Robotics: Science and Systems 2019
Freiburg im Breisgau, June 22-26, 2019

Automated shapeshifting for function recovery indamaged robots
Sam Kriegman1 , Stephanie Walker2 , Dylan Shah2 , Michael Levin3 , Rebecca Kramer-Bottiglio2 , Josh Bongard1
1

University of Vermont, 2 Yale University, 3 Tufts University

Fig. 1. After learning to walk, a simulated quadruped is subjected to unanticipated insult: its legs are cut off. An evolutionary algorithm searches for
deformations to the postdamage structure that, when coupled with the predamage controller, result in function recovery. One of the evolved solutions (shownhere) yields the spontaneous “regeneration” of the lost legs, which was manually transferred to reality (youtu.be/afOXX2r54mQ).

Abstract—A robot’s mechanical parts routinely wear out fromnormal functioning and can be lost to injury. For autonomous
robots operating in isolated or hostile environments, repair froma human operator is often not possible. Thus, much work has
sought to automate damage recovery in robots. However, every
case reported in the literature to date has accepted the damaged
mechanical structure as fixed, and focused on learning new ways
to control it. Here we show for the first time a robot that
automatically recovers from unexpected damage by deforming its
resting mechanical structure without changing its control policy.
We found that, especially in the case of “deep insult”, such as
removal of all four of the robot’s legs, the damaged machine
evolves shape changes that not only recover the original levelof function (locomotion) as before, but can in fact surpass theoriginal level of performance (speed). This suggests that shapechange, instead of control readaptation, may be a better method
to recover function after damage in some cases.

I. I NTRODUCTION
Certain remote, hazardous or otherwise inaccessible environments preclude human intervention when a robot fails
or is damaged. It would thus be advantageous for systems
operating in such environments to have some capacity for self
-maintenance and -repair.
Indeed, much work has investigated how, in the absence of
external supervision, a robot can automatically learn new ways
to control its body when damaged [6, 10, 13, 20, 24, 26, 34].
While a diverse set of recovery mechanisms have been proposed, they all shared a common assumption: The damaged
mechanical structure could be reconfigured, but not fundamentally deformed.
This assumption is reasonable in classical robots, whichare, generally, jointed collections of rigid links. But recent

advances in materials science and 3D printing are enabling
the construction of soft machines with theoretically infinite
degrees of freedom and thus capable of deforming their structures so as to regenerate a lost part or embrace an entirely new
geometry in the face of unanticipated insult. The possibilityof such change affords a completely novel mode of damage
recovery: No robot built to date has altered its resting structure
in order to recover function lost due to damage.
Previous computational studies have demonstrated structural
but non-functional change in discrete models. For example, cellular automata have been trained to grow a target
structure from a single cell [14, 29]. Similar growth rules
could in principle be instantiated in self-assembling modular
robots [44, 46]. However, structural change would require
access to additional modules in the environment, redundant
modules on the body, or the ability to internally generatethem. Moreover, it is unclear how or if such rules could dictate
continuous geometric deformation in soft robots.
The present work builds on two closely-related research
projects in which injured robots automatically generate andtest candidate control policies in order to find compensatory
behaviors that work in spite of damage [6, 13].
In the first, Bongard et al. [6] demonstrated how, under theright conditions, an autonomous robot could internally model
its own geometry with minimal sensorimotor experiment. The
benefit of this approach is that, once a sufficiently accurate
self-model has been established, actions can be internally rehearsed, discarding those which are unsuccessful or dangerous,
before attempting them in reality. If model accuracy drops, asfrom structural changes due to damage, modeling resumes andcontinues until the robot’s current morphology is adequatelyreflected in the robot’s model of self.
The main drawback of this approach is that internal modeling requires additional computation, and there are circumstances in which the robot cannot afford—in terms of time,money, energy, stability, and the overall well-being of itself
and others—to remain stationary for extended periods of time.
To speed recovery, Cully et al. [13] proposed that robots
should instead exploit the fact that resources prior to deployment are relatively cheap in terms of the factors listed
above. A large, behavioral repertoire composed of mappingsfrom behaviors (for the undamaged robot) to their predictedperformances can therefore be modeled in simulation beforehand, and come preinstalled on the robot. Assuming damage is
detected by an external mechanism, the authors showed how,under certain conditions, such a map can be rapidly updated
and traversed to find successful behavior, which is implicitly
robust to differences between the current and pre-deploymentmorphologies.
The robots used in this past work consisted of rigid components attached together with a handful of mechanical degrees
of freedom: The quadruped in [6] had 8 motors and 4 DOF;
the hexapod in [13] had 18 motors and 12 DOF. The control
problem was greatly impacted by these mechanical details andtheir intrinsic dynamics, but they were taken as given, evenwhen damaged, because these robots simply could not deformtheir resting structure.
Instead of treating the body as just the problem domain,
we here modify it as part of the computational loop. This ispossible because our robot has many more (140) mechanicaldegrees of freedom, and the ability to change the volume,
rather than just the relative displacement, of each component.
This flexibility enables a heretofore unexplored mode ofdamage recovery: keep the existing controller but deform theresting structure. Existing approaches to controller adaptation
could in principle (although this is not investigated here) bepaired with such changes to morphology. However, in manycases, it would be desirable to retain a previously optimized
and fine-tuned controller, especially if missing structure cansimply be regenerated.
We here show that, under a wide range of damage scenarios,
automated shapeshifting can be advantageous, and that, inmost of the cases tested, shapeshifting alone (holding theexisting controller fixed) outperforms controller adaptation
alone (holding the damaged shape fixed), in terms of recovered
mobility.
II. M ETHODSThis section describes the hardware, simulation and controlof our robot, the damage scenarios it faces and its options
for recovery: shapeshifting and controller adaptation. We also
define a tripartite classification—of ‘structure’, ‘shape’ and‘configuration’—that forms the basis of our argument, whichis, briefly, that the way in which our robot recovers fromdamage—shape change—was outside the scope of any robot
previously reported in the literature.

