eds)(mit Press). pp Multi-Objectivity for Brain-Beavior Evolution of a Pysically-Embodied Organism Jason Teo and Hussein A. Abbass Artificial Life and Adaptive Robotics (A.L.A.R.) Lab, Scool of Computer Science, University of New Sout Wales, Australian Defence Force Academy Campus, Canberra, Australia. {j.teo,.abbass@adfa.edu.au} Abstract In tis paper, we present a pareto multi objective approac for evolving te beavior and brain (an artificial neural network (ANN)) of embodied artificial creatures. We will attempt to simultaneously minimize te network size wile maximizing orizontal locomotion. A variety of network sizes and beaviors were generated by te pareto approac. Te best networks exibited a iger level of sensory-motor coordination and te creature was able to maintain te walking beavior under different environmental setups. Introduction Multi-objective optimization as been previously introduced for action selection in beavior-based robotics using conventional teory (Pirjanian 1998) and for te design of a robot arm using evolutionary teory (Coello Coello, Cristiansen, & Aguirre 1998). In tis paper, a multi-objective approac is investigated for evolving artificial neural networks (ANNs) tat act as controllers for te legged locomotion of a -dimensional, artificial quadruped creature simulated in a pysics-based environment. Te Pareto-frontier Differential Evolution (PDE) algoritm is used to generate a pareto set of ANNs tat trades-off between locomotion beavior and brain (ie. neural network) size. Te concept of pareto defines a partial order dominance over te set of solutions. A solution X is said to be non dominated (pareto) iff tere is no oter solution Y in te population were Y is better tan X wrt all objectives. Te operational dynamics of te evolved creatures are analyzed to provide an insigt into ow a variety of controllers wit different beaviors emerge from te evolution. A comparison between a set of pareto controllers sowed tat different brain sizes exibit noticeably different locomotion beaviors. Altoug tis may seem obvious, maintaining a variety of brain sizes and beaviors is mainly contributed by te optimization of conflicting objectives. We also found tat a muc iger level of sensory-motor coordination is present in te best evolved controller. Finally we investigated te effects of environmental, morpological and nervous system canges on te artificial creature s beavior. Similar to oter studies, certain canges were found to be detrimental to te creature s walking-pat. In contrast to oter studies, owever, te creature was able to maintain te walking beavior in a large majority of te experiments. Situated and Embodied Evolution Te study of evolving pysically situated and embodied artificial creatures as been a otbed of researc in recent years. Te availability and maturation of commercial-off-te-self pysics engines coupled wit te dramatic increase of personal computing power ave encouraged researc into tis intriguing field of artificial life (Taylor & Massey 1). Since te pioneering work of Sims (Sims 1994), tere were notably few significant advancements in tis field until very recently. Researc in tis area generally falls into two categories: (1) te evolution of controllers for creatures wit fixed (Arnold 1997; Bongard & Pfeifer ; Gritz & Han 1997; Harvey 1997; Ijspeert ; Reeve 1999) or parameterized morpologies (Lee, Hallam, & Lund 1996; Paul & Bongard 1), and () te evolution of bot te creatures morpologies and controllers simultaneously (Bongard ; Hornby & Pollack 1; Komosinski & Rotaru-Varga ; Lipson & Pollack ; Ray ; Sims 1994; Taylor & Massey 1). Some work as also been carried out in evolving morpology alone (Eggenberger 1997) and evolving morpology wit a fixed controller (Lictensteiger & Eggenberger 1999). Related work using weeled robots ave also sown promising results in robustness and te ability to cope wit canging environments by evolving plastic individuals tat are able to adapt bot troug evolution and lifetime learning (Floreano & Urzelai 1998; ). Te empasis of most of tese studies ave been on te role of genetic encodings and ow different types of genotype-penotype representations allow for greater evolvability (Bongard ; Hornby & Pollack 1; Komosinski & Rotaru-Varga 1). Tere ave also been some investigations into te role of fitness functions and ow tey affect te direction of te evolu-

