The document describes a simulation of snake-like swimming using a granular model. A molecular dynamics model was constructed to simulate the motion, applying forces from muscles, buoyancy, gravity, and viscosity. The simulation produced directional motion but was not very effective. Further improvement to better model the changing muscle lengths observed in real snakes is needed.

1. The 4th International Biology
Conference (IBOC)
13 October 2018, Surabaya, Indonesia 1
Simulation of Snake-Like
Swimming System using
Granular Model
S Viridi*, L L Fitri, N Nuraini, Suