From tadpole to frog : artificial metamorphosis as a method of evolving self-reconfiguring robots

We show how the concept of metamorphosis, together with a biologically inspired model of multicellular development can be used to evolve soft-bodied robots that are highly adapted to two radically different environments (e.g., aquatic and terrestrial). Each evolved solution defines two pairs of morphologies and controllers, together with a process of transforming one pair into the other. Animats develop from a single cell and through divisions and deaths reach their initial “larval” form adapted to the first environment. To obtain “adult” form adapted to the second environment, the larva undergoes metamorphosis during which new cells are added or removed and its controller is modified. Importantly, our approach assumes nothing about what morphologies or methods of locomotion are preferred. Instead, it successfully searches the vast space of possible designs and comes up with complex, life-like solutions de novo. In this paper, we describe the approach we employ and present examples of metamorphic soft-robots. We compare two different approaches to evolving aquatic and terrestrial animats, investigate evolved motion strategies, the process of metamorphosis and its evolution.


Introduction
Metamorphosis is a process during which an organism that has already finished its embryonic development undergoes a relatively fast and considerable change to its body structure through cell growth, differentiation and death.It is often accompanied (or actually necessitated) by a change of environment the organism lives in.Metamorphosis is exhibited by a wide variety of taxa as different as insects, mollusks or amphibians.In the latter case it testifies to amphibians' evolutionary ancestry: land based amphibians begin their lives in aquatic environment and develop first into a fish-like larval stage (a tadpole).Maturing tadpoles undergo metamorphosis which allows them to switch to a terrestrial habitat.This involves changes such as the loss (reabsorption) of gills, tail, lateral-line system and the gradual growth of jaw and limbs.Importantly, the processes that occur during metamorphosis are the very same processes that shape organism during its embryonic growth.Metamorphosis is a manifestation of multicellular development and just like all development, it is deeply tied to species evolutionary history (see, e.g., Carroll et al., 2004).
The field of artificial embryogeny, to which this work belongs, attempts to capture the seemingly endless capability of nature to generate forms by reproducing key properties of development in silico.This typically involves bio-inspired construction process in which a structure (such as a robot's body) is progressively built from smaller elements.Depending on the chosen level of abstraction this may involve elements such as rods (Komosinski and Rotaru-Varga, 2002), primitives and joints (Sims, 1994;Pilat et al., 2012), or artificial cells, as in the case of the system employed by us and related ones (Dellaert and Beer, 1996;Eggenberger Hotz, 1997;Schramm and Sendhoff, 2011;Bongard and Pfeifer, 2003).Self-assembly from higher level components such as blocks and joints or using an even higher level abstraction of development such as CPPN (e.g., Cheney et al., 2013) has been demonstrated to be an effective way to generate interesting robotic designs.In our line of work, however, we aim to explore the potential and scalability of a much more biologically inclined and more fine-grained artificial development, where arbitrary morphologies can be freely assembled from large numbers of cells (hundreds, thousands), each taking independent decisions about their fate and interacting through simulated physics of developmental environment.So far we have demonstrated how this approach allows us to evolve a rich variety of complex soft-bodied animats with emergent higher level features such as appendages constructed of dozens of cells and acting as artificial legs (Joachimczak et al., 2014).
In this paper we show how the concept of metamorphosis can enhance artificial development by allowing evolutionary algorithm to automatically produce solutions (here, softrobots) that can take two potentially very different forms, each adapted to its target environment.Importantly, one form can transform into another, offering exciting potential for designing robots that could efficiently operate in radically different environments: a rescue robot launched for a mission from sea could swim to a shore, transform into terrestrial form and continue its mission on its newly grown legs.
The idea of combining metamorphosis with an evolutionary algorithm is by itself not new.For example, Bongard (2011) demonstrated how morphological change during a legged robot's lifetime (progressive extension of its legs) facilitates evolution of higher quality gait controllers.The nature of the change and the morphology were however predefined.In another, more conceptually similar work (Tufte, Michał Joachimczak, Reiji Suzuki, Takaya Arita (2015) From tadpole to frog: artificial metamorphosis as a method of evolving self-reconfiguring robots.Proceedings of the European Conference on Artificial Life 2015, pp.51-58 2011) metamorphosis was used to evolve simple digital circuits implemented as cellular automata and producing new functionality through rearrangement.To our knowledge, this is however the first case of using metamorphosis and evolution to automatically discover robots that have forms adapted to two different environments, without specifying desired morphologies or the nature of the transformation.

Developmental model
In the following sections we provide a short overview of the essential concepts behind our artificial embryogeny approach to evolving soft-bodied robots.It is a refined version of the system we introduced in Joachimczak et al. (2014), of which some aspects were simplified in order to further reduce complexity (both conceptual and computational).Namely, we allowed for only non-recurrent networks that control cells' behaviour, only one type of gene activation function (sigmoidal) and we also simplified mechanism of actuation (and made it similar with the one in Joachimczak and Wróbel, 2012).We believe an even simpler and more straightforward design of our developmental system makes for a more convincing argument about applicability of metamorphosis approach to other developmental systems.
We assume that each animat begins its life as a single cell and grows through subsequent cellular divisions and deaths (apoptosis).The fate of every cell is determined by a shared control mechanism: a simple abstraction of gene regulatory network (GRN) in the form of a feed forward neural network.Despite being controlled by the same network, cells will act differently as the external signals that are fed to the inputs of the network depend on cell's position in the growing embryo, as well as signals received from neighbouring cells.After the development has finished, the resultant multicellular structure is used as a template for a morphology of soft-bodied animat that can move by contracting and expanding regions of the body surrounding each cell (Fig. 1).
Physics of development Development takes place in a continuous 2-D space.Cells are represented as discs and undergo elastic collisions simulated with springs.A cell's physical state is defined by its position, its velocity, and orientation vector which determines the direction of division.All cells have uniform size and mass.Springs connect only the nearest neighbours and are determined dynamically, as the embryo grows, with the resting length set to the sum of attached cells' radii.We use Delaunay triangulation to determine the connectivity between cells and then remove links longer than 150% of cell's diameter.Disjoint structures are prevented from occurring (see Joachimczak et al., 2014, for details).

Control gene network
The control network present in all cells has 6 inputs in total.This includes a fixed bias signal and time signal that is linearly increasing from 0 to 1 over the course of development.Given that the networks governing cellular behaviour in the presented experiments are stateless, spatially differentiated signals are the only way for cells to take on different behaviours.We have provided a simple, maternal gradient-like mechanism in the form of cell's X and Y coordinates available as inputs to the network.Additionally, to simulate simple morphogens produced by cells themselves, the control network has two "morphogen" outputs and two associated "morphogen" inputs.For any given cell, the activation of the latter is set to be an average of the corresponding morphogen outputs of its neighbours.Apart from the two above mentioned outputs, cells have 5 other outputs that determine actions taken by them.This includes an output whose non zero activity prevents division, a signal that controls the angle of division, a signal that causes aptoptosis (cell's death) and two outputs that determine frequency and phase shift of "muscle" contractions during the locomotion stage.
The control networks were updated in all cells synchronously.This involved setting the state of input nodes and propagating signals the number of steps equal to the longest path between input and output found in the network.
Cell division and death All cells are bound to divide with each subsequent update of gene regulatory network (occurring every 30 steps of developmental simulation) unless the output inhibiting division is active.Division is allowed to occur if and only if the space in the direction of division is not occupied already by another cell (the rationale for this approach can be found in Joachimczak et al., 2014).
The newly created cell is placed next to the original cell in the direction determined by its orientation vector.Its angle is determined at the moment of division, based on the state of the associated output of regulatory network.The angle is interpreted as relative to the angles of cell's nearest neighbours and thus, unless the state is different from zero, all cells will simply divide in the same direction.The new cell is controlled by the same network, hence any change in the patterns of network activities is the result of symmetry being broken owing to the differences in external signals perceived by each of the cells.
Apoptosis (cellular death) occurs whenever the state of associated network output is found to be above zero and leads to the cell being removed from the embryo.
We used a hard limit of 256 cells and, additionally, we Michał Joachimczak, Reiji Suzuki, Takaya Arita (2015) From tadpole to frog: artificial metamorphosis as a method of evolving self-reconfiguring robots.Proceedings of the European Conference on Artificial Life 2015, pp.51-58 penalized individuals that have created more than 1024 cells during their development by reducing their fitness value by 90%.We did so to limit the occurrence of "wasteful" solutions in which cell creation and death is kept in balance and never stops.While we have shown in our previous work (Joachimczak et al., 2014) that solutions that self-terminate growth are not difficult to evolve in our approach, they come at a cost, both computational and in reduced quality of obtained solutions.Although promoting self-termination facilitates emergence of beneficial properties of development such as increased robustness (Devert et al., 2011), in this work we opted for the simple and more manageable scenario, in which evolution can exploit the hard limits of developmental time and cell count to stop development.