2 in Artificial Life VIII, Standis, Abbass, Bedau (eds) (MIT Press). pp 1 18 tionary process (Floreano & Urzelai ; Komosinski & Rotaru-Varga ; Ray ). A very recent investigation explored ow morpological complexity itself affects te emergence of more complex beavior in artificial creatures (Bongard & Pfeifer ). Considerably little as been said about te role of controllers in te artificial evolution of suc creatures. It as been noted tat te potential of designing more complex artificial systems troug exploitation of sensory-motor coordination remains largely unexplored (Nolfi & Floreano ). As suc, tere is currently a lack of understanding of ow te evolution of controllers affects te evolution of morpologies and beaviors in pysically simulated creatures. It remains unclear wat properties of an artificial creature s controller allow it to exibit te desired beavior. A better understanding of controller complexity and te dynamics of evolving controllers sould pave te way towards te emergence of more complex artificial creatures wit more complex morpologies and beaviors. Muc work in evolutionary robotics ave focused on evolving controllers for weeled locomotion (Lee, Hallam, & Lund 1996; Floreano & Urzelai 1998; ; Nolfi & Floreano 1998). Less work ave been conducted on evolving controllers for legged locomotion suc as (Arnold 1997; Reeve 1999). Here we are attempting to evolve controllers tat can generate walking beaviors for a four-legged creature. Metods Te Pysics Simulator Te simulation is carried out in a pysically realistic environment wic allows for ric dynamical interactions to occur between te creature and its environment. Tis in turn enables complex walking beaviors to emerge as te creature evolves te use of its sensors to control te actuators in its limbs troug dynamical interactions wit te environment. Furtermore, te accurate modelling of te simulation environment plays a crucial part in producing artificial creatures tat move and beave realistically in D (Taylor & Massey 1). A dynamic rater tan kinematic approac is paramount in allowing for effective artificial evolution to occur. Pysical properties suc as forces, torques, inertia, friction, restitution and damping need to be incorporated into te artificial evolutionary system. To tis end, te Vortex pysics engine (Critical Mass Labs ) was employed to generate te pysically realistic artificial creature (Figure 1) and its simulation environment. Te artificial creature is a basic quadruped wit 4 sort legs. Eac leg consists of an upper limb connected to a lower limb via a inge (one degree-of-freedom) joint and is in turn connected to te torso via anoter inge joint. Te mass of te torso is 1 and eac of te limbs is.5. Te torso as dimensions of 4 x 1 x 4 and eac of te limbs as dimensions of 1 x 1 x 1. Te inge Figure 1: Screen capture of quadruped in te simulation environment. joints are allowed to rotate between -7 to radians for limbs tat move counter-clockwise and to 7 radians for limbs tat move clockwise from teir original starting positions. Eac of te inge joints are actuated by a motor tat generates a torque producing rotation of te connected body parts about tat inge joint. Te creature s overall central nervous system is illustrated in Figure. y6 y5 y y1 LFL UFL x UBL LBL x6 x1 x5 x1 x9 x1 x11 x8 x x7 x4 LFR UFR UBR LBR Figure : Te quadruped s central nervous system. Correspondingly, te artificial creature as 1 sensors and 8 actuators. Te 1 sensors consist of 8 joint angle sensors (x 1, x, x, x 4, x 5, x 6, x 7, x 8 ) corresponding to eac of te inge joints and 4 touc sensors (x 9, x 1, x 11, x 1 ) corresponding to eac of te 4 lower limbs of eac leg. Te 8 actuators (y 1, y, y, y 4, y 5, y 6, y 7, y 8 ) represent te motors tat control eac of te 8 articulated joints of te creature. Tese motors are controlled via outputs generated from te ANN controller wic is ten used to set te desired velocity of rotation of te connected body parts about tat joint. Controller Evolution Using PDE Similar to (Abbass 1; ), our cromosome is a class tat contains one matrix Ω of real numbers representing te weigts of te artificial neural network and one vector ρ of binary numbers (one value for eac idden unit) to indicate if a idden unit exists in te network or not; tat is, it works as a switc to turn a idden unit on or off. Te sum of all values in tis vector rep- y8 y4 y y7

3 in Artificial Life VIII, Standis, Abbass, Bedau (eds)(mit Press). pp 1 18 resents te actual number of idden units in a network. Tis representation allows simultaneous training of te weigts in te network and selecting a subset of idden units. In te PDE algoritm for evolving ANNs, an entire set of controllers is generated in eac evolutionary run witout requiring any furter modification of parameters by te user. Te algoritm consists of te following steps: 1. Create a random initial population of potential solutions. Te elements of te weigt matrix Ω are assigned random values according to a Gaussian distribution N(, 1). Te elements of te binary vector ρ are assigned te value 1 wit probability.5 based on a randomly generated number according to a uniform distribution between [, 1]; oterwise.. Repeat (a) Evaluate te individuals in te population and label tose wo are non-dominated. (b) If te number of non-dominated individuals is less tan repeat te following until te number of non-dominated individuals is greater tan or equal to : i. Find a non-dominated solution among tose wo are not labelled. ii. Label te solution as non-dominated. (c) Delete all dominated solutions from te population. (d) Repeat i. Select at random an individual as te main parent α 1, and two individuals, α, α as supporting parents. ii. Crossover: wit some probability Uniform(,1), do ρ cild oterwise i ω α 1 i + N(, 1)(ωα i ωα i ) (1) j 1 if (ρ α 1 + N(, 1)(ρα oterwise ρα )).5 () i ω α 1 i () ρ cild ρ α 1 (4) and wit some probability Uniform(,1), do o ω α 1 o + N(, 1)(ωα o ωα o ) (5) oterwise ωo cild ω α 1 o (6) were eac weigt (ω i, ω o ), and idden unit flag, ρ, in te main parent are perturbed by adding to tem a ratio, F N(, 1), of te difference between te two values of tis variable in te two supporting parents. At least one variable must be canged. iii. Mutation: wit some probability Uniform(,1), do i o i + N(, mutation rate) (7) o + N(, mutation rate) (8) ρ cild (e) Until te population size is M j 1 if ρ cild = oterwise. Until maximum number of generations is reaced. (9) Experiments Experimental Setup A total of 48 evolutionary runs were conducted wit varying population sizes, crossover rates, and mutation rates wile fixing te fitness evaluation window to timesteps. Te crossover rates used were,.1,.,.5 and 1 and te mutation rates used were also,.1,.,.5 and 1. Te evolutionary setup wit a crossover rate of and a mutation rate of was omitted since tis setup does not generate any variability at all in te population. Te maximum number of idden units permitted in evolving te artificial neural network was fixed at 15 nodes. Eac experimental setup was repeated using 1 different seeds to allow te artificial evolution to commence from different starting points in te searc space. Two population sizes of and were used wit te corresponding number of generations being and respectively. Te use of a small population size and number of generations is a feature of PDE since genetic diversity is naturally maintained by te pareto selection mecanism. Te total number of genotypes over te entire span of te evolutionary process was kept constant at 6 genotypes in bot tese setups. In te final set of experiments, te creature was subjected to environmental, morpological and nervous system canges to observe te resultant cange in its beavior. Te details of tese canges are presented along wit te results and discussions of tese experiments. Results and Discussion Evolutionary Parameters First we analyzed te effect of population size on te evolved locomotion beaviors. Overall, tere did not appear to be any obvious differences in te range and quality of te evolved controllers between population sizes of and. Bot produced a considerably similar quality of locomotion beaviors altoug a larger population size did seem to produce controllers tat were sligtly better in terms of average locomotion fitness. However, te difference was not significant to investigate larger populations. Different combinations of crossover and mutation rates did appear to produce results tat varied across two broad spectrums. Wit bot population sizes of and, two distinct groups of controllers were generated troug te evolutionary process: (1) runs tat produced ig quality solutions but wit a low spread of genotypes, and () runs tat produced mediocre solutions wit a ig spread of genotypes. Again, te quality of solutions refers to te average locomotion fitness and te spread of genotypes refers to te number of ANNs wit different sizes in terms of idden units. Te first group of pareto optimal solutions wit ig quality and low spread were observed wen fairly low mutation rates of.1 and. were used in combination wit a low to medium crossover rate of between.1 to.5. Te sec-