A. The source code.
github.com/skriegman/2019-RSS
B. The robot.
The robot is an isobilaterally symmetrical quadruped constructed from 140 inflatable silicone “voxels” (Figs. 1f and 2).
We here present a method for creating air-filled voxel membranes with relatively uniform thickness.
Creating thin, hollow 3D
silicone structures is challenging due to several factors, including mold precision and potential for damage during release frommolds. One effective but
labor-intensive method is tomake the 3D shapes by ad- Fig. 2. The blue robot, made fromhering 2D films at their thin-walled inflatable elastomer voxels.
joints [31]. Here, inspired by a scalable 2-axis rotational
molding technique [45], we employ a 1-axis rotational dripmolding machine.
First, silicone (Dragon Skin 10 Fast; Smooth-On, Inc.) was
poured into an open-face acrylic mold and a tongue depressor
was used to roughly spread the silicone along the walls. The
mold was then attached to the rotational molding machinewith the rotation axis oriented downward at 45 degrees relative
to horizontal, and run through cycles comprising a 90° turn,stopping for 45 seconds after each turn to allow the silicone toflow and evenly coat each side. Excess silicone dripped out of
the mold, leaving a thickness which was dependent on several
interrelated factors including the cure time, viscosity, and theinteraction between the silicone and acrylic.
After the silicone cured, excess material was cut away. A
silicone base-layer was then rod-coated onto a flat acrylic
sheet. Next, the bottomless cubes were placed on the baselayer and allowed to cure, sealing air inside each voxel. The
voxels were then cut from the sheet and a small hole waspunched in each voxel for tubing. Finally, silicone tubes wereinserted and bonded with Sil-Poxy (Smooth-On, Inc.).
The overall robot consists of a 6×6×3 voxel torso and four
removable 2 × 2 × 2 voxel legs (Figs. 1f-j and 2). Sil-Poxyand Ecoflex 00-50 were used to improve adhesion between
voxels. To explore the effect of layer thickness on the rangeof attainable morphologies, two versions of the robot were
fabricated: The blue robot (Fig. 2) consists of voxels madewith one layer of silicone, while the purple robot (Fig. 1f-j)
consists of thicker-walled voxels made with two layers ofsilicone.
Individual cubic voxels were manually inflated at pressuresless than 20 kPa, and approached a spherical shape as pressure
increased. When patterned together into a robot, selective
inflation of a subset of voxels induces overall robot shapechange. To reduce friction and weight effects in the robots,
they were placed on top of a glass crystallizing dish, which
lifted their legs off the table surface. While this arrangement
made motion difficult, it allowed us to conduct a preliminaryinvestigation of the feasibility of transferring simulated shapechange to a physical system. In future implementations, themanual inflation could be replaced by pressure regulators [7],allowing the robot to approach the continuous control achievable in simulation.
To understand some of the trade-offs between design parameters, consider a spherical pressure vessel in uniform free
expansion:p=