Soft-bodied locomotion
The multicellular morphology of an embryo obtained at the end of developmental stage was used as a template for a softbodied animat that was evaluated for its capability to move in a simulated environment during locomotion stage.Although both representations are a spring-mass system and rely on the same physics simulation engine, the physical constants and the rules that govern reshaping of each structure differ between the stages.Namely, development occurs always without gravity in a fluid-like environment and involves continuous reorganization of connectivity between cells.On the other hand, during the locomotion stage, cells no longer divide or die, and the connectivity between the cells remains fixed (the animat however does undergo elastic changes).More precisely, during the locomotion stage animat is represented as a spring-mass system with point masses located at the centres of cells in the embryo and with springs forming a triangular mesh.The outline of the shape is defined by the outer cells of the embryo, while the inner part of the animat is triangulated using Delaunay algorithm, as a way of approximating uniformly elastic material.As this approach can produce a morphology with a protrusion that is connected by a single spring to the main body, such protrusions are cut off from the soft-body representation.
The resting lengths of springs are assigned based on the distances between cell centres at the end of developmental stage.Springs in our system are governed by the Hooke's law with damping.Additionally, each triangular region has an equilibrium pressure S 0 (determined based on its surface area at the end of development) providing animat with a hydrostatic skeleton and preventing excessive compression or stretching of body regions.All springs share the same Hooke's constant value k but can have different resting lengths.To avoid self penetration of animat bodies, masses representing cells undergo elastic collisions with springs.
Actuation is achieved by modifying resting lengths of springs attached to a given cell.This results in the region around the cell contracting or expanding.The change in length is driven by a sinusoidal oscillation pattern associated with every cell.The period of oscillation and the phase shift for every cell is determined by 2 corresponding GRN outputs at the end of developmental stage.During locomotion, the default resting length L 0 of a given spring is modified according to: where t is simulation time, A is the amplitude (A = 0.2), T 1 , T 2 are the evolved periods of oscillation (scaled to span desired range), and φ 1 , φ 2 are evolved phase shifts (scaled to −π to π).To prevent sudden changes in resting length for cells with non-zero phase shift at the start of the locomotion stage, the amplitude is progressively increased during a short "warm-up" period.
Terrestrial environment was constructed by placing animats on top of a horizontal flat surface and introducing gravity and friction between animat's nodes and the surface.For a fluid based environment gravity was disabled and fluid drag was introduced.We used fluid drag model based on Sfakiotakis and Tsakiris (2006) which assumes that the fluid is stationary and that the force acting on a single edge on the outline of the body is the sum of tangential and normal drag components for the motion of this edge against fluid.

Genetic encoding and genetic algorithm
The neural network model and genetic representation is based on the MultiNEAT library (Chervenski and Ryan, 2014, see reference for the configuration file used), the implementation of the NEAT evolutionary algorithm (Stanley and Miikkulainen, 2002).In the NEAT method networks are represented in the genomes as a list of nodes and their types (input, output, normal) and a list of connections.The algorithm keeps track of innovations history and uses it to perform crossover.It also uses fitness sharing approach with the goal of preserving diversity and protecting new solutions before they have to compete with the rest of the population.We used population sizes of 300 and runs of 2000 generations.Initial population was created as a fully connected feed-forward network with a hidden layer and random weights.To prevent emergence of recurrent networks, mutations that created cycles in the network were rejected.