4 4 in Artificial Life VIII, Standis, Abbass, Bedau (eds) (MIT Press). pp 1 18 ond group of pareto optimal solutions wit lower quality but wit a muc wider spread of controller sizes were observed wen a ig mutation rate of 1 was used. Operational Dynamics In tis section, we analyze five pareto optimal controllers resultant from a typical run. To conduct tis analysis, te ANNs were used individually to control te quadruped and te simulation period was extended to timesteps. Tis enables analysis of not only te evolved beavior but also its beavior beyond te fitness evaluation window. Te correlation analysis of te best evolved controller wit 4 idden units as 6 strongly positive correlation coefficients (>.7). Tis indicates tat te creature as evolved an ANN tat as learned ow to coordinate te movement of 7 sets of its limbs in order to acieve te most successful locomotion beavior among te pareto optimal controllers. Wit a correlation of.98, tere is almost perfect coordination between te upper front left (UFL) and lower front rigt (LFR) limbs. Anoter almost perfectly coordinated motion comes from te upper back left (UBL) and upper back rigt (UBR) limbs wit a correlation of.95. Tere is also a ig level of correlation between te upper front left (UFL) and upper front rigt (UFR), lower front left (LFL) and upper front left (UFL), lower front left (LFL) and upper front rigt (UFR), upper front rigt (UFR) and lower front rigt (LFR), and lower front rigt (LFR) and lower front left (LFL) limbs. Figure illustrates te correlation between te 8 limbs during motion over timesteps along wit te number of times eac leg makes contact wit te ground. Negative and positive correlation coefficients are drawn in dased and solid lines respectively. 7LFL LFR Hidden LFL LFR LFL LFR Hidden LFL LFR Hidden Hidden 91 LFL LFR 4 Hidden Figure : Illustration of correlation between limbs for pareto optimal controllers. Analysis of te less successful pareto optimal networks reveals tat tere is far less coordination acieved by tese controllers. At most strongly correlated sets of limb movements were obtained using tese controllers compared to 7 strongly correlated sets of limb movements using te best evolved controller. Furtermore, 5 strongly negative correlations (<-.8) were detected in te controller wit 1 idden unit. Tese limbs are not only uncoordinated but are generating forces tat act in direct opposition to eac oter, tereby furter indering te creature s ability to move. Finally, we analyze te pat of movement tat was taken by te creature in attempting to maximize its orizontal distance covered during te extended simulation window of timesteps. Here we compared te pats of all networks on te pareto-frontier of te last generation of controller evolution Controller wit Hidden Units Controller wit Hidden Units Controller wit 4 Hidden Units Controller wit 1 Hidden Units Controller wit Hidden Units Figure 4: Pat of movement using controller wit 1. top left: ;. top rigt: 1;. middle left: ; 4. middle rigt: ; and 5. bottom: 4; idden units. An interesting outcome from tese multi-objective evolutions is tat we get a range of controllers tat vary in arcitectural complexity and locomotion capability. On te one and, we ave a totally random ANN wit no idden nodes (Figure 4.1) but wic is still able to move te creature away from its origin, altoug te movement acieved witin te stipulated timesteps is extremely minimal (approximately.5m). In tis random network, tere is still an act of force on te creature permitting te small initial movement but it is unable to perform furter locomotion due to te lack of syncronization ability. On te oter and, we ave te 1 1 1

5 in Artificial Life VIII, Standis, Abbass, Bedau (eds)(mit Press). pp best ANN tat uses 4 idden nodes (Figure 4.5) and is able to move almost 1m witin te same time period. In addition, we ave a furter ANNs (Figure 4.,,4) tat utilize between 1 and idden nodes wic again ave differing locomotion capabilities. Tus, te multi-objective approac is able to provide te experimenter wit a wole range of controllers witin a single run tat trades off between te individual optimization goals. Tis represents a significant advantage over single-objective evolutionary systems tat need to be rerun multiple times in order to test te effect of oter factors suc as number of idden units on te performance of artificial creatures (Bongard & Pfeifer ). Effects of Friction In tis section, we analyze te effects of canging some of te environmental parameters of te creature s world and observe te cange in its beavior. Here, te same controller, wic is te best evolved ANN wit 