Material properties affect evolution’s ability to exploit morphological computationin growing soft-bodied creatures

Francesco Corucci∗1,3, Nick Cheney2,3, Hod Lipson4, Cecilia Laschi1 and Josh C. Bongard3

1The BioRobotics Institute, Scuola Superiore Sant’Anna, Pisa, Italy2Department of Biological Statistics and Computational Biology, Cornell University, Ithaca, NY, USA

3Morphology, Evolution & Cognition Lab, University of Vermont, Burlington, VT, USA4Creative Machines Lab, Columbia University, NY, USA

*f.corucci@sssup.it

Abstract

The concept of morphological computation holds that thebody of an agent can, under certain circumstances, exploitthe interaction with the environment to achieve useful be-havior, potentially reducing the computational burden ofthe brain/controller. The conditions under which such phe-nomenon arises are, however, unclear. We hypothesize thatmorphological computation will be facilitated by body planswith appropriate geometric, material, and growth properties,while it will be hindered by other body plans in which one ormore of these three properties is not well suited to the task.We test this by evolving the geometries and growth processesof soft robots, with either manually-set softer or stiffer mate-rial properties. Results support our hypothesis: we find thatfor the task investigated, evolved softer robots achieve bet-ter performances with simpler growth processes than evolvedstiffer ones. We hold that the softer robots succeed becausethey are better able to exploit morphological computation.This four-way interaction among geometry, growth, materialproperties and morphological computation is but one examplephenomenon that can be investigated using the system hereintroduced, that could enable future studies on the evolutionand development of generic soft-bodied creatures.

IntroductionEvolving complete and intelligent artificial creatures is oneof the long-term goals of artificial life and evolutionaryrobotics researchers. More than two decades after the firstpioneering attempts (Sims, 1994), we are still far frommatching the complexity exhibited by even the simplest or-ganisms. Nevertheless, many insights have been gained todate, and many limitations overcome.

Hand in hand with similar developments in robotics (Kimet al., 2013; Rus and Tolley, 2015), substantial steps for-wards in the complexity and interestingness of evolved vir-tual creatures have been recently made, by allowing evolu-tion to make use of soft materials (Hiller and Lipson, 2010,2012; Joachimczak and Wrobel, 2012; Joachimczak et al.,2014; Cheney et al., 2013; Rieffel et al., 2014; Lessin andRisi, 2015). In addition to enhancing morphological and be-havioral diversity, the use of soft materials allows morpholo-gies that more closely mimic biological ones, thus enabling

Figure 1: A soft (a-d) and stiff (e-h) robots evolvedto grow towards two lateral light sources. Red voxelsexpand in response to environmental stimuli, blue onesshrink. While the soft robot only employs expanding vox-els and effectively exploits morphological computation, pas-sive dynamics, and the interaction with the environmentto solve the task, the stiff one is prevented from doing sodue to its unsuitable material properties, and had thus toevolve a more complex and active form of control in or-der to achieve the same result. See them in action at:https://youtu.be/Cw2SwPNwcfM

the investigation of additional aspects of evolution and de-velopment that were previously beyond reach. Here we fo-cus on two such aspects relevant to soft-bodied creatures.

The first regards morphological plasticity: the abilityto change some aspects of the body during one’s life-time. Here we investigate environment-mediated morpho-logical development — growth in response to environmen-tal stimuli — referred to henceforth simply as growth. Al-though it has been shown that morphological growth canprovide adaptive advantages for machines (Bongard, 2013),previous work only focussed on rigid-bodied agents andenvironment-insensitive growth processes. Yet there is ev-idence that biological development is influenced and drivenby the environment. For example, plant roots follow gra-dients of nutrients in the soil, while human bones and tis-sues alter their properties in response to mechanical loading(Wolff, 1986). Moreover, when compared to rigid-bodied

creatures, soft ones more naturally allow for some forms ofmorphological plasticity, that are already within the reachof soft robotics technology as well. Despite that, probablydue to the lack of a general understanding of why, when,and how these new capabilities should be exploited, theserobots feature to date basic forms of morphological plas-ticity (Shepherd et al., 2011; Corucci et al., 2015b,c), or noplasticity at all (Calisti et al., 2015; Corucci et al., 2015a;Cacucciolo, Corucci et al., 2014).

The second aspect we explore is the influence of materialproperties on the evolution and development of adaptive be-havior. The behavior of soft-bodied creatures is to a largeextent determined by their material properties, yet in softrobotics these are often fixed a priori and for the whole life-time of an agent, perhaps after a limited number of heuris-tic tests. Some recently proposed ideas suggest that thoseproperties — and softness in particular — can have implica-tions for the development of intelligent behavior (Pfeifer andBongard, 2006), but few studies (Nakajima et al., 2013) andtheoretical frameworks (Hauser et al., 2011, 2012) elucidateand quantify these implications, typically not embracing anevolutionary and developmental approach.

Here we investigate the evolution and development of softrobots. In this context we hypothesize that with the rightcombination of geometry, material properties, and growthprocess, a robot can exploit morphological computation(Paul, 2006; Hauser et al., 2014) better than one for whichone or more of these aspects is not well adapted. We testthis hypothesis by evolving the body plans and developmen-tal trajectories of simulated soft robots for a phototaxis task.Two variations of such robots are evolved: softer and stifferones. We find that the former achieve better performances,despite their evolved growth processes being simpler, ac-cording to an information theoretic measure. By interpretingenvironment-mediated growth as a form of control, it is sug-gested that the softer robots are in fact exploiting more mor-phological computation than the stiffer ones. This hypoth-esis is but one of many that can be tested using the systemhere introduced. These include the investigation of generalrelationships among morphology, control, evolution, and de-velopment. Such studies could provide a deeper comprehen-sion of biological systems, with potential implications forthe development of more complex, autonomous and adap-tive machines.

MethodsSimulated task and environment. In this work soft-bodied creatures are simulated in the VoxCad environment(Hiller and Lipson, 2014). A number of changes and newfeatures have been introduced in the simulator in order toenable our experiments.

First, sources of environmental stimuli can now be addedto the environment. These sources are characterized by afixed 3D location, and robot’s voxels can sense the distance

from each of them.Second, the base of each robot is fixed to the ground for

the entire simulation. If a robot does not touch the ground atthe beginning of the simulation, it is translated along the zaxis before the simulation starts, until it does. This is doneto put emphasis on growth and deformability, ruling out lo-comotion strategies to approach the light sources.

Third, differently from other works adopting VoxCad(Cheney et al., 2015, 2013; Methenitis et al., 2015), in thisexperiment there is no fast-twitch actuation mechanism (i.e.the fast control based on an oscillating global signal is dis-abled). A distributed growth mechanism has been imple-mented instead, acting at a slower time scale (more below).

The task is inspired by plants, and consists in perform-ing stationary phototaxis: growing towards static sourcespresent in the environment. While reaching a single sourceis not a particularly difficult task, simultaneously pointingtoward multiple ones becomes more challenging, as it re-quires the ability to evolve modular, branching structures.The specific growth mechanism is detailed in the next sec-tions, as well as the underlying developmental paradigm.

Developmental paradigm. Different approaches havebeen adopted in the literature in order to model developmen-tal processes (Stanley and Miikkulainen, 2003). Those canbe roughly classified based on the level of abstraction withrespect to the biological phenomenon they try to capture.Among high-level abstractions we find grammar-based ap-proaches (Rieffel et al., 2014; Hornby and Pollack, 2002)and CPPN-based ones (Stanley, 2007; Cheney et al., 2013;Auerbach and Bongard, 2014). Lower-level abstractions,broadly referred as cell chemistry approaches (Doursat et al.,2013; Joachimczak et al., 2014; Bongard and Pfeifer, 2003),model finer details of developmental processes, such as generegulatory dynamics.

Despite many achievements in cell chemistry, a drawbackof these approaches lies in their complexity. On the otherhand, when adopting a high-level perspective, the risk ex-ists of overlooking potentially useful aspects of develop-ment. As an example, CPPNs and grammatical encodingsneglect both the unfolding over time of biological develop-mental processes as well as the interaction of the creaturewith the environment during those processes.

The approach proposed here is based on CPPNs, but em-powers them by joining their ability to capture the forma-tion of regular patterns (Stanley, 2006) with an environment-mediated developmental stage that unfolds over time. Whilethe implications of such a choice deserve to be thoroughlyinvestigated in future work, we note that this approach en-ables potentially interesting feedback loops during develop-ment: growth is guided by environmental stimuli, but mod-ifies in turn the sensory information the creature will expe-rience next. Also, as mutation effects may arise at differentpoints during development, the ability to enact changes later

Figure 2: Different attributes of the robot can be ”painted”by different CPPNs. CPPN1 dictates the geometry of therobot, while CPPN2 determines its growth properties. Inthe current system red voxels expand in response to envi-ronmental stimuli, while blue ones shrink.

in development may allow for smoother fitness gradientsthan all-or-nothing mutations (Hinton and Nowlan, 1987).

