Subtract to adapt: Autotomic robots

2023 IEEE International Conference on Soft Robotics (RoboSoft) | 979-8-3503-3222-3/23/$31.00 ©2023 IEEE | DOI: 10.1109/ROBOSOFT55895.2023.10122102

Q. Tyrell Davis1 , Stephanie Woodman2 , Melanie Landesberg2 , Rebecca Kramer-Bottiglio2 , and Josh Bongard1

Abstract— Robot adaptation is typically limited to adaptive
control policies or actuated morphology changes (such as shapechange). When part of a robot body is removed it is typicallyviewed as an injury that must be adapted to; the potential
for adaptation through subtraction by removal of body components has not yet been considered. Biological systems, on theother hand, provide many examples of subtractive adaptation,
including gene or nucleotide deletion at the evolutionary scale,apoptosis at the cellular scale, and autotomy (the deliberate
loss of an appendage) at the organismal scale. In this work,
we consider the adaptive potential of evolved autotomy insimulated soft robots. To do so we jointly evolved the bodyplans, control policies, and/or which body parts to remove
for soft robots. Our results show that autotomy, rather thanpolicy adaptation, sometimes evolved to change the robot’s
heading when commanded. In most trials, policy adaptation
was favored by the evolutionary algorithm over autotomy forchanging heading. But the fact that autotomy appeared as a
viable solution in some evolving populations, both when starting
body plans were evolved or set manually, suggests that thisform of morphological adaptation may be useful for future soft
robots.

I. INTRODUCTION
Humans tend to overlook subtraction as a meansof problem-solving, as demonstrated experimentally in[Adams et al., 2021]. Although [Adams et al., 2021] showthat individuals have a tendency to overlook subtractive
change, they also demonstrated that specific prompts, ora decrease in cognitive load, help beneficial subtractive
adaptation—removal of one or more components from a system to improve its operation—to be discovered more often.
Natural selection has no such bias: subtractive adaptation
occurs at all biological levels of organization. By incorporating these lessons from biology, we posit that deliberately
considering subtractive change for adaptation in engineered
systems may improve overall performance and facilitate
adaptation by providing an alternative to policy adaptation.
It may also serve as an alternative to additive adaptation, in
which the robot can add spare parts to itself, assuming thatit can carry them, rotate them into an appropriate position,
and activate them.
A. Morphological Change and Robotic Adaptation
From a robotics perspective, the loss of an appendage
or its function usually presents a challenge to be coped*This work was supported by the National Science Foundation under theEmerging Frontiers in Research and Innovation (EFRI) program (EFMA1830870)
1 Department of Computer Science, University of Vermont, Burlington,
VT 05405, USA [qdavis|jbongard]@uvm.edu
2 School of Engineering and Applied Science, Yale University, New
Haven, CT 06511, USA [rebecca.kramer | stephanie.woodman]@yale.edu

with and is not used as an adaptive mechanism of its own.
[Najarro and Risi, 2020] evolved Hebbian learning rules insimulated robots as a means of meta-learning locomotion
tasks starting from randomized neural network control policies, including in the context of a non-functional limb.
[Horibe et al., 2022] combined differentiable programmingand neural cellular automata to ‘regrow’ damaged body plansin simulated soft robots.
Schemes for robotic adaptation, when faced with damage, are not limited to changes in control policy.
[Kriegman et al., 2019] evolved morphological changes in asoft robot to adapt to limb removal in a quadrupedal bodyplan. The actuators in a physical implementation were notstrong enough to achieve the evolved posture, but the change
recovered mobility in simulation. [Bongard et al., 2006] approached the problem of control recovery after partial limb
removal by instilling self-modeling capabilities in a physicalrobot.
B. Biological Inspiration for Robotic Autotomy
Biological systems exhibit many examples of subtractive
adaptation at multiple temporal and spatial scales. At the cellular scale, apoptosis (programmed cell death) is crucial forshaping the central nervous system [Wong and Marı́n, 2019]and other tissues [Yan and Shi, 2005] during development.
Apoptosis also helps to mitigate substantial costs of damaged cells, and evading apoptosis is one of the classic hallmarks of cancer [Weinberg and Hanahan, 2000],[Hanahan and Weinberg, 2011]. At evolutionary scales,
gene deletion plays an important role in evolution[Albalat and Cañestro, 2016], and nucleotide deletion isa substantial driver of antibody diversity during somatic hypermutation in mammalian immune systems[Bowers et al., 2014]. In this project, we are primarily concerned with a robotic version of autotomy, the deliberate
removal of one or more appendages by an organism.
In mature organisms, autotomy is usually seen as ameans to escape predation, escape encumbrance, or reduce the cost of maintaining a (typically injured) limb
[Emberts et al., 2020]. Autotomy is also sometimes used toenhance a positive capability, such as the deliberate removalof the sperm-carrying hectocotylus arm in Argonauta sp.
octopuses [Battaglia et al., 2021]. Several theories for theevolution of autotomy have been proposed in the literature. Slow autotomy, not very useful as an antipredation
mechanism, is seen as an intermediate step for the fast
autotomy demonstrated by lizards [Zani, 1996], arthropods[Emberts et al., 2020], [Emberts et al., 2019], and amphibians [Wake and Dresner, 1967] to facilitate quick escapes.