Evolution of metamorphic animats
We base our approach to evolving metamorphic individuals on a simple idea: we evolve growing multicellular animats similarly to how we would evolve morphologies and controllers capable of locomotion in a given environment in our previous work.However, rather than evaluate animat's morphology performance in a virtual environment after its development is finished, we evaluate it twice, at different stages of development.More precisely, we allow each genome to control embryonic development for 600 time steps.The performance of emerged morphology is evaluated in the first environment (e.g., for its capability to swim).Next, the de-Michał Joachimczak, Reiji Suzuki, Takaya Arita (2015) From tadpole to frog: artificial metamorphosis as a method of evolving self-reconfiguring robots.Proceedings of the European Conference on Artificial Life 2015, pp.51-58 velopment is allowed to continue for another 600 time steps and the resulting morphology is evaluated one more time in the second environment.Importantly, beyond defining the multicellular growth and locomotion models, our approach assumes nothing (other than the limits of the system) about desired size or complexity of the animats, nor the type of locomotion that is preferred for each environment.It also does not explicitly assume that metamorphosis has to happen if development is continued beyond the "larval" stage.
The discontinuity between developmental and locomotion stages that is inherent to our approach necessitates some trade-offs.After the "larval" stage has been evaluated for its performance as a soft-bodied robot, the system needs to return to the developmental stage to continue growth.If development was simply allowed to continue after the positions of cells have been rearranged during locomotion, the course of growth would be highly influenced by the temporal configuration of cells at the end of evaluation in the first environment.As we considered this undesirable and likely deceptive for evolutionary search, we chose to simply resume development from the exact state it was before entering the first locomotion stage, disregarding any elastic changes that occur during locomotion.Fig. 1 provides a concise summary of our approach.
Given the need to optimize individuals with respect to two objectives (the performance of larva and adult) the fitness was determined through a simple scalarization: and adult stages, respectively.While we expect an algorithm dedicated to solving multi-objective problems would be advantageous, we opted for the simple scalarization as it allowed us to perform the experiments without the need to modify the NEAT library we were using (Chervenski and Ryan, 2014).

Results
We performed two types of experiments.The aim in both cases was to evolve individuals that would be adapted to swimming in a fluid environment and moving in a land based one at different stages of their development.In the first scenario, we evaluated developed individuals first in an aquatic environment (as a larva), allowed them to continue growth (hence, potentially undergo metamorphosis) and then evaluated them again in a terrestrial one (as an adult).In the second scenario the order of stages was reversed: we evaluated embryos first in terrestrial environment and then in the aquatic one.Each type of experiment consisted of 20 independent evolutionary runs (using different random generator seeds).

Evolved morphologies
All of the evolutionary runs we performed resulted in individuals undergoing metamorphosis, i.e., they would employ different morphologies for each of the two types of environments they were tested in.The fact that growth occurred Michał Joachimczak, Reiji Suzuki, Takaya Arita (2015) From tadpole to frog: artificial metamorphosis as a method of evolving self-reconfiguring robots.Proceedings of the European Conference on Artificial Life 2015, pp.51-58 when the developmental process was allowed to continue is not surprising by itself as, unless the growth inhibition genes were active, the cells would continue to divide.Since, contrary to our earlier work (Joachimczak et al., 2014), we did not apply evolutionary pressure to self-terminate growth, continued divisions were the most likely outcome.What was however surprising was to observe how individuals adapted their "larval" and "adult" stages to each environment.Two examples of such adaptation (belonging to the most successful individuals obtained in 20 evolutionary runs) are shown in Fig. 2 (see also Fig. 4 for their development, discussed in the next section).Their "larval" stages, having elongated, streamlined morphologies are clearly adapted to swimming in water environments and move with an undulatory, fish-like motion pattern.The pattern itself is a result of waves of cellular contractions that travel through the body in the direction perpendicular to that of movement.On the other hand, their "adult" stages clearly display non-trivial adaptation to land locomotion, having grown leg-like appendages to support their body and moving by cyclically shifting their centre of weight between them.We find it remarkable that an artificial evolution system converges to solutions reminiscent of amphibian lifecycles, with a tadpole-like stage that undergoes metamorphosis by shedding part of its tail and growing appendages.
To find out whether the observed morphologies were a result of evolutionary pressure or a simple side effect of some property of our developmental model (e.g., the bias towards Videos can be accessed at: http://goo.gl/3pqksv and http://goo.gl/YnwCFucontinued growth), we performed the same experiment with environments for each stage inverted: larva had to move on land and adult had to be able to move in the water environment.Fig. 3 shows results of two evolutionary runs that led to high fitness individuals.We were able to observe how, again, locomotion relying on simple appendages emerged in the land based environment, whereas the aquatic adult forms displayed elongated morphologies and undulatory patterns of locomotion.This result indicates high evolvability of our approach, as it has no problem discovering legged locomotion and undulatory swimming regardless of the order of developmental stages.
Finally, although the direction of motion between larval and adult stage is similar in the figures shown, it was not uniformly the case in other evolutionary runs.However, since our virtual animats do not have any sensors and therefore no concept of front or back, there is no direct reason for evolution to maintain the direction of movement unchanged.