Time scales. The proposed developmental paradigm em-beds all three time scales experienced by living systems:the evolutionary/phylogenetic time scale, the developmen-tal/ontogenetic time scale, and the sensorimotor dynamicstimescale (Pfeifer and Bongard, 2006). The sensorimotortimescale is here represented by the interaction of the bodywith the environment during growth (e.g. gravity, collisions,detected light levels, etc.).

The genotype. The encoding here adopted is based onCPPNs (Stanley, 2007). Designed to capture the forma-tion of regular patterns in developmental systems withoutmodeling development per se (Stanley, 2006), CPPNs arenetworks that convolve incoming spatial information to pro-duce outputs that tend to exhibit symmetry, repetition, andrepetition with variation.

In order to enforce a distinction between geometric andgrowth properties, here we adopt two different CPPNs (Fig.2) that are queried for each voxel of a cubic workspace.They receive the same inputs: the 3D location of the voxel(x, y, z), the polar radius (d), and a constant bias (b).

The first CPPN, determining the creature’s geometricalstructure, has a single output o ∈ [−1, 1] that dictateswhether a voxel should be empty (o < 0) or filled (o ≥ 0).Differently from similar setups (Cheney et al., 2013), evo-lution is provided with a single material in the experimentshere reported, that is assigned to all non-empty voxels. Adifferent stiffness can be specified for this material in differ-ent evolutionary runs, though all voxels in each run share aglobal and constant stiffness parameter.

The second CPPN determines the growth properties ofeach voxel. It also has a single output ∈ [−1, 1] henceforthreferred to as the growth rate (grv), whose role is describedin detail in the next section.

Description

D(t)v Linear dimension of voxel v at time t

s(t)v Scaling factor of voxel v at time t

Dvn Nominal dimension of voxel v (set to 1)

ga Growth amplitude ∈ (0, 1) (equal ∀ voxel, set to0.5)

N Number of environmental sourcesi A specific source

s(t)vi Influence of source i on the scaling factor s(t)v

sv min Lower bound for s(t)v (set to 0.1)

grv Growth parameter of voxel v (∈ [−1, 1])

di(t)

Distance of voxel v from source i, normalizedby voxel size (the latter being set to 0.01)

Table 1: Description of parameters appearing in Eq. 1

Environment-mediated morphological development.We simulate environment-mediated growth by enablingvoxels to change volume in response to environmentalstimuli (i.e. distance from each light source). This choiceis motivated by the fact that localized volumetric changesare easy to achieve with currently-available soft robots(e.g. exploiting pneumatic actuation). A localized changein stiffness is also within the reach of current technology(Majmudar et al., 2007), making this kind of plasticity thenext candidate to be integrated into our system. Topolog-ical modifications are, on the other hand, more difficultto achieve in real soft robots, as they require adding orremoving material. Nevertheless, attempts have been madein this direction as well (Brodbeck et al., 2012).

The growth process is governed by equations and param-eters reported in Eq. 1 and in Tab. 1:

∀ voxel v, at each time step t

D(t)v = s(t)v ·Dvn

s(t)v = max

[ga · tanh

(N∑i=1

s(t)vi

)+ 1, sv min

]s(t)vi = grv · di

(t)

(1)

The growth rate parameter grv determines the quality andthe extent of the localized volumetric change for each voxel.When grv > 0 the voxel will expand when close to a source,when grv < 0 it will shrink. When grv is exactly zero, thevoxel is insensitive to environmental stimuli. The greater themagnitude of grv for a particular voxel, the more pronouncedwill be its volumetric variation, that is also modulated bythe distance from the sources. Each voxel can experiencea considerable modification due to development: having set

ga = 0.5 entails a 50% linear contraction/expansion withrespect to the nominal size, resulting in a ∼ 238% variationin volume. The parameter sv min ensures that the voxel doesnot shrink below a given size (here the 10% of the nominalsize), for stability of simulations. The quantity ∆sv max (notreported in Eq. 1 for ease of reading) dictates the maximumallowed ∆sv = |s(t)v − s

(t−1)v | between two subsequent time

steps, as follows:

if (∆sv > ∆sv max) then:

s(t)v = s(t−1)v + sign(∆sv) ·∆sv max

In addition to influencing the stability of the simulation, thisparameter (set to 0.0005 in our experiments) regulates thespeed of the growth process: the higher ∆sv max, the morerapid the growth. The value for ∆sv max was selected insuch a way that development acts over a slower time scalewith respect to the typical sensorimotor dynamics (such asthose generating locomotion or grasping behavior), thus im-plementing the developmental time scale.