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Fig. 2.
Body plan modes. Black=rigid and passive units. Gray=softand passive units. Orange=units containing horizontal linear actuators.
Blue=units containing vertical ones.

II. METHODS

Fig. 1. Overview. (a) Each robot is initially rewarded for maximizing
rightward movement. If a sufficient distance is achieved, the environment
provides a signal to the policy’s input that reward is now provided formoving leftward. Additionally, at this moment, the robot may elect todiscard one or more modules (squares lacking asterisks denote those that are
discarded). (b) Each robot in the evolving robot population has three data
structures associated with it: its body (orange denotes squares containing
horizontal linear actuators; blue=those with vertical ones); which (if any)
body parts to remove (red crosses); and its control policy. In the cases
where the body plan is manually set, the first data structure is not evolved.
Summary video at https://youtu.be/rm_N4FvrOwU.

To investigate whether and how autotomy might be usefulfor soft robots, simulated robots were optimized using anevolutionary algorithm to exhibit a particular behavior, but
to also be capable of changing behavior when supplied withan external cue1 (Fig. 1). The evolutionary algorithm wasconfigured such that robots could evolve to switch behavior
by jettisoning some of the modules comprising them, orby evolving a policy that altered behavior appropriately if
supplied with the external cue. To determine whether the
choice of robot structure affects whether or not autotomy
is useful, we conducted two experiments: In the first, theevolutionary algorithm could also set the physical structureof the robot. In the second set of experiments, three different
manually-designed robots were tested (Fig. 2).
A. The environment.

[Emberts et al., 2020] used a combination of bioinformatic,morphological, and behavioral evidence to support the hypothesis that selection for slow autotomy to reduce the costof failed molts or injuries paved the way for fast autotomy
to evolve in leaf-footed insects in the order Hemiptera.
C. Contributions
In this work, we investigate the artificial evolution of
autotomy, not as an escape mechanism but as a means ofadapting the morphologies of simulated soft robot bodies
to facilitate achieving a changing objective. Our task andenvironment are simple: to achieve mobility in one direction
followed by movement in the opposite direction in the 2D
soft robotics simulator, Evogym [Bhatia et al., 2021].

The robots were evolved in Evolution Gym, a 2D soft
physics simulator and a suite of reinforcement learning
environments for joint evolution of morphology and control[Bhatia et al., 2021]2 . The task in our environment is toreach a goal location 16 squares to the right of the origin.
If a robot manages to reach this threshold, the task reverses
and the objective is to make progress to a goal location 16
squares to the left of its current position (this second phaseoccurs in the same simulation). A robot that moves 16 ormore units to the right, and then the 16 or more units to theleft is considered to have solved the task. The environment
consists of flat terrain and no obstructions. If a robot jettisons
1 Code available at https://github.com/jbongard/autotomy.
2 https://github.com/EvolutionGym/evogym

