Regenerating Soft Robots through Neural Cellular Automata
RRegenerating Soft Robots throughNeural Cellular Automata
Kazuya Horibe , , , Kathryn Walker , and Sebastian Risi IT University of Copenhagen, Copenhagen, Denmark Osaka University, Osaka, Japan Cross Labs, Cross Compass Ltd., Tokyo, Japan
Abstract.
Morphological regeneration is an important feature that highlights the environ-mental adaptive capacity of biological systems. Lack of this regenerative capacity significantlylimits the resilience of machines and the environments they can operate in. To aid in ad-dressing this gap, we develop an approach for simulated soft robots to regrow parts of theirmorphology when being damaged. Although numerical simulations using soft robots haveplayed an important role in their design, evolving soft robots with regenerative capabilitieshave so far received comparable little attention. Here we propose a model for soft robotsthat regenerate through a neural cellular automata. Importantly, this approach only relieson local cell information to regrow damaged components, opening interesting possibilitiesfor physical regenerable soft robots in the future. Our approach allows simulated soft robotsthat are damaged to partially regenerate their original morphology through local cell inter-actions alone and regain some of their ability to locomote. These results take a step towardsequipping artificial systems with regenerative capacities and could potentially allow for morerobust operations in a variety of situations and environments. The code for the experimentsin this paper is available at: github.com/KazuyaHoribe/RegeneratingSoftRobots . Keywords:
Regeneration · soft robots · neural cellular automata · damage recovering. Many organisms have regenerative capabilities, allowing them to repair and reconfigure their mor-phology in response to damage or changes in components [3]. For example, the primitive organismsHydra and Planaria are particularly capable of regeneration and can thus achieve complete repair,no matter what location of the body part is cut off [49,29]. Furthermore, salamanders are capableof regenerating an amputated leg [48]. Many biological systems achieve regeneration by retaininginformation on the damaged parts [2].While biological systems are surprisingly robust, current robotic systems are fragile and of-ten not able to recover from even minor damage. Furthermore, the majority of damage recov-ery approaches in robotics has focused on damage compensation through behavioral changesalone [6,8,20,41,26]; damage recovery through the regrowth of morphology has received compa-rable little attention.In this present study, we develop a neural cellular automata approach for soft robot locomotionand morphological regeneration. Cellular automata (CA) were first proposed by Neumann andUlam in the 1940s and consist of a regular grid of cells where each cell can be in any one of a finiteset of states [35]. Each cell determines its next state based on local information (i.e. the statesof its neighboring cells) according to pre-defined rules. In a neural cellular automata, insteadof having hand-designed rules, a neural network learns the update rules [5,32,36]. In a recentimpressive demonstration of a neural CA, Mordvintsev et al. trained a neural CA to grow complextwo-dimensional images starting from a few initial cells [33]. In addition, the authors successfullytrained the system to recover the pattern, when parts of it were removed (i.e. it was able to regrowthe target pattern). The neural network in their work is a convolutional network, which lends itselfto represent neural CAs [13]. Earlier work by Miller showed that automatically recovery of simplerdamaged target patterns is also possible with genetic programming [32].In this study, we extend the neural CA approach to simulated soft robots, which develop from asingle cell, and are able to evolve the ability to locomote and regenerate. The results show that whenthe simulated soft robots are partially damaged, they are capable to move again by regrowing a a r X i v : . [ c s . N E ] F e b K. Horibe et al. morphology close to their original one. Our approach opens up interesting future research directionsfor more resilient soft robots that could ultimately be transferred to the real world.
The evolution of virtual creatures first began with Karl Sim’s seminal work nearly three decadesago [44], with creatures composed of blocks interacting with their environment and other individualsin a virtual physical space, evolving their own body plans. Since then many researchers haveexplored the use of artificial evolution to train virtual creatures and even transferred some of thesedesigns to the real world [9,10,14,18,30,40,42]. It should be noted, however, that in each of theabove examples, the morphology of the evolved robot is fixed; it does not develop over its lifetime.More recently, this research field has embraced approaches based on compositional patternproducing networks (CPPN) [45,7,4], which are a special kind of neural network. Furthermore, usingCPPN-based approaches, researchers have been able to explore evo-devo virtual creatures, wheredevelopment continues during interaction with the environment, further increasing the complexityof the final body plans [22,23]. However, the lifetime development of these creature tends to belimited to material properties, rather than growth of complete body parts.Kriegman et al. also proposed a modular soft robot automated design and construction frame-work [24]. The framework’s ability to transfer robot designs from simulation to reality could bea good match for our neural CA method in the future, which increases morphological complexityduring development.