Development is based on distributed sensing and actua-tion: each voxel senses the distance from all the sourcesand acts accordingly. Nevertheless, coordinated behavioremerges, for at least two reasons: first, nearby voxels ex-perience similar sensory stimuli, and second, CPPNs tendto produce patches of tissue with homogeneous or smoothlyvarying growth parameters.

Optimization. A multi-objective implementation ofNEAT (Cheney et al., 2015) has been adopted. Beforeperforming selection, pareto ranking is applied, accordingto three objectives: the order in which sorting is performeddetermines the relative importance of each of them. Theobjectives are listed below from the most to the leastimportant:

1. Minimize the distance from each of the sources

2. Minimize the number of employed voxels

3. Minimize the age of each individual

The first objective selects for phototaxis. This is imple-mented by minimizing the sum

∑Ni=1 dmin i, where N is the

number of sources and dmin i is the minimum distance be-tween the robot and the i-th source. The second objectiveselects for smaller robots. The first two objectives are an-tagonistic as it is easier, in general, for larger robots to becloser to the sources (even if they do not grow at all). Thecombination of the two objectives thus selects for robots thatexploit the growth process and their deformability to accom-plish the task. The third objective helps maintain diversityin the population (Schmidt and Lipson, 2011).

Morphological computation and control complexity.Morphological computation (Hauser et al., 2014) has beendefined as ”computation obtained through the interaction of

physical forms” (Paul, 2006). When it comes to roboticsand embodied cognition (Pfeifer and Bongard, 2006), theidea is that part of the computation needed to perform atask can take place (implicitly or explicitly) not only inthe brain/controller, but also within the body itself, pro-vided that it has suitable characteristics. It has been arguedthat this property can alleviate the computational burden ofthe brain, simplifying the controller and achieving a morebalanced brain-body trade-off (Pfeifer and Bongard, 2006;Paul, 2006; Hauser et al., 2011) that could hold the key tomore intelligent, effective and natural behaviors. Many ex-amples have been described in the literature (Pfeifer andBongard, 2006). It is often postulated that systems bene-fiting from morphological computation tend to exploit theinteraction and dynamical coupling with the environment ina beneficial way, e.g. leveraging passive dynamics in placeof active control.

We hypothesize that material properties can affect evolu-tion’s ability to exploit morphological computation. To testthis, we here define morphology as the robot’s shape and ma-terial properties, and its ‘controller’ as the distributed growthmechanism which achieves phototaxis. We defend this latterdefinition as, like control, growth here closes the sensation-action feedback loop (although over a slower time scale).

For our purposes, we can thus define morphological com-putation as a property that simplifies the growth controllerby exploiting in a beneficial way the interplay between ma-terial, geometric, and growth properties through the dynam-ical interaction with the environment.

To measure the extent of morphological computation in agiven robot, we define control complexity as follows:

H(gc) = −n∑

i=1

pi log2 pi (2)

where:

gc = {grv ∀ voxel v}

pi =

∫ xi+1

xi

p(x) dx

xi = −1 + 0.02i i = 0 . . . 100

(3)

The real-valued random variable gc is associated to thegrowth rate quantity (Eq. 1, Tab. 1), embracing all param-eters that collectively shape the growth trajectory of a givenrobot. The quantity H(gc) is the Shannon entropy (Shannon,1948) of such a variable, whose probability density functionp(x) is discretized using n = 101 uniform bins (Eq. 3).

The control complexity of gc thus corresponds to thenumber of bits that are necessary to describe the pattern ofgrowth parameters: the higher this number, the more com-plex the controller. Consider two robots (r1, r2) and theirassociated growth controllers (gc1, gc2). We will state thata difference ∆H = H(gc2) − H(gc1) > 0 between the

two controllers indicates that gc2 is more complex than gc1.Moreover, if the two robots happen to score the same fitness,we will argue that r1 better exploits morphological compu-tation, as it requires simpler control to produce an equallyeffective behavior. It should be made clear that we are notproviding here a general information theoretic metric to cap-ture morphological computation (Zahedi and Ay, 2013), butrather a proxy to measure its effect in our setting.

Experiments Populations composed of 30 individuals areallowed to evolve for a maximum of 1500 generations. Themaximum evaluation time for each individual is 3.5s (simu-lation time, wall time is higher). The simulation is stoppedearlier if the robot settles into a static conformation beforethe allocated time elapses. The growth process starts afterthe first 0.5 seconds, which usually allows the initial shapeto settle into an equilibrium position.

A first set of experiments is performed to qualitativelyassess the overall ability of the system to evolve effectiverobots. To this end, 10x10x10 and 8x8x8 robots have beenevolved in several environments, differing in the number(from 1 to 4) and position of environmental sources (Fig.3). Material stiffness is set to E = 5 MPa, correspondingto a rather soft material (comparable to rubber). Five runswere performed for each configuration.

A second set of experiments is then performed with6x6x6 robots, characterized by different stiffness values(E1 = 500 MPa, E2 = 5 MPa) evolving in the same en-vironment (2 laterally placed sources). Twenty independentruns were performed for each treatment. Reported confi-dence intervals are computed with a bootstrapping method,while p-values are the result of the Mann-Whitney U test.

The code used to produce these results is publicly avail-able at: https://goo.gl/cA2luO. A video show-ing some of the creatures in action is available at:https://youtu.be/Cw2SwPNwcfM

Results and DiscussionA sample of the fittest morphologies evolved in preliminarytrials is reported in Fig. 3 and in the accompanying video.Symmetry and modularity can be observed, with the latterproperty evidenced by the emergence of relatively indepen-dent appendages. As these features are ubiquitous in nat-ural systems, their presence here may suggest the potentialfor more competent and scalable virtual creatures. More-over, these properties appear to be selected for by our taskand environment, as this level of morphological regularity isnot common in similar settings (Cheney et al., 2013, 2015;Methenitis et al., 2015).

It can be noted that the best individuals from these runstend to only exploit expanding (red) tissue, and not shrink-ing (blue) voxels (Fig. 3). Evolved creatures appear able toleverage their passive deformability and interaction with theenvironment in order to solve the task, rather than requiring

Figure 4: Average fitness over 20 independent runs. Softerrobots have an evolutionary advantage over stiffer ones inthis task/environment.

differential expansion and contraction to point towards lightsources. For example, cantilevers spontaneously evolve (Fig3b). Like human-built cantilevered structures, these robotsdistribute stresses across themselves with a minimum of sup-port structure. Moreover, the curvature needed to point to-wards the two lateral sources spontaneously emerge from thepassive interaction of the expanding body with the environ-ment (and with gravity, in particular), rather than throughinternal actuation of the creature. This corresponds, intu-itively, to the idea of morphological computation.

Given the scarce presence of highly-fit robots exploit-ing more complex forms of control — based on the com-bination of shrinking and expanding voxels — we hypoth-esize that it may be easier for evolution to discover solu-tions based on morphological computation rather than ex-plicit control, provided that material properties allow it todo so. This would confer, in general, an evolutionary advan-tage to robots that have the ”right” material properties for agiven task/environment. This hypothesis is tested with thesecond set of experiments.

Geometry, materials, growth, and morphological com-putation. Fig. 4 reports the evolution of robots with stiffer(E1) or softer (E2) material properties, optimized to simul-taneously approach two lateral light sources placed on op-posite sides of the creature. Results show that softer robotshave an evolutionary advantage over stiffer ones in this par-ticular task/environment, which may be attributed to evolu-tion’s ability to better exploit morphological computation in-stead of developing more complex and active forms of con-trol to regulate their shape. This can be qualitatively ob-served in the comparison of two highly-fit robots reported inFig. 1 (see them in action in the accompanying video). Withthe softest material, evolution produced a passive cantilever,taking advantage of gravity to unfold the shape towards thetwo sources during growth. Under the effect of gravity, the

Figure 3: A small sample of the growing soft creatures, evolved in environments featuring: a-c) two lateral sources d) foursources placed at the corners. a,d) top view, b,c) front view. Most of the highly fit soft robots only exploit expanding tissue.

structure passively deforms and achieves an effective curva-ture, being able to sustain its own weight and point towardsthe sources at the same time. On the other hand, the stifferrobot fights gravity holding the two rigid arms horizontally,achieving the curvature needed to direct its appendages to-wards the sources through the antagonistic action of shrink-ing and expanding voxels in the central part of the body.