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body parts, these do not collide and/or otherwise obstruct the
robot or impinge on its sensors.
B. The robot.
The simulated robot is comprised of a set of twodimensional deformable squares, serving as a minimal approximation of 3D voxel-based soft robots (e.g.
[Kriegman et al., 2019]). Each robot can contain at most
5 × 5 squares. If a square is present, it may contain ahorizontal actuator that extends or contracts its width or avertical actuator that alters its height.
C. The policy.
At every time step of the simulation, the relative locationand orientation of each square are supplied to a neuralnetwork control policy. It is structured as a feed-forward
multilayer perceptron with a single, 16-unit hidden layer
and rectified linear unit activation. The output layer dictates
extension or contraction commands to the actuator insideeach active square. The input layer also receives a binary
signal indicating whether the robot will receive reward formoving to the right (the first half of the simulation) or left(the second half of the simulation). If a robot elects to discard
body parts, the input neurons corresponding to the lost parts
are supplied with zero values. The values arriving at theoutput neurons corresponding to those parts are discarded.
D. Optimization.
Each robot is constructed from a genome G = {B, A, π}.
B describes the robot’s starting body shape: it is an integer
5×5 matrix: Bij = 0 denotes square [i, j] is absent. Bij = 1
dictates that that square is rigid and passive. Bij = 2 dictatesthat that square is soft and passive. Bij = 3 dictates that thatsquare contains a horizontal actuator. Bij = 4 dictates thatit contains a vertical actuator. A, the autotomy map, denotes
whether and how that robot will exhibit autotomy. It is abinary 5 × 5 matrix: if the external cue switches, indicatingthat reward will now be provided for leftward rather thanrightward motion, any values in A that equal one causes
those squares to be jettisoned. π dictates the robot’s control
policy: it contains all the synaptic weights within the policy.
We used a genetic algorithm derived from the opensource bevodevo library3 to evolve these parameters. An
initial population of 64 randomly-generated genomes was
generated. Each B was then used to initialize an EvoGym
simulation. Reward is computing while that robot moves inthe simulation. If it reaches the goal of moving 16 squares
in distance to the right, the external cue is switched, and therobot begins to collect reward if it moves to the left. Notethat a robot that never moves 16 units to the right, or thatmoves that distance and then continues moving to the rightwhen it should not be doing so, may accrue less than 16
units of reward.
Once all G’s in the population have been evaluated in thismanner and reward assigned to each, those with lower reward
3 Available under the MIT license at https://github.com/
rivesunder/bevodevo

are deleted. For each gap in the population, a surviving G ischosen at random, and one or more of the parameters in its B,
A, or π are randomly modified. These mutation operators areconstrained in several ways. B is constrained so that it produces just one robot: there is only one connected component
in B. A is constrained so that it also contains one connectedcomponent, and that every element in that component has acorresponding non-zero element in B. Mutations to B maychange the shape and topology of the robot, as well as theorientation of its actuators. Mutations to A affect how orwhether the robot will attempt autotomy when the externalcue changes. Mutations to π affect how the robot will move
before and after the external cue changes, regardless ofwhether the robot attempts autotomy (A contains non-zerovalues) or it does not (A=0).
E. Experimental modes.
To determine whether the robot’s structure affects whether
or not it evolves to make use of autotomy, four different
experimental modes were pursued (Fig. 2). In the first mode,
the robots’ body plans evolved during optimization (B wasaltered by the evolutionary algorithm). In the second, third,
and fourth modes, three manually-designed robots were
employed (B was set by the authors). Seventeen independent
evolutionary trials were conducted for each of the fourmodes, allowing for the determination of whether and how
often autotomy evolved as a strategy for altering behavior.
III. RESULTS
Across 17 different trials, at least 3 evolved populations
in each of the four modes used autotomy in the population’s
fittest individual (champion) at the end of the trial.The mostprevalent use of autotomy occurred in mode 1 with a squarestarting body plan. Joint evolution of body plan alongside
the control policy and autotomy map (mode 0) produced
the fewest examples of autotomy with just 3 champions
using autotomy, each pared down to a single actuating square
after autotomy.Examples of autotomized champions for eachmode are shown in Figure 3.
Champion agents used a variety of strategies to solve thetask. Examples of solutions with and without autotomy are
shown in Figure 4. Some agents used autotomy to modify
their body plans to solve the locomotion task in the second
direction, but others changed their orientation to accomplish
the same (as in Figure 4) and others changed direction solely
through their control policy.
Not all populations produced champion individuals thatsolved the task after 85 generations, and solve rates ranged
from slightly above half (52.9% in mode 2) to a clear
majority (88.2% solve rate in mode 1). Individual fitness
curves, and autotomy usage, for all 17 trials in each modeare visualized in Figure 5.
The average fitness for each mode was above the solution
threshold of 32.0, a threshold corresponding to the robot
reaching both goal locations, but the average fitness of champions that used autotomy was slightly below the solution
threshold for mode 2. There is substantial variation in fitness

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Fig. 4. Examples of body plans used to solve the full forward and reverse
displacement task, both with (left column) and without using autotomy (rightcolumn). The population fitness curves for each example are shown in thebottom row.