2E ·  · t0 · (1 − δ)
2E ·  · t=,rr0 − 

(1)

where t0 [m] is the thickness of the pressure vessel, r0 [m]is the radius,  is the linear strain due to expansion, E [MPa]is Young’s modulus, and δ is the radial strain (which isdetermined from  and the material’s Poisson’s ratio). Notethat each voxel can push outward with a force proportional tothe pressure. Examining Eq. 1, we see that at a given strain
rate and initial dimensions, the internal pressure scales linearly with both thickness and modulus. Thus, when choosing
thickness of voxels, there was a tradeoff between weight andinternal pressure: doubling the wall thickness doubled weight,
in exchange for doubled operational pressure.
C. The simulation.
To simulate the robot, we use the voxel-based physics
engine Voxelyze [16], which simulates elastic voxels using
two elements: particles and beams. Particles have mass androtational inertia, and are connected on a cartesian grid byspring-like beams (with translational and rotational stiffness).
For visualization and reference, part of a voxel mesh is drawn
around this structure such that each voxel has a single particle
at its center (Fig. 3).
Two adjacent voxels arevoxel1voxel2connected, centerpoint tobeam
centerpoint (i.e., particle toparticle), by a single, sharedcenterpoint
beam. Material properties(particle)(e.g., volume and elasticity)
are specified at the parti- Fig. 3. Voxels are simulated by beams
cles but implemented as at- (springs) and particles (masses).
tributes of beams (e.g., their rest length, and how easily they
twist and stretch). Where two adjacent particles disagree in
their “desired” attributes of a shared beam, an average is taken.
A beam exits a voxel normal to, and in the center of, oneof the voxel’s faces. Although the mesh is drawn such thatvoxel edges bend around the underlying beam-mass network(see, e.g., Fig. 1), a spherical envelope is used for collision
detection, thus approximating the spherical expansion of thephysical voxels (with maximal expansion occurring at thecenter of each face). For more details see [16].

bit value vi denote the presence (vi = 1) or absence (vi = 0)of a voxel at index i. The structure,S = {i : vi = 1},

is thus a set of voxel coordinates.
The shape, S, of a robot is determined by the resting volumeof each voxel, which is expressed in simulation as the resting(or, equilibrium) lengths of the beams connecting adjacentparticles, and in reality as a resting pressure within each voxel(though the exact pressure, pi , is not measured here). Let thefloating point value bi denote the beam rest length stored at
the i-th simulated voxel. The shape,
Ssim = {bi : i ∈ S} ∼ Sreal = {pi : i ∈ S},

The structure, S, of a robot is determined by the number
and placement of voxels, and simulated by the presence andabsence of particles on a regular grid in the workspace. Let the(3)is thus a set of voxel resting volumes.
The robot has a quadrupedal predamage structure (Figs. 1a,f
and 2) with atmospheric voxel resting pressure, which isapproximated by nominal beam rest lengths of 1 cm. Damage
removes structure (voxels) (Fig. 1b). Postdamage structuraldeformation—shape change—is executed by pressure changes
in the remnant structure (i.e., mutations in Sreal ) (Fig. 1h-j)
and approximated by local adjustments in the remaining
beam-mass network (i.e., mutations in Ssim ) (Fig. 1c-e). The
mechanical structure and its resting shape are fixed prior to
behavior during the evaluation period (20 actuation cycles).
E. The controller and configuration of a robot.
The controllers continuously reconfigure the volume of agiven mechanical structure during the evaluation period. We
here consider open loop control of ±0.5 cm3 volumetricchange (±50% from nominal), at each voxel, with a phaseoffset relative to a central pattern generator, for 4 sec.
Controllers are here encoded as neural networks that map
the indices of voxels in 3D space (Eq. 2) to a phase offset
value, φi , between −2π and 2π. We chose this particular
encoding, which is commonly referred to as a Compositional
Pattern-Producing Network, or CPPN [38], because spatial
regularities (in structure and actuation) are known to facilitate
locomotion. (For more details about this encoding, see [11].)
The instantaneous configuration, C, of a robot is determined by an oscillating adjustment to the volume (and thuspressure) of each voxel, centered around its shape S. In simulation, rest lengths are periodically varying (f = 5 Hz) aroundtheir baseline, bi , with constant amplitude (A ≈ 0.145 cm),but damped by ξ. Damping prevents contracting voxels fromoverlapping by decreasing their oscillation amplitude as theirrest length approaches a lower bound of bi = 0.25 cm.
The instantaneous adjustment to the rest length of the i-th
simulated voxel, at time t, is thus:

where:
D. The structure and shape of a robot.