4 idden units, is used to control te creature across all different environmental conditions. Te resultant beavior is again monitored over timesteps. First, we discuss te results obtained from canging te original frictional coefficient of to lower values of, 5, 1 and 15. Te purpose of tis analysis was to investigate ow te creature s ability to move would be affected by reduced amounts of grip wit its locomotion Te creature surface. was not able to move orizontally at all wit no ground friction. Its main movement ere was mainly along te vertical direction as it attempted to stand up and repeatedly failed due to te lack of friction. Wit a very small friction of 5, te creature was able to move forwards altoug te overall distance travelled was less tan in te original environment tat ad a significantly iger friction of. However, te pat travelled in te environment wit a friction of 5 was muc straigter tan in te original environment. Tis occurrence suggests tat friction plays a larger role in making te creature turn compared to making it move forwards. From te next two environments wic ad increasingly iger frictions of 1 and 15, te overall trajectory of te pats begin to ave more curvature as well as increasing overall distance travelled. Hence, it appears tat varying locomotion surface conditions noticeably affect te creature s ability to walk bot in terms of its trajectory as well as total distance travelled. Effects of Gravity In tis next section, we again cange te environmental conditions but instead of surface condition, tis time we cange te world s gravitational field to approximately simulate conditions of tat on te moon, Mars as well as Jupiter. Te purpose of tis set of experiments was again to see ow te creature s beavior would be affected by environmental canges as well as exploring ow ypotetical robots tat are built under our planet s condition may be able to also function on numerous oter planets tat ave significantly different gravities. Suc robots may be desirable because firstly building tem under normal terrestrial conditions will be significantly less complex tan trying to simulate extra-terrestrial conditions. Secondly, if robots were able to perform reasonably independent of gravitational canges, ten only a single group of similar robots need to be designed wic would be able to explore multitudes of moons and planets wit different surface gravities. Te creature was still able to function under te moon s muc smaller gravity altoug te overall distance travelled was less tan on Eart. Tere was also noticeably more vertical movement during te creature s locomotion as would be expected because of te smaller gravity. Under Mars gravity, te creature s familiar U- saped pat becomes visible again altoug te overall distance travelled is again less tan tat acieved on Eart. Te creature was significantly less successful under Jupiter s muc iger gravity were after standing up, it was only able to move a small distance forward. From tis analysis, it can be seen tat te creature was still able to function under very different gravitational forces altoug it s locomotion was less successful tan under Eart s normal gravity. Effects of Morpological Canges Next, we analyze te cange in te creature s beavior wen tere is a cange in its morpology. Again te best evolved controller wit 4 idden units was used to control te creature and allowed to move for timesteps. In tese experiments, we doubled te mass in certain parts of te creature s morpology. Very pronounced canges were observed in te creature s locomotion beavior as a result of doubling te masses of all of its front limbs (Figure 5.1) and all of its back limbs (Figure 5.). Te doubling of mass in its front legs resulted in a locomotion pat tat ad a straigter eading compared to te pat observed wit te original uniform mass distribution. Conversely, te doubling of mass in its back legs resulted in an even more pronounced curved locomotion trajectory tan te original U-saped pat, were in tis case te creature almost completed a full circle back to its original starting position. Tese penomena may be explained by te fact tat te creature acieved its locomotion from te coordinated movement of front limbs and back limbs respectively. As suc, mass redistribution affecting entire front and back sections of te creature s body can be expected to result in significant canges to its locomotion beavior. Te doubling of te creature s torso mass seemed to cause te creature s movement to ead more directly towards te Z axis after making its initial left turn (Figure 5.). Te effect of doubling te mass of te front left and back rigt legs did not appear to alter te creature s pat significantly except reducing te