Instead of a CPPN-based approach, which relies on having access to a global coordinate system, weemploy a neural cellular automata to grow virtual soft robots solely based on the local interactionof cells. As previously discussed, cellular automata (CA) were first studied by Neumann and Ulam[35] in the 1940s, taking inspiration from observations of living organisms. When correctly designed,CAs have been able to reproduce some of the patterns of growth, self-replication, and self-repairof natural organisms, only through local cell interactions.Wolfram exhaustively examined the rules of one-dimensional CAs and classified them accordingto their behaviors [50]. Later, Langton discovered that behavior of CAs could be determined witha single parameter [27]. Similar dominant parameters and behaviors have been searched for intwo-dimensional CAs using tools from information theory and dynamical systems theory [38].More recently, optimization methods (e.g. evolutionary algorithms, gradient descent) have beenemployed to train neural networks that in turn dictate the behaviour (i.e. growth rules) of a CA.Such a CA is called a neural cellular automata [33,37,36]. Neural CAs are able to learn complexrules, which enable growth to difficult 2D target patterns [32,37], and can also regrow patternswhen they are partially removed [33]. In this paper, we extend the work on neural CAs to softrobots, which can move and regrow once their morphologies are damaged.
Krigeman et al. evolved robots that were capable of adapting their resting volume of each voxelin response to environmental stress [25]. In recent years, not only the locomotion performance oforganisms, but also their environmental adaptability through shape change has attracted attention.For a recent review of approaches that allow robots to transform in order to cope with differentshapes and tasks, see Shah et al. [43].In terms of damage recovery, traditionally approaches have focused on the robot’s control systemto combat loss of performance. Building on ideas from morphological computation and embodiment,more recently morphological change has been investigated as a mechanism for damage recovery.Such work includes that by Kriegman et al.[25], where silicone based physical voxel robots wereable to recover from voxel removal. Furthermore, Xenobots, synthetic creatures designed frombiological tissue [24], have shown to be capable of reattachment (i.e. healing after insult). egenerating Soft Robots through Neural Cellular Automata 3
Our model uses only local information (i.e. each cell only communicates with its neighbors)and could be applied as a design method for regenerating soft robots composed of biological tissueusing techniques which control gene expression and bioelectric signaling [1,47]. We believe that byusing only local information, our method is particularly biologically plausible and therefore mightwork on real robots in the future, with the help of various biological tissues editing technologies.In particular, an exciting direction is to combine the approach with biological robots such as theXenobots [24].
The neural CA representation for our soft robot is shown in Fig. 1. For each cell, the same networkmaps the neighborhood cell’s input to a new cell state. The cell states are discrete values froma finite set, which we map to a continuous value before passing it to the neural network. Thedimension of the input layer corresponds to the number of cell neighbors (e.g. Neumann and Moorneighborhood). The neural network has one output for each possible cell state and is assigned thestate that corresponds to the largest activated output.Fig. 1:
Neural CA representation.
The center cell and its neighboring cells are shown. Each cellstate is an input to the neural network (bottom). The center cell transitions to the state with thehighest network output.We use a three-layer networks with tanh activation functions. We experiment with both feedforward (the hidden layer is a linear layer) and recurrent networks (the hidden layer is an LSTMunit [16]), which means that each cell has its own memory. The dimension of the hidden layer in thispaper is set to 64 unless otherwise noted. The recurrent setup is inspired by recent experimentalreports that organisms store information about the original morphology in a distributed mannerin the bioelectrical signaling networks [28,31].Following Mordvintsev et al. [33], the network has an additional alpha channel output ( α ) thatdetermines the maturity of a cell. If α is greater than 0.1, the cell is tagged as “living”. A cell with0 < α < . K. Horibe et al.
All soft robot experiments are performed in the open-source physical simulator Voxelyze [15]. Weconsider a locomotion task for soft robots composed of a 7 × × × × × × × × × .
25 seconds, or 10 actuation cycles in2D (Fig. 2c) and for 0 . .
25 or 0 . To evolve a neural CA, we use a simple genetic algorithm [17,11] that can train deep neural net-works [46]. The implemented GA variant performs truncation selection with the top T individualsbecoming the parents of the next generation. The following procedure is repeated at each gen-eration: First, parents are selected uniformly at random. They are mutated by adding Gaussiannoise to the weight vector of the neural network (its genotype): θ (cid:48) = θ + σ(cid:15) , where (cid:15) is drawn from N (0 , I ) and σ is set to 0 .
03. Following a technique called elitism, top N th individuals are passedon to the next generation without mutation. To confirm the promise of neural CAs for growing soft robots, we first apply them to simpler 2Drobot variants. Here, robots have a maximum size of 7 × × ,
3) and 10 steps of development are performed. Asresult, 11 morphologies are obtained. (Fig. 2a). Afterwards, the final grown robot is tested in thephysical simulator and allowed to attempt locomotion for 0.25 seconds (10 actuation cycles). Thefitness of each robot is taken to be distance travelled by the robot from its starting point. These2D experiments use a population size of 300, running for 500 generations. One evolutionary runon 8 CPUs took around 12 hours.Results are shown in Fig. 2, which were obtained from ten independent evolutionary runs,using both recurrent and feed forward networks. The training mean together with bootstrapped95% confidence intervals is shown in Fig. 2b.Evolution produced a variety of soft robots (Fig. 2c). A “Hook” type is distinguished by itshook-like form and locomotion, which shakes the two sides of the hook and proceed to hook theremaining one side to the floor. The “S” shaped-robot is distinguished by its sharp and peristaltic egenerating Soft Robots through Neural Cellular Automata 5(a) 2D robot development(b) Training (c) 2D robot locomotion
Fig. 2:
Evolution of 2D soft robots (a) Development of 2D soft robots through a neural cellularautomata. (b) Training fitness for the recurrent/feed forward setup. (c) Time series of soft robotbehaviors as they move from left to right. From top to bottom, we refer to them as Hook type,S-type, Biped, L-type, and Zigzag.motion with amplitude in the same direction as the direction of travel. The “Biped” has two legsand its locomotion resembles that of a frog, with the two legs pushing the robot forward. The “L”type displays a sharp and winged movement. Finally, the “Zig-zag” shows a spring-like movementby stretching and retracting the zigzag structure. Enabling the cells to keep a memory of recentdevelopmental states through a recurrent network improved performance, although only slightly(Fig. 2b). Investigating what information the evolved LSTM-based network is keeping track ofduring development is an interesting future research direction.
In this section we now extend our methodology to grow 3D robots. For these 3D robots themaximum size of the morphologies is 9 × ×
9. Since the neural CA uses a Moor neighborhood, theinput dimension of the neural network is 3 × × , ,
4) and 10 stepsof growth are performed (Fig. 3a). The final soft robot grown after 10 steps is tested in the physicalsimulated and, as with the 2D robots, the distance of the robot’s center of gravity from its startingpoint was used as part of the fitness function. Additionally we include a voxel cost in the fitnesscalculation:
F itness = (
Distance ) − ( V oxelsCost ). We added a “voxel” cost because preliminaryresults indicated that without this additional metric all the soft robots simply acquired a box-likemorphology. Including the voxel cost metric increased diversity in the population. Note that voxelcost is the number of voxels that are neither empty nor dead.For our 3D experiments the evaluation time is increased to 0 .