(2)

ψi (t) = A · sin(2πf t + φi ) · ξ(bi ),

(4)



4b − 1.
ξ(b) = min 1,
3(5)

The configuration,
Csim (t) = {bi + ψi (t) : i ∈ S},(6)

is thus a cyclical adjustment in the rest length between adjacentsimulated voxels (implemented when computing the elastic
force between them) throughout a structure S with shape Ssim .
Although simple, open loop control has the ability to
produce complex behaviors, such as symmetrical and asymmetrical gaits (from patches of voxels that oscillate in counterphase), or propagating waves of excitation (from a sequence ofvoxels with increasing or decreasing phase offsets). Indeed, it
is well known that central pattern generators in the mammalianspinal cord (and elsewhere in invertebrate systems) produce
the basic, rhythmic motor patterns of locomotion, such as
stepping, independently of sensory input [15].
F. The damage scenarios.
We here consider nine damage scenarios—we amputate: (i)half of a leg; (ii) one entire leg, (iii) two adjacent legs, (iv)
two diagonal legs, (v) three legs, (vi) all four legs; (vii) one
quarter of the robot’s body, (viii) one half of the body, and(ix) three quarters of the body.

Fig. 4. The various amputations applied in our experiments. The predamage
robot (amputation = ‘none’) is shown for reference.

G. The recovery options.
Each damage scenario removes structure and breaks therobot’s functionality: the robot loses voxels and its ability to
walk. We here consider two options for function recovery:1) Controller readaptation. A new controller is optimized
for locomotion with the damaged structure, as in [6, 13].
The only parameter subject to (re)optimization is thephase offset, φi , of each voxel.
2) Shapeshifting. The shape of the damaged structure is
optimized for locomotion with the existing controller.
The only parameter subject to optimization is the baseline rest length, bi , of each voxel.
H. The shape change.
The body is reshaped prior to behavior (i.e., before thecontroller is turned on), analogous to a prenatal developmental
stage. This is done by adjusting the robot’s shape, S, as definedin Eq. 3. Then, behavior results from oscillations that aresymmetrically distributed about this shape (Eq. 6).
The same kind of neural network that encodes controllers(i.e, a CPPN) was also used to encode the robot’s shape.
However, the shape-encoding networks output a rest beam
length, bi , between 0.25 and 2 cm (instead of a phase offset,

φi , between −2π and 2π). Subject to the constraints outlined
above, optimization searches for shape-encoding networks that
result in resting shapes that, when coupled with the original
open-loop controller (previously optimized for the undamaged
robot), synergize to recover forward movement.
I. The optimization algorithm.
Shapes and control policies are here optimized to displace
the (simulated) robot in any direction using Age-Fitness-Pareto
Optimization [35], an evolutionary algorithm that uses theconcept of Pareto dominance and an objective of ‘age’ (inaddition to displacement) intended to promote diversity among
candidate designs and prevent premature convergence.
A trial is initialized with a population of 50 randomlygenerated designs with age zero. Every generation, the population is first doubled by creating modified copies of eachindividual in the population (i.e., offspring, in which ‘age’is set equal to that of the parent), where modification occurs
only to the encoding-network that is currently being optimized(either that of φ or b). The age of each individual is then incremented by one. Next, an additional random individual (withage zero) is injected into the population (which now consistsof 101 designs). Finally, selection reduces the population to its
original size (50 designs) according to the two objectives ofnet displacement (maximized) and age (minimized): Startingwith nondominated designs (N = 0), successive Pareto fronts(containing designs dominated by exactly N alternatives, for
N = 1, 2, . . .) are kept in their entirety until doing so would
overfill the population past its original size; then, designs are
selected one-by-one with probability proportional to their net
displacement. (The 51 unselected designs are deleted.)
This process of random variation and directed selection isrepeated for G generations, in which both the architectures andweights of the encoding networks are optimized: Mutations
add, modify or remove a particular vertex or edge. Where
modification of an edge reweights it (within -1 to 1 bounds)
by adding a value randomly drawn from a normal distribution
with mean zero and standard deviation 0.5. Vertex modification
swaps the node’s activation function with a randomly chosen
function in the set (adopted from [23]): sin(), abs(), square(),sqrt(abs()); and the negations of those four.
III. R ESULTS
Prior to damage, twenty controllers were optimized (forG = 1500 generations) to generate forward movement in thesimulated quadruped during an evaluation period of 4 sec (withnumerical integration time steps of 0.000151 sec). Predamage
displacement ranged from 37 to 46 cm (6.2 - 7.7 body lengths).
In order to isolate the effect of shape change relative tothat of controller adaptation, across a diversity of insult, thesimulated robot is copied 9 ∗ 2 ∗ 20 = 360 times; once for eachunique damage scenario (9 total), recovery option (2 total)and controller (20 total) triplet. Each copy is thus given an
optimized controller and recovery option, cut according to its
particular damage case, and then reoptimized for displacement(for G = 500 postdamage generations).