Fig. 3.
Out of the 17 evolutionary trials conducted in each of theexperimental modes, 3, 9, 5, and 5 of those trials yielded championsthat employed autotomy, respectively. Teal borders report champions, post
behavior switching, that used autotomy to change direction; red borders
indicate champions that employed autotomy as well but did not solve thetask. The pre-autotomy body plans for modes 1 through 3 are shown below
the black line, and an example evolved body plan for mode 0 is shown
below the black line in the first column.

within each mode, so while we can say that each mode can besolved by an agent utilizing autotomy, we are not confident
to claim a statistical difference for any of the conditions ormodes. That being said, the data in Tables I and II and theresults in Figure 3 do suggest the hypothesis that autotomy
is most useful for the square starting body plan of mode 1,
autotomy may be of no consequence for modes 3 and 0 andmight even be detrimental in mode 2.
Mode 1 had both the highest solve rate and the highest
rate of champions using autotomy. This mode also produced
the highest empirical probability of solving the task giventhat the champion used autotomy (8 out of 9 autotomouschampions solved the task).
The average body size for evolved body plans in mode 0
was 4.42 ± 3.11 (standard deviation) before autotomy and4.12 ± 3.31 after autotomy; every autotomized body plan in

Mode
Mode 0Mode 1Mode 2Mode 3Fitness ± std. dev.
34.8 ± 8.34
37.3 ± 7.65
34.8 ± 8.34
34.2 ± 7.53

with autotomy
35.2 ± 9.38
36.7 ± 9.34
26.9 ± 9.43
33.9 ± 8.25

no autotomy
34.7 ± 8.1
38.0 ± 5.02
36.1 ± 5.92
34.3 ± 7.2

TABLE IP ERFORMANCE ACROSS N =17 EVOLUTIONARY TRIAL PER MODE .

mode 0 was a single vertically-actuating square. The evolved
body plans from mode 0, 14 of which did not use autotomy
and 3 that did, are visualized in Figure 6. Mode 1 starts with
25 squares and the average final body plan size was 15.06 ±9.53 (6.22 ± 2.39 for morphologies that used autotomy).
Starting from a body plan with 19 squares, mode 2 has
an average final body plan size was 14.21 ± 6.64 (4.40 ±1.02 for morphologies that used autotomy). Mode 3, startingwith the smallest body plan consisting of 13 squares, had an
average final body size of 10.41 ± 4.09 (4.20 ± 1.47 formorphologies that used autotomy).
IV. DISCUSSION
The fittest agents demonstrated a variety of strategies insolving our locomotion task in two directions, including
autotomy, adopting a new orientation, or simply througha flexible control policy. Notably, our control policy is a
simple multilayer perceptron with 1 hidden layer and no
ability to modify its parameters; different behaviors are mediated through the binary task indication in the observations
provided by the environment, and differences in the relative

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Mode
Mode 0Mode 1Mode 2Mode 3

Solve rate (s)
0.588
0.882
0.529
0.647

Autotomy rate (a)
0.176
0.529
0.294
0.294

P (a|s)
0.2
0.533
0.222
0.273

P (s|a)
0.667
0.889
0.4
0.4

TABLE IITASK SOLVE AND AUTOTOMY USAGE RATES (N =17 TRIALS / MODE ).

Fig. 6. Body plans evolved in mode 0. a shows the 14 body plans that
did not use autotomy. b shows the initial body plans for the additional threechampions that used autotomy and c shows the corresponding body plans
after autotomy.

overhangs that prevent the jumping strategy employed bysingle-square body plans, might reduce the evolutionarypressure that selects for minimal body plans.