Further analyses suggest the generality of these observa-tions in this task/environment. Figure 5 shows that stifferrobots use substantially more shrinking voxels in general.Their growth processes involve more active control in thesense that the appendages are pulled as well as pushed toachieve proximity to the environmental sources. This sug-gests that for stiffer robots, simpler strategies in which cur-vature is achieved passively in response to weight are eitherharder to find in the search space or are not viable at all.

Given the fitness benefit of expanding voxels, enlargingthe volume of the robots and allowing them to approachthe sources more closely, we would expect shrinking voxelsonly to be employed when necessary to control the directionof evolved appendages. Thus, the presence of more shrink-ing voxels in the stiffer robots suggest that they are unableto perform passive pointing from their material propertiesalone, as exemplified in the softer robots (Fig. 1).

The intuitive considerations regarding control complex-ity and morphological computation are also confirmed by aninformation theoretic analysis of the evolved robots: the av-erage control complexity H(gc) (the global entropy acrossgc) is significantly higher for the stiffer robots than for thesofter ones (Fig. 6). In other words, stiffer robots employmore complex and active controllers. This again suggeststhat their morphologies are unable to perform the task to thesame level without control.

In summation, softer robots better exploit morphologicalcomputation in this particular task/environment, achievingbetter performances (Fig. 4) with simpler controllers (Fig.

E1 = 500 MPa (stiffer) E2 = 5 MPa (softer) 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

p−value = 0.0011439

% s

hrin

kin

g v

oxe

ls

Figure 5: Stiffer robots tend to employ significantly moreshrinking voxels than softer ones (p < 0.002), in the attemptto actively control the shape.

5, 6). This confers an evolutionary advantage to them overstiffer robots, if evolved alongside.

It should be noted that these results do not mean thatsofter is always better. It would be possible to define atask/environment that confers an advantage to stiffer robots(e.g. grow towards sources placed mid-air, where it is eas-ier for stiffer robots to sustain their weight). What has beendemonstrated is that for a specific task/environment, mate-rial properties can have a pronounced effect on evolution’sability to exploit morphological computation, i.e. to producewell adapted morphologies that exploit the interaction withthe environment in a beneficial way.

Conclusions and Future WorkIn this paper a novel system to study the evolution and de-velopment of soft-bodied creatures has been presented. Thesystem is able to evolve robots that exhibit desirable mor-phological properties such as symmetry, modularity, and ex-

E1 = 500 MPa (stiffer) E2 = 5 MPa (softer) 0

1

2

3

4

5p−value = 0.0042667

Gro

wth

co

ntr

olle

r e

ntr

op

y H

(gc)

Figure 6: Stiffer robots exhibit more complex growth con-trollers than softer ones (p < 0.005), yet the latter achievebetter performances (Fig. 4). It is argued that this differenceis due to morphological computation, strictly connected tothe material properties of robots in the two treatments.

ploitation of morphological computation. More specifically,it was shown that certain combinations of geometry, mate-rial properties, and environment-mediated growth make itmore or less difficult for evolution to discover phenotypesthat exploit morphological computation. Despite being afundamental aspect of soft robotics, the interplay amongthese properties remains to date largely unexplored. Re-sults also suggest that arbitrarily fixing even one of thesedimensions can make it difficult for evolution to produce ef-fective behaviors. Ideally, all of them should be put underevolutionary and/or developmental control, so that an opti-mal combination can be discovered. Future work will bedirected towards exploring the potential evolutionary advan-tage of morphological plasticity, as well as possible benefitsin terms of adaptivity and robustness. The environmentalinfluence during development deserves special attention aswell: its potential benefits for organisms as well as adap-tive machines will be investigated. Another major topic thatcan now be studied is the general relationship between evo-lution, development and adaptive behavior. We believe thatmany interesting questions can be answered using the ap-proach described here, and could help shed light on bio-logical questions, while simultaneously contributing to en-gineering fields such as soft robotics.

Acknowledgments

This work was supported by the Vermont AdvancedComputing Core, the National Science Foundationthrough grants PECASE-0953837 and INSPIRE-1344227,and NASA Space Technology Research Fellowship#NNX13AL37H for N. Cheney. Thanks to Dr. MarcinSzubert for proofreading and useful discussion.

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