A. The performance recovered after damage.
Relative displacement

amputation = 1/2 leg

amputation = 1 leg

amputation = 2 adj. legs

amputation = 2 diag. legs

amputation = 3 legs

amputation = 4 legs

amputation = 1/4 body

amputation = 1/2 body

1.25
1.00
0.75
0.50
0.25
0.00

Relative displacement

1.50
1.25
1.00
0.75
0.50
0.25
0.00

Relative displacement

1.50
1.25
1.00
0.75
0.50
0.25
0.00

Relative displacement

1.50
1.25
1.00
0.75
0.50
0.25
0.00

Overallamputation = 3/4 body

1.50

Relative displacement

Figure 5 plots mean relative performance (i.e., postdamage
displacement as a fraction of predamage displacement), with
99% bootstrapped confidence intervals, for the two recovery
options in each damage scenario.
There are two, independent recovery options: controller
readaptation (control) and shapeshifting (treatment). For eachdamage scenario, the data consist of two random samples,a sample from the control population (20 independent trials,
holding the shape of the damaged structure fixed) and an independent sample from the treatment population (20 independent
shape optimization trials, holding the controller fixed). On thebasis of these samples we wish to investigate the presence ofa treatment effect that results in a shift of location (median).
The null hypothesis is that of no treatment effect; the samples
can be thought of as a single sample from one population.
We used a distribution-free rank sum test (Wilcoxon, Mannand Whitney) for the hypothesis of no treatment effect, with
Bonferroni correction for nine comparisons. The corrected
rank sum test and the 99% bootstrapped CIs (of the mean)
are in agreement. That is, statistical significance between
shapeshifting and controller adaptation, at the 0.01 level, canbe correctly inferred, for each damage scenario, by visualinspection of Fig. 5 (i.e., no overlap in the shaded confidence
intervals here implies rejection of the null hypothesis).
Overall, shape change was more successful (often betterand never worse) than controller adaptation. Interestingly, theproportion of fitness recovered was in some cases higher thanone. This could be due to a lack of volume conservationand the possibility that larger robots simply run faster thansmall ones. However, many robots recovered by reducing theiroverall volume (e.g., Figs. 7 and 8). Moreover, controller
adaptation also achieved higher-than-predamage performancein one case (amp. = 2 adj. legs), and this phenomenon was
also documented in [13] but not via shape change.
To explicitly control for the effect of body size, we optimized the controller of an otherwise identical quadruped that is
twice the size of the original (Fig. 6). Isometrically increasing
volume did not affect speed: There was no significant difference in speed (at the 0.01 level) between the enlarged andoriginal quadruped. This is because the controller oscillations
are added on top of (not relative to) the root shape (Eq. 6).
The enlarged robot has eight times the volume of the original,
beam length oscillations still have the same amplitude.
Despite the fact that control was optimized for the original
quadruped, and that amputation of all four legs removes 23%of the original volume and actuation (Fig. 4), robots thatrecovered from this particular insult through shape change(Fig. 1) move significantly faster than both the original andisometrically enlarged quadrupeds (Fig. 6). It follows thatthe efficacy of shapeshifting is not due simply to increased
volume; rather, it is due to where and how the remnant
structure’s shape is deformed, which affects (e.g.) the robot’s
posture and mass distribution, its points of contact with theground, and the storage and release of elastic strain energy,

1.50

shape change
controller adaptation
original (predamage)

1.25
1.00
0.75
0.50
0.25
0.00
0

100

200

300

400

Generations since damage

500

0

100

200

300

400

500

Generations since damage

Fig. 5. Mean relative displacement (i.e., recovered performance) with 99%
CIs, at each generation (g) of reoptimization since damage occurred (g = 0).