Fig. 5. Evolution progress curves for modes 0 through 3. Lighter green
lines indicate generations where the best agent used autotomy and the darker
purple lines indicate populations that produced champions without using
autotomy. The darker purple background region is below a fitness of 32,
the threshold for success.

orientation and velocities of the body components. Althoughmodes 1 through 3 started with body plans made up of 13,
19, or 25 squares, the body plans after autotomy have on
average 4.64 squares ± a standard deviation of 2.44, or 5.21
± 2.12 if we exclude the autotomized morphologies frommode 0, which were all made up of 1 square. Autotomized
morphologies are diverse, but in mode 0 (evolved bodyplans), post-autotomy morphologies are uniformly comprisedof a single actuating square.
The convergence on smaller body plans is noteworthy
because there is no explicit penalty for energy considerations
or larger, more complicated designs. Instead, the fitnessof smaller body plans derives from the simulator physics
and task specification. Speculatively, more complex terrainthat requires robots to cross gaps or climb obstacles, or

Sim2real— Simulation provides a valuable tool for rapidly
designing and testing control policies and robot morphologies, but for robots to meet their full potential theymust eventually be embodied in the physical world. The
reality gap remains a perpetual challenge, as we draw
from robotics, machine learning, and simulation to develop
robots ready for deployment in real-world environments[Mouret and Chatzilygeroudis, 2017].
The reality gap can be particularly wide in soft robotics.
The same positive characteristics that make soft robots desirable (compliance, robustness, flexibility) also make accurate
simulation, and consequently transfer to the real world, difficult [Pinskier and Howard, 2022], [Howard et al., 2019].
The many degrees of freedom, complexity, and often large
manufacturing tolerances inherent to robot prototypes all
contribute to the difficulty of matching simulation in aphysical implementation (and vice-versa).
Considering the transfer of the autotomic robots simulated in this work to hardware, we foresee several
challenges. While previous elastomeric, pneumatic “voxelbots” inspired by simulated voxelbots have been realized[Hiller and Lipson, 2011], in some cases, their behavior has
contradicted the behavior of the same design in simulation: in[Kriegman et al., 2020] and [Kriegman et al., 2021], somehardware voxelbots traveled in the opposite direction to

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their simulated counterparts. We attribute such results tounmodeled frictional interactions or forces from the realrobot’s pneumatic tether. Tethers can have a non-negligible
effect on behavior, particularly when a robot is small or weakrelative to the tether’s mass, as is the case for soft robots
constructed of pneumatic silicone voxels.
If the physics surrounding a hardware robot’s behavior are
understood or discovered by machine learning, they can beembedded in the form of constraints within the simulationand optimization algorithms. Although, we note that simulation software for soft robots is typically fast or accurate, but
not both, and the tradeoff must be considered. Nevertheless,connecting data from the real world back to simulation via
reality-assisted artificial evolution [Howison et al., 2020] is
an increasingly important aspect of building soft robots ingeneral, and autotomic soft robots specifically.
V. CONCLUSIONSIn our experiments, a subset of evolved populations fromeach mode were capable of solving a locomotion task using
autotomy, by adapting their control policy, or both. While we
did not discover a clear advantage for simulated soft robots
using autotomy, autotomy did not create a clear hindrance
either, and in mode 1 more than half of evolved populations
produced a champion agent that uses autotomy.
Psychologists describe a systematic tendency for people
to overlook subtractive changes, even when they may be themost advantageous solution available [Adams et al., 2021].
This bias appears to apply to robotics researchers as well,
as demonstrated by the prevalence of adaptive shape change
and relative paucity of subtractive adaptation in the literature.
In situ resource extraction or an inventory of spare materials may enable robotic systems to adapt to new conditions
far from home, but subtractive shape change can facilitate
adaptation without requiring additional inventory. Although
there may be real-world task environments in which autotomy would clearly be useful, such as increasingly narrow
apertures, the fact that autotomy was employed for the
locomotion over flat ground task above suggests there may
be other, more realistic but less obvious task environments
where autotomy will eventually prove useful.
By deliberately cuing engineering processes to consider
subtractive problem solving, taking advantage of the myriad
examples where less is more useful in biology, we canpotentially evolve and engineer more robust, life-like systems
and avoid overlooking unintuitive optimal solutions.
ACKNOWLEDGMENT
This work was supported by the National Science Foundation under the Emerging Frontiers in Research and Innovation (EFRI) program (EFMA-1830870).
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