Authors: Kazuya Horibe, Walker Kathryn, Risi Sebastian Conference:Genetic Programming: 24th European Conference, EuroGP 2021, Held as Part of EvoStar 2021, Virtual Event, April 7–9, 2021, Proceedings Paper: https://arxiv.org/pdf/2102.02579.pdf

1. 4.7-9 EuroGP2021@Seville, Spain
Regenerating Soft Robots
through Neural Cellular Automata
Kazuya Horibe (@khoribe3)1,2,3 , Kathryn Walker1 , Sebastian Risi1
1 IT University of Copenhagen
2 Osaka University
3 Cross Labs, Cross Compass Ltd.
1

2. 2
Background
Morphological regeneration is an important feature that highlights
the environmental adaptive capacity of biological system.
[Mitoh+2021, Current Biology]
Extreme autotomy and whole-body regeneration in photosynthetic sea slugs.

3. 3
Lack of this regenerative capacity significantly limits the resilience of
machines and the environments they can operate in.
Can we give regenerative capacity to soft robots?
Background
[Shah+2020, Advanced Materials]
Regeneration
[Mitoh+2021, Current Biology]
Regeneration can make a new dimension of freedom for shape.
Machines Biological System
[Kriegman+2020, PNAS]
Soft robots using biological tissues
Hybrid System
XenoBod

4. 4
Method: Soft robots simulator
We propose a model for soft robots that regenerate through
a neural cellular automata.
evosoro: soft robot simulator
• Python soft robot simulation library based on the Voxelyze physics engine.
• High-level interface for the dynamic simulation and automated design of soft multimaterial robots.
[Hiller+2014, Soft Robotics]
[Cheney+2013, GECCO]
Type of voxels

5. 5
[Mordvintsev+2020, Distill]
Applying neural cellular automata (NCA) to growth and
regeneration rule of soft robots.
Method: Neural Cellular Automata
NCA can learn growth and regenerative rule. Applying NCA to 2D soft robots
[Nichele+2017, IEEE Transactions on
Cognitive and Developmental Systems]
Feed forward (Linear unit)
Recurrent (LSTM unit)
Network structure
Hidden layer: 64 hidden state
[Hochreiter1997, Neural computation]
Input layer: Number of neighborhood
Output layer: Number of voxel states

6. 6
Method: Training for locomotion
Training for locomotion of soft robots through genetic algorithm
Get phenotype
(Morphology of soft robots)
Locomotion Evaluation
In a constant time
Fitness value
(Travel distance of Center of Mass)
[Such+2017, arXiv preprint]
Evolve weight of genotype (NCA)
Grow soft robots through NCA from single voxel (10 steps)

7. 7
Research strategy
Growth rule for 2D soft robots
Growth rule for 3D soft robots
Regenerative rule for 3D soft robots
We investigate that neural cellular automata can learn growth and
regenerative rule for soft robots.

8. 8
Result 1
2D soft robots get various morphology through evolution.
Training curve
10 independent runs each condition
We confirmed NCA works well for growing rule of soft robots.
Feed forward
Feed forward Recurrent
Recurrent
300 population and 500 generation
Common grown soft robots
S-type
Biped L-type
Zigzag

9. 9
Training curve
24 independent runs each condition
We tried a more complex task: 3D soft robots locomotion
Result 1
Feed forward
Feed forward
Feed forward
Feed forward
Feed forward
Recurrent
Recurrent Recurrent
Recurrent
Feed forward
2D Group 3D Group
100 population and 300 generation
Common grown soft robots
Roller
Jumper
Pull-Push
Slider
Jitter
Crawler
Slider
Pull-Push
L-Walker
Jumper

10. 10
Partial Summary
Partial Summary for growth capacity of soft robots
We gave growth capacity to 2D and 3D soft robots through neural
cellular automata.
An advantage of the presence of cellular memory (LSTM unit) was
depend on tasks.
A morphology (e.g. Tripod) that did not appear in previous studies using
CPPN [Cheney+2013, GECCO] was acquired.

11. 11
We investigate the ability of the soft robots to regenerate their body
parts to recover from morphological damage.
NCAs that are trained for locomotion failed regeneration.
Result 2
Regrowing 10 steps from damaged morphology

12. 12
Training for regeneration of soft robots through genetic algorithm
Get phenotype
(Morphology of soft robots)
Similarity Evaluation
between the original morphology
Fitness value
(Similarity)
[Such+2017, arXiv preprint]
Evolve weight of genotype (NCA)
Grow soft robots through NCA from damaged morphology (10 steps)
Method: Regeneration task
Regrown Original
Compare position (x, y, z) and type of voxel (Muscle, Tissue, Bone, Empty) for 9*9*9=729 voxels.

13. 13
Soft robots are almost regrown through NCA.
Result 2
Training curve
1 independent run
1000 population and 1000 generation
100% (729/729) is completely consistent with the original morphology.

14. 14
Soft robots are partially recover their locomotion.
Result 2
Tripod
Travel distance
40.4 1.63 (3.6%) 20.3 (45%)

15. 15
Summary
Summary
We gave growth capacity to soft robots through neural cellular automata.
An advantage of the presence of cellular memory (LSTM unit) is depend on tasks in
our experiments.
A morphology (e.g. Tripod) that did not appear in previous studies using CPPN
[Cheney+2013, GECCO] was acquired.
We gave regenerative capacity to soft robots through neural cellular automata.
This model requires two different neural cellular automata for growth and regeneration.

16. 16
Discussion
[Kriegman+2020, PNAS]
Biological organisms can memorize a global morphology through bioelectric signaling network.
[Levin+2017, Annual Review of Biomedical Engineering]
Bioelectric signaling network can modify using extrinsic electrical stimuli.
Hybrid soft robots may realize the regenerative ability of machines.
XenoBod