Displacement (cm)

60
50
40
30
20

original
2x orig. size
amp. = 4 legs

10
0
0

250

500

750

1000

1250

1500

Generation

Fig. 6. Mean displacement with 99% CIs of controller optimization in the
predamage quadruped isometrically enlarged to maximal volume, compared
to shape optimization after amputation of all four legs.

during locomotion.
B. The found techniques of recovery.

ΓWe found that the optimizer discovered diverse recovery
strategies through shape change (Figs. 7-9), whereas controller
readaptation often converged on the same strategy. For example, with all four legs removed due to damage, the robot is
reduced to a cuboid, and the only viable locomotion techniquefound by controller readaptation was crawling. During postdamage optimization, many of these robots evolved crawlingby peristalsis or in a manner that resembles the serpentine
crawling of snakes [1].
Deforming the structure, even in a random manner, tends to
produce greater frictional anisotropy which enhances peristalsis and serpentine crawling, and enables yet simpler forms of
movement such as two-anchor crawling [1].
Nevertheless, crawling is inefficient because of drag. Here,in many damage cases, behavioral competence was recovered
through shape changes that partially or completely (but, due
to material constraints, never perfectly) regenerated missing
legs. Notably, when all four legs were amputated, recovery
strongly converged on the solution of regeneration, and theresulting designs were some of the fastest overall (Fig. 1).
Note that the objective function does not assume or directly
select for legged locomotion.
Other amputations, however, can be beneficial, if they resultin a shape that is easier to efficiently control than the original:
Prior to damage, the robot’s sagittal silhouette resembles a Π.
When two adjacent legs are amputated, the resulting Γ shape,
due to gravity, tends
which initially falls forward like thisto rapidly surpass predamage performance through controller
readaptation alone, despite its diminished size.
When only half of a leg was lost to injury, some robots
contracted all of the undamaged legs to recover a stable but
shorter quadrupedal form. Others seemed to simply regenerate
the missing part through local volumetric expansion at the siteof damage: The stump was isometrically expanded into a legthat was the same length as the original but much wider.
On closer inspection, however, many of those who regenerated a limb also made various other compensatory shapechanges away from the site of damage, such as expanding andcurving their spine. Thus even when damage is isolated to asmall part of the robot’s structure, global changes, in addition
to local repairs, can sometimes streamline recovery.
When damage was distributed across a wider portion of thebody, a diversity of solutions were discovered. For example,
after the amputation of a quarter of the robot’s body, the robot
occasionally splayed out its pelvis to form a straighter andfaster shape (Fig. 7). And, after the amputation of three legs,
some robots once again grew replacements, but, because ofother changes (e.g., a greatly expanded back), the remaining“genuine” leg needed to be partially contracted and tucked
inward for balance (Fig. 10).
In the case where half of the robot’s body is removed, theundeformed structure falls under gravity onto its side; one
local optima was thus to crawl “facedown”. A better strategy
was found in which the robot could remain upright by using
the two remaining limbs as forelegs and expanding the stump
to form a wide hind leg. An equally proficient strategy wasobserved in which the robot diminished one or both of its legs,
expanded its spine, and moved longitudinally (Fig. 8).
There were many successful variations on this theme, but
one of the best designs in this case did the exact opposite:
The robot expanded its remaining limbs to their maximum
volume, contracted its spine, and flipped over (once) to walklongitudinally with the added momentum generated fromlarge, swaying front and back limbs (Fig. 9).
However, after the most extreme insult, when all but aquarter of the robot is lost, there is insufficient material toregenerate legs or execute other more extreme shape changes.
Neither recovery option cultivated (visually) appreciable gains
in fitness. Yet, while this case removes 71% of the original
volume it is significantly less deleterious to controller optimization than amputating the four legs, which removes just
23% of the original volume. Insult is thus a matter of kind,
not degree.
C. The transferal of recovery strategies to reality.
To investigate the potential for directly transferring recovery
strategies from simulation to reality, we aimed to transfer theoverall shapes that are pictured in Figs. 1 and 10. In theseparticular cases, the optimizer found shapes with contiguous
sections of voxels actuated to similar levels. Thus, we here
examine the one-actuator case, in which the voxels with thelargest rest volumes—the top layer of (6 × 6 = 36) voxels andthe two corner voxels just below the top layer, on each cornerof the torso (8 in total)—were connected to the same air inlet.
Voxels not hooked into the air line were punctured to allow
for passive deflation and contraction of the robot, mimicking
the simulated robot’s ability to contract voxels by decreasing
the rest lengths bi .
The purple robot adequately expands the top layer of voxels
in both cases (Figs. 1j and 10j), but fails to reach the overalltarget shapes drawn in Figs. 1e and 10e. Although further
increasing pressure did indeed lead to larger deformations,the outer voxels inflate farther than interior ones, limiting
the maximum viable actuation pressure. The thinner voxel
walls of the blue robot exacerbated this issue (Fig. 10k-o), butdictated by the form of damage, predamage structure of therobot, and its task environment.
A. Biological regeneration.

Fig. 7.
This damaged robot (amp. = 1/4 body) contracted its hips andexpanded its pelvis to recover function (youtu.be/UBvsR6tZf5c).

Fig. 8. Shape change in this damage case (amp. = 1/2 body) enabled upright,
lengthwise movement, instead of falling over (youtu.be/nfCaVZVBmKI).

Fig. 9. This damaged robot (amp. = 1/2 body) contracted its spine, expanded
its limbs, and flipped over onto its back to walk lengthwise and exploit theelastic properties of its new arms (youtu.be/WwYdSnuJBBA).

their increased flexibility enabled a more faithful transferal of
overall surface curvature. Another limitation we discovered
was friction. Fully realizing the target shape in Fig. 10erequires the robot to drag its leg inward across the floor,
tucking it under its body; but the silicone leg often stuck tothe surface, preventing the prescribed maneuver in reality.
The silicone design and 1-axis rotational molding technique
are still quite promising. Even when inflated at high enoughpressures to make the outer voxels approximately spherical(Fig. 10o), the voxels did not rupture. To achieve moreconsistent expansion of interior and exterior voxels, the later
should be inflated at a lower pressure than the former. By
incorporating strain sensors [43] and closed-loop control in
future, the robot could correct for this variation on the fly. By
actuating different voxels at different pressures, and enabling
active contraction in addition to expansion, a much wider
range of simulated shapes could be attained in reality.
IV. D ISCUSSION
In this paper, a new approach to robot damage recovery
has been proposed. Instead of presenting the remnant shapeof the damaged robot to optimization as fixed, we enableoptimization to change this shape as the essential part of
the recovery process. In doing so we realized a machine thatrecovered more function than an otherwise equivalent systemthat could adapt its controller but not deform its shape.
In future work we will improve the transferal of simulated
morphing machines to physical ones using existing sim2real
methods [2, 6, 13, 17, 24, 40] adapted appropriately to meet
the additional transferal demands dictated by soft materials [27]. We will also generalize our optimization method
such that control and shape readaptation can be combined as

In past work, rigid-bodied robots have been venerated fortheir ability to “adapt like animals” [6, 13]. These machines,
which were constructed from undeformable metals and hardplastics, automatically learned to control their bodies in spiteof missing or broken legs. But when an animal loses one ormore of its legs to injury, it does not adapt by merely searchingfor a new mental representation of behavior that successfully
maps onto the damaged body. Rather, they often fundamentally deform their damaged “hardware” into something more
controllable.
Evidence for this abounds. A famous example is the congenitally two-legged goat described by Slijper [37]: an otherwise
normal goat which was born without forelegs adopted an
upright posture and learned to walk on its hind legs alone. In
addition to enlarged hind legs, striking changes in morphology
were documented, including a greatly elongated gluteal tongue
and an innovative arrangement of small tendons, a narrowed
pelvis, an oval (rather than V-shaped) thoracic cross-sectional
shape, a curved spine, and an unusually large neck [42]. The
animal’s body resembled that of a kangaroo more closely thanthat of a normal goat.
Other animals can regenerate. The planarian flatworm canbe cut into many pieces (the record is 279) all of which growback to a full organism, regenerating not just tail and head,but eyes and the complete nervous system [30]. Vertebrates,
such as frogs, also display the capability of regenerating limbs,
jaws, eyes and a variety of internal structures [8]. Humans
too (especially children) are sometimes capable of fingertip
regeneration after distal phalange amputation [18].
B. Mechanisms of biological regeneration.
Several of the mechanisms by which organisms achievethese forms of self-editing of their own anatomy pose design
challenges and future research directions for robotics.
First is the ability to harness the behavior of low-levelcomponents (cells) towards a specific large-scale goal-state:salamanders can regenerate whole limbs, eyes, tails, ovaries,
and other organs [28], but growth and remodeling ceases
when a correctly shaped and sized organ is complete [33].
Second is the flexibility and robustness of systems under novel
conditions. For example, tadpoles whose facial organs areexperimentally placed in abnormal configurations will undergo
novel rearrangements to still give rise to normal frog faces
during metamorphosis [41], showing that the genome encodes
not a hardwired set of movements for each organ but rather
specifies a machine that can remodel toward the same target
morphology from a variety of unexpected starting states. Thus,
it is critical to understand and exploit the ability of evolution
to give rise to hardware that is well-adapted to the normal
environment but also retains significant plasticity [39].
Third is the fact that during regeneration, the tissues making
growth and morphogenesis decisions are themselves beingFig. 10. After losing three legs to injury (amp. = 3 legs), the former quadruped is reduced to a monopedal structure (a), the shape of which was then
optimized for locomotion speed, resulting in an expanded spine, the folding-inward of the remnant predamage leg, and the “regeneration” of the three missing
legs (c-e). This simulated strategy was then realized in two implementations using pneumatically-actuated, cubic elastomer bladders. The purple robot (f-j)
consists of two layers of drip-molded silicone; the blue robot (k-o) consists of a single layer, and is thus less stable but more deformable. A single air inlet
here yields the rudiments of appropriate shape change, but pressure oscillations in this setup did not yield locomotion (youtu.be/A2KTGhCFxK8).

drastically rearranged: thus, the computational control circuitry
is itself the object of the deformation actuators, forming
a closed loop in which information is reliably processedin a medium that is constantly changing [32]. Finally, theremarkable robustness of morphological computation extends
to information learned within the lifetime of the organism [4].
Butterflies, which result from a caterpillar brain that is almost
completely dissolved during metamorphosis, still remember
information learned during the caterpillar stage [3]. Flatworms,
which regrow their entire heads, still remember information
they learned prior to decapitation [12, 36].
Attempts to implement these capabilities in artificial systems (whether robotic or via synthetic biology) are likely toenrich not only engineering technology, but also to feed backto the biological sciences and biomedicine. The current understanding of computation in biological tissues has numerous
gaps, which are only likely to be filled by attempts to build
these capabilities from the ground up [19].
C. Metamorphosing machines.
It has been shown here that robots, too, are not only capableof regenerating limbs, but that such deformation can manifest
by selecting for function recovery alone, instead of a target
legged shape.
However, this ability largely depends on the material withwhich robots are made, for even if morphology is free tochange in rigid bodies, the ways in which such change canoccur are limited at best. In [5], robots used a combination ofrotary and linear actuators to slowly angle appendages downward and extrude them outward, thus simulating limb growth.
In softer machines, there are more ways for morphology tochange: The soft robot used here was able to locally deform

its geometry to bend, twist, compress or expand throughout its
body. Its also possible, although not investigated here, for soft
robots to change their material properties, such as stiffness,through (e.g.) granular jamming [9, 23].
The possibility of this latter change highlights the inadequacy of the name “soft robot”. When a granular jamming
robot jams (removes excess internal air to become stiff) doesit cease to be a soft robot? What if it never unjams? For the
purposes of damage repair, the most important property ofsoft robots is not that they are soft per se, but that they may
easily change their structural and material properties (possibly
including stiffness). One can envisage future “rigid” nanobots
capable of self-assembling into a protean metamachine thatcan rearrange so as to regrow a lost part; but that day seems faroff, whereas soft robots, capable of continuous morphologicalchange, are already becoming a reality.
The future of this line of work promises not just new
robotic systems but also new science. Shapeshifting robots,recast as scientific tools, can shed new light on old biologicalquestions about developmental plasticity, regeneration andhomeostasis [21, 22, 25]. And, symmetrically, new theories
about the mechanisms that lie at the heart of such questions
can be physically instantiated and optimized in a new breedof useful, autonomous and adaptive machines.
ACKNOWLEDGEMENTS
This work was supported by NSF award EFRI-1830870
and DARPA contract HR0011-18-2-0022. Dylan Shah was
supported by NASA STRF-80NSSC17K0164. Computation
was provided by the Vermont Advanced Computing Core. We
thank Gabrielle Branin for the sim2real demonstration videos.

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