Development and metamorphosis
In order to gain insight into how animats undergo metamorphosis we visualized developmental processes of the 4 individuals depicted in Figs. 2 and 3.In each case (Figs. 4  and 5), metamorphosis proceeds by adding cells to the larval stage, resulting in a structure that is considerably larger and has the previous developmental stage (or a part of it) "embedded" inside.Apoptosis occurring during metamorphosis was not uncommon and can be observed in the individual seen in Fig. 4a (note the loss of the "tail" on the left side by comparing shapes at t = 860 and t = 1080) and in the individual in Fig. 5b (removal of cells at the top of the body, compare shapes at t = 850 and t = 1200).
Michał Joachimczak, Reiji Suzuki, Takaya Arita (2015) From tadpole to frog: artificial metamorphosis as a method of evolving self-reconfiguring robots.Proceedings of the European Conference on Artificial Life 2015, pp.51-58 While the metamorphosis of a water larva to a land based adult involved growth of appendages, the metamorphosis of land larva to an aquatic adult involved growth process that filled the space between the appendages, producing a more streamlined shape while at the same time growing tail.
The adult stage being larger than the larval form was universally observed and, as suggested previously, can be largely explained by the developmental model being biased towards non self-terminating growth.

Analysis of evolutionary runs
In order to obtain a more quantitative overview of the evolutionary trends occurring in our experiments, we analysed multiple independent evolutionary runs.Fig. 6 shows how fitness changed over evolutionary time for both types of experiments.Given the fitness function being a square root of the product of distances achieved by each developmental stage in their respective environments, the fitnesses obtained in both types of experiments are of the same level, with some potential for improvement given longer evolutionary runs and, possibly, a slight fitness advantage in the second type of experiment.
However, analysing performance of each developmental phase independently paints a very different picture (Fig. 7).The "from water to land" scenario achieves its fitness owing to swimmers that swim small distance and very efficient runners, capable of traversing on average 4 times larger distance.On the other hand, the "from land to water" scenario achieves its fitness owing to much better swimmers and much weaker runners, traversing about the same distance in their respective environments.What is the source of this discrepancy?We suspect it can be explained by a combination of properties of simulated physics and biases introduced by the developmental model.For one, given that there are no costs involved in growing/actuating larger bodies, being bigger allows to traverse longer distances.More precisely, in the water, the available power of actuators will be proportional to the number of cells (roughly equivalent to the 2-D animat's surface area) whereas the fluid drag will be proportional to the body's cross section (roughly proportional to the square root of the surface area).Similarly, in terrestrial environment, the amount of friction that needs to be overcome will on average be proportional to the perimeter length.Thus, as long as fitness is calculated as absolute distance (rather than, e.g., in relation to body size), the forces exerted by animats increase faster with body size than drag forces do.Furthermore, our experiments with evolving specialized individuals (i.e., adapted to only a single environment) suggest that individuals with the same size limit achieve, on average, higher absolute distances on land than in the virtual fluid.Therefore, with the bias for "adult" stage being bigger than "larva" and ground based locomotion allowing to reach higher speeds in general, the experiments in which "adult" form is terrestrial further amplify the speed advantages of ground locomotion, whereas the experiments where the "larva" moves on land (and thus is smaller), reduce the speed advantage of ground based locomotion.Finally, it is possible that this result indicates that the evolutionary acquirement of developmental path from land larvae to a water adult is generally more difficult, however, given the biases present in the system, without additional experiments, the biases are the parsimonious explanation of the observed results.
Finally, to better understand the scope of change that happens during metamorphosis, we analysed how many cells are created and removed during the transformation.We plotted the result over evolutionary time in Figs. 9 and 8.The number of cells created varied greatly between the runs, reaching values between 90 and almost 400 (note that 256 cells were the maximum allowed, therefore a number that high also implies a large number of cells removed).First 200 generations would show a steady growth in the amount of cells added during metamorphosis and likely indicate period in which first functional metamorphic individuals are being discovered.Since all cells grown during metamorphosis originate from the cells in the larva, scaling the number of cells by its size would reveal a flatter curve (not shown).Be- yond first 500 generations there is little difference between the two types experiments in absolute terms, with both displaying an average of around 200 cells added during metamorphosis and a very large discrepancy between the runs.This however meant adults being on average around 5 times larger than larva in the "water to land" scenario and 3.5 times larger in the reversed one.
The amount of cells that are removed during metamorphosis also displays very high variation between the evolutionary runs with values between 0 and 75 (more than 150 in one case).Although not occurring in all evolutionary runs, apoptosis was a common phenomenon during metamorphosis in both types of experiments.This is a highly interesting result, as it indicates that evolution is eager to adapts apoptosis as a method of reshaping morphology in our system, a process well known to be essential in the growth of biological organisms.