5s for 20 actuation cycles to adjustfor the increased complexity of the robots. Each generation has a population size of 100 and thenext generation is selected from the top 20%. The number of generations is set to 300. Note thatboth the generation number and population size are reduced from those values used in the 2Dexperiments as simulated the larger 3D robots has a higher computational cost. One evolutionaryrun on 1 CPU took around 80–90 hours.Results are based on 24 independent evolutionary runs for both the recurrent and feed forwardtreatment (Fig. 3b). Interestingly, the feed forward setup for the 3D robots has a higher fitnessthan the recurrent one, in contrast to the 2D soft robot results (Fig. 2b). We hypothesize thatwith the increased numbers of neighbors in 3D and more complex patterns, it might be harderto evolve an LSTM-based network that can use its memory component effectively. Because the
K. Horibe et al.(a) 3D soft robot development (b) Training(c) 2D Group (d) 3D Group
Fig. 3:
Evolution of soft robots (a) A robots shown at different timesteps during its development.(b) Fitness over generations for the recurrent/feed forward setup. (c) Time series of common 2Dsoft robot behaviors as they move from left to right. From top to bottom, we refer to them asJumper, Roller, Pull-Push, Slider, and Jitter. (d) Common grown 3D robots: Pull-Push, L-Walker,Jumper, Crawler, and Slider.dynamics of LSTM-based networks are inherently difficult to analyse, more experiments are neededto investigate this discrepancy further.Similarly to CPPN-encoded soft robots [7], 3D robots grown by an evolved neural CA (Figure 3)can be classified into two groups: the first group is the two-dimensional group of organisms (Fig. 3c),where planar morphology was acquired by evolution. Exemplary classes of locomotion in this groupinclude the jumper, which is often composed of a single type of muscle voxel. Once a soft robot sinksdown, it use this recoil to bounce up into the air and move forward. The morphology determinesthe angle of bounce and fall. The Roller is similar to a square; it moves in one direction by rotatingand jumping around the corners of the square. The Push-Pull is a widely seen locomotion style.A soft robot pushes itself forward with its hind legs. During this push, it pulls itself forward,usually by hooking its front legs on the ground. The Slider has a front foot and a hind foot, and byopening and closing the two feet, it slides forward across the floor. The two legs are usually madeof a single material. The Jitter moves by bouncing up and down from its hind legs to back. It hasan elongated form and is often composed of a single type of muscle voxel. The second group is thethree-dimensional group of organisms, as shown in Fig. 3d. The L-Walker resembles an L-shapedform; it moves by opening and closing the front and rear legs connected to its pivot point at thebend of the L. The Crawler has multiple short legs and its legs move forward in concert. egenerating Soft Robots through Neural Cellular Automata 7
Here we investigate the ability of the soft robots to regenerate their body parts to recover frommorphological damage. We chose three morphologies from the previous experiments, which areable to locomote well and as diverse as possible: the Biped (feed forward), Tripod (feed forward),and Multiped (recurrent). The morphologies of each of these three robots are shown in Fig. 4a andthe locomotion patterns in Fig. 3d.In these experiments, we damaged the morphologies such that one side of the robot was com-pletely removed (Fig. 4a). In the left side of these damaged morphologies, the cell states were setto empty and the maturation alpha values were set to zero. For the recurrent network, the memoryof LSTM units in each cell were also reset to zero.We initially attempted regeneration using the original neural CAs of these three robots butregeneration failed and locomotion was not recovered. Therefore, we evolved another neural CA,which sole purpose it is to regrow a damaged morphology. In other words, one neural CA growsthe initial morphology and the other CA is activated once the robot is damaged. Fitness for thissecond CA is determined by the voxel similarity between the original morphology and the recoveredmorphology (values in the range of [0; 729]). The maximum fitness of 9 × × ,
000 generations with a population size of 1 , LocomotionMorphology (Net-work) Similarity Original Damaged RegrownBiped (feed forward) 98% (718/729) 40.4 27.2(67%) 35.1(86%)Tripod (feed forward) 99% (728/729) 44.5 1.63(3 . Table 1: Morphology similarity and locomotion recovery rate.For all three morphologies we trained both feed forward and recurrent neural CAs. The bestperforming network types for damage recovery were consistent with the original network type forlocomotion in all morphologies (biped = feed forward, tripod = feedforward, multiped = recurrent). The results with the highest performing network type are summarised in Table 1 and damagedmorphologies for each of the robots are shown in Fig. 4a. The results indicate that the Multipedwas the hardest to reproduce, followed by the Biped and then the Tripod. The Tripod had ahigher similarity than the other morphologies and the neural CA almost completely reproducedthe original morphology with the exception of one cell. We hypothesise that regeneration for theTripod is easier because it only requires the regrowth of one leg, a simple rod-like shape with onlya few cells.For comparison, we then measured the locomotion of the original, damaged, and regrown mor-phology with an evaluation time of 0 .
5s for 10 cycles in VoxCad. The ratio of regrowth and traveldistance to the original morphology are shown in Table 1 and its locomotion in Fig. 5. The damagedBiped maintained 67% of its original locomotion ability; it replicated a similar locomotion patternto the one observed in the L-Walker. As the Tripod lost one of its three legs, it was incapable ofsuccessful locomotion. Furthermore, the Multiped lost all locomotion – the robot simply collapsedat the starting position.These results suggest that the location of the damage is important in determining how muchthe robot loses in terms of locomotion performance. For instance, in the case of the Biped, theleft hand side and right hand side are symmetrical. This means that when the left hand side wasremoved, the right hand side was able to locomote in the same, almost unaffected way. Therefore,despite having the lowest similarity value between the initial and regrown morphologies, there islittle loss in performance. In contrast the Tripod regained less than half the locomotion of theoriginal morphology, despite regaining its original morphology almost completely. It would appearthat the one voxel it is unable to regenerate is necessary to prevent the robot from spinning,allowing it to move forward. The damage recovery results show potential for soft robots capable of
K. Horibe et al. regrowth, but regrowth mechanisms that are not dependant of damage location are an importantfuture research direction. (a) Original, damaged and regrown (b) Biped regereration(c) Tripod regereration (d) Multiped regereration(e) Fitness function of each morphology
Fig. 4:
Regenerating soft robots (a) Original, damaged, and regrown morphology. (b)-(d) Softrobot development after damage shown at different timesteps. (e) Training performance for recur-rent/feed forward setup.
The ability to control pattern formation is critical for the both the embryonic development ofcomplex structures as well as for the regeneration/repair of damaged or missing tissues and organs.Inspired by this adaptive capacity of biological systems, in this paper we presented an approachfor morphological regeneration applied to soft robots.We developed a new method for robot damage recovery based on neural cellular automata.While full regeneration is not always possible, the method shows promise in restoring the robot’slocomotion ability after damage. The results indicate that the growth process can enhance theevolutionary potential of soft robots, and the regeneration of the soft robot’s morphology andlocomotion can provide some resilience to damage. egenerating Soft Robots through Neural Cellular Automata 9
Fig. 5:
Recovery of locomotion.
The regrown morphologies are shown semi-translucent. Fromleft to right: Biped, Tripod, and Multipod.The fitness landscape of the developmental evolving soft robot is likely very complex, and thesimple evolutionary algorithm employed in this paper is therefore getting stuck in some of theselocal optima. This limitation could explain why we needed two neural CA, one for growing the initialmorphology and one for regeneration, and why it was sometimes difficult for evolution to find anetwork that could completely replicate the original morphology for damage recovery. We anticipatethat the variety of quality diversity approaches that reward more exploration during evolutionarysearch [39], such as MAP-Elites [34], could allow for an even wider range of morphologies andescape some of these local optima.Additionally, the locomotion and regeneration task in this paper is relatively simple. Excitingfuture work will explore more complex tasks (e.g. recovery form more types of damage) thatcould benefit from morphological growth/regeneration, such as object manipulation, adaptation toenvironmental changes, task-based transformation, and self-replication.Recently, soft robots designed using computer simulations have recently been recreated in realrobot using a variety of materials [19]. With the development of material science, a variety ofsoft robots that can change their shape have been born [12]. Currently, the technology of tissueculture has been developed, and hybrid robots with dynamic plasticity are being developed [21].In the future, it may be possible to create a hybrid robot that can grow spontaneously and recoverits function from damage by creating a soft robot designed using the proposed model with livingtissue. Because the approach presented in this paper only relies on the local communication ofcells, it could be a promising approach for the next generation of these hybrid robots.
Acknowledgements
This work was supported by the Tobitate! (Leap for Tomorrow) Young Ambassador Program, aSapere Aude: DFF-Starting Grant (9063-00046B), and KH’s Academist supporters (Takaaki Aoki,Hirohito M. Kondo, Takeshi Oura, Yusuke Kajimoto,Ryuta Aoki). References
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