6 6 in Artificial Life VIII, Standis, Abbass, Bedau (eds) (MIT Press). pp Mass: Front x Mass: Torso x Mass: Front Rigt x, Back Left x Mass: Back x Mass: Front Left x, Back Rigt x 1 1 a armful effect on its locomotion beavior. It struggled in trying to stand up and upon visual inspection of te simulation, tis was explained by te fact it could not maintain its balance. As a result, te creature could not perform any orizontal movement at all. On te oter and, disabling te back left leg did not seem to cause as muc arm to te creature s ability to move altoug its overall distance travelled was still significantly less compared to te original creature wic ad no impairments. In fact, upon closer inspection, te distinctive U-saped locomotion pattern could still be observed but on a smaller scale. Tese analyzes again seem to suggest tat te contribution of different legs to te overall locomotion beavior appeared to differ quite significantly depending on te position of te legs relative to te orientation of te creature s body and direction of movement. Tus disabling particular legs in certain positions resulted in dramatically different beaviors. 1 Figure 5: Pat of movement wit mass doubled in 1. top left: front legs;. top rigt: back legs;. middle left: torso; 4. middle rigt: front left and back rigt legs; 5. bottom: front rigt and back left legs. magnitude and turning effect of its orizontal movement (Figure 5.4). Te most pronounced cange in te creature s overall eading was observed wen te front rigt and back left legs were doubled in mass (Figure 5.5). Tis set of morpological canges appeared to ave altered te nature of te creature s locomotion pat from a predominantly left-turning trajectory to a rigt-turning trajectory. Tis may suggest tat te contribution to overall movement from different legs are very different depending on te relative position of te legs wit respect to te creature s body and direction of motion. Effects of Sensory-Motor Failure In tis section, we were interested in observing wat would appen to te creature s locomotion beavior if some sensory motor failure occurred. Tis would be akin to partial paralysis in four-legged animals were tere is loss of sense and movement in some of teir limbs. Here we disabled te joint angle and touc sensor as well as te inge motors in te creature s entire front rigt limbs in te first setup and te entire back left limbs in te second setup. Te best evolved controller wit 4 idden units was again used to operate te original creature wit uniform mass distributions over timesteps. Disabling te creature s front rigt leg seemed to ave 1 Conclusion We ave demonstrated te use of a multi-objective evolutionary algoritm for evolving artificial neural networks tat act as controllers for te legged locomotion of an embodied and pysically situated quadruped. We ave sown tat multi-objectivity allows for te natural maintenance of genetic diversity. Te pareto-frontier tat resulted from eac single evolutionary run produced a set of ANNs tat maximized te locomotion capabilities of te creature and at te same time minimized te size of te controller. Te correlation and pat analyzes of te pareto optimal controllers in operation provided an insigt into ow te complex coordination between te quadruped s different limbs generated te emergent locomotion beavior. Finally, we also observed tat certain environmental, morpological and nervous system canges markedly affected te creature s overall locomotion beavior and in some cases caused total failure of its orizontal locomotion capability. References Abbass, H. A. 1. A memetic pareto evolutionary approac to artificial neural networks. In Stumptner, M.; Corbett, D.; and Brooks, M., eds., Proceedings of te 14t Australian Joint Conference on Artificial Intelligence, 1 1. Berlin: Springer-Verlag. Abbass, H. A.. An evolutionary artificial neural network approac for breast cancer diagnosis. Accepted to appear in Artificial Intelligence in Medicine. Arnold, D Evolution of legged locomotion. Unpublised masters tesis, Scool of Computing Science, Simon Fraser University, Burnaby, Canada. Bongard, J. C., and Pfeifer, R.. A metod for isolating morpological effects on evolved beavior. In Accepted to appear in Proceedings of te Sevent International Conference on te Simulation of Adaptive

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