Summary and future work
In this preliminary work, we have shown how it is possible to evolve soft-robots that are adapted to two different environments by being able to transform their morphology from one form to another.Doing so required relatively small changes on top of artificial development system we have recently introduced (Joachimczak et al., 2014).Evolving metamorphic individuals turned out to be a relatively easy task for the evolutionary algorithm and, remarkably, the scope of changes that occurred during metamorphosis from aquatic "larvas" to terrestrial "adults" commonly included growth of supporting leg-like appendages, as well as a loss of "tail".Changes that, at least at a superficial level, are surprisingly similar to changes that occur during life cycles of amphibians such as frogs and toads.On the other hand, attempting to evolve individuals in which "larva" is terrestrial and "adult" form is aquatic resulted in solutions that once again discovered appendages as a method of locomotion on land, to later grow cells around appendages and produce streamlined, elongated shapes well adapted to swimming.The fact that evolved types of morphologies and motion patterns were roughly Figure 9: The number of cells that are added during metamorphosis over evolutionary time for the two types of experiments in evolving metamorphic individuals.Lines show averages of 20 independent evolutionary runs each, colour stripes represent 95%, bootstrapped confidence intervals for the averages.common between two cases of experiments suggests, on one hand, that these morphologies are a result of evolution converging to effective modes of locomotion rather than just an idiosyncrasy of the developmental model we employ.On the other, the way to obtain high fitness in each case was very different (Fig. 7).This means that the environmental dynamics in the life history can significantly affect the evolution of metamorphic and survival strategy due to the existence of developmental constraints, even if a highly efficient type of morphology for each stage of life exists.
The methodology presented in this paper can be seen as a way of evolving dual designs in which one genotype encodes two different specialized phenotypes, together with a method of reconfiguring one morphology into another.Coupled with an adequate modular substrate, such as the recently presented swarms of inexpensive small robots (Rubenstein et al., 2014), our approach offers exciting potential of automatically discovering morphologies consisting of hundreds of smaller, uniform cell-like components together with methods of self-assembling and transforming them to reflect changes occurring in their environments.
At the same time, given that the essential factors of metamorphic processes in multicellular organisms are incorporated into our abstract model, we believe it can also contribute to the better understanding of origin and evolution of metamorphosis.Furthermore, as it would require only a simple change of evolutionary pressures to model a progressive transformation of aquatic population into a land dwelling one, our approach could be used as a basis for a further, artificial life study that would help us understand the relationship between genetic and morphological changes that occur during major evolutionary transitions, such as when our fish ancestors started to adapt to living on land.
One aspect of artificial metamorphosis that we plan to further explore relates to the fact that genetic machinery responsible for the two morphologies of a metamorphic individual is shared.As such, it must introduce certain tradeoffs and limitations on the designs that could be achieved using this approach.After all, the morphology grown for Michał Joachimczak, Reiji Suzuki, Takaya Arita (2015) From tadpole to frog: artificial metamorphosis as a method of evolving self-reconfiguring robots.Proceedings of the European Conference on Artificial Life 2015, pp.51-58 the first stage of life has to not only be adapted to its specific environment, but also be "malleable" to environment it has to perform in during the second stage of life.Comparing our results with performance of individuals that were evolved to be specialized for each type of environment, or were evolved to be robust in both, will shed light on the cost of this malleability.Furthermore, we can envision scenarios in which the necessity to evolve "malleable" designs would actually make it easier to evolve useful solutions by directing evolution towards promising regions in the search space.For example, if the goal was to evolve individuals that can run on a horizontal surface and uphill, the morphology of good solutions for each case may be very similar and differ just by the length of appendages.Metamorphic solution could then potentially be found more easily than two separate solutions.This is because in the case of attempting to evolve a specialized individual for running uphill, the evolutionary algorithm is likely to have a problem bootstrapping the search (by finding initial individuals that move up rather than simply roll down the slope).It may also be the case that metamorphic individuals, even if not showing better performance, may be better in some respects, e.g., be more robust or having higher quality gaits, as shown in Bongard (2011).We plan to investigate this in our future work, together with investigating other methods of evolving metamorphic individuals, such as novelty search (Lehman and Stanley, 2011).
The metamorphic robots introduced in this paper undergo a single transformation.It would however be straightforward to extend this approach to a larger number of stages (or consider ability to return to a previous one).Nonetheless, having a single transformation would easily find its applications, for example in sea deployed rescue robots bound for a mission on land.
Finally, we would like to note that the potential of using artificial metamorphosis is tightly coupled with the use of artificial development and, essentially, its natural consequence.As such, artificial metamorphosis should be applicable to many other artificial embryogeny systems, further revealing the hidden potential of this highly biologically inspired approach to automatic design.

Figure 1 :
Figure 1: Conceptual overview of single genome's evaluation allowing for evolution of metamorphic individuals.

Figure 2 :
Figure 2: Motion snapshots of two solutions (a,b) evolved to move first in aquatic environment and then in terrestrial environment (left: before metamorphosis, right: after metamorphosis).Arrows indicate direction of movement, snapshots were selected to represent one motion cycle.Larval and adult stage are not to scale (larva is smaller).Colours represent whether the region of the body is currently expanded (red), contracted (blue) or at its resting size (white).Videos for (a) can be accessed at http://goo.gl/GozK89 and http://goo.gl/19rJAf,videos for (b) at http://goo.gl/aQUbPj and http://goo.gl/nM47Lb

Figure 3 :
Figure 3: Motion snapshots of two solutions (a,b) evolved to move first in terrestrial environment and then in aquatic environment (left: before metamorphosis, right: after metamorphosis).Arrows indicate direction of movement, snapshots were selected to represent one motion cycle.Larval and adult stage are not to scale (larva is smaller).Colours represent whether the region of the body is currently expanded (red), contracted (blue) or at its resting size (white).Videos for (a) can be accessed at http://goo.gl/XZLVtx and http://goo.gl/DgLI97,videos for (b) at http://goo.gl/VTZYUV and http://goo.gl/o2r5bh

Figure 4 :
Figure 4: Developmental processes of the two individuals shown in Fig. 2. Dashed line separates larval stage from the beginning of metamorphosis.Upper rows show multicellular representation that is used during development, bottom rows show a preview of soft-bodied representation (note that protrusions with a thickness of 1 cell only are removed during this transformation).Soft bodied representation is however used only at the end of each developmental stage, i.e., at 600 and 1200 time steps.Labels indicate developmental time.Blue colour depicts cells that were created during the larval stage, red depicts cells created during metamorphosis.Videos can be accessed at: http://goo.gl/ejHz9T and http://goo.gl/929Ch6

Figure 5 :
Figure 5: Developmental processes of the two individuals from reversed stages experiment shown in Fig. 3. Dashed line separates larval stage from the beginning of metamorphosis.Upper rows show multicellular representation that is used during development, bottom rows show a preview of soft-bodied representation.Soft bodied representation is however used only at the end of each developmental stage, i.e., at 600 and 1200 time steps.Labels indicate developmental time.Blue colour depicts cells that were created during the larval stage, red depicts cells created during metamorphosis.Videos can be accessed at: http://goo.gl/3pqksv and http://goo.gl/YnwCFu

Figure 6 :
Figure 6: Fitness of the best individual in population over evolutionary time for the two types of experiments in evolving metamorphic individuals.Lines show average fitnesses of 20 independent evolutionary runs each, colour stripes represent 95%, bootstrapped confidence intervals for the averages.

Figure 7 :
Figure 7: Distances achieved by each developmental stage of the best individual in population for both types of experiments.Lines show average distances from 20 independent evolutionary runs of each experiment type, colour stripes represent 95%, bootstrapped confidence intervals for the averages.Dashed line represents "larval" stage performance, solid represents "adult" stage.

Figure 8 :
Figure 8: The number of cells that undergo apoptosis during metamorphosis over evolutionary time for the two types of experiments in evolving metamorphic individuals.Lines show averages of 20 independent evolutionary runs each, colour stripes represent 95%, bootstrapped confidence intervals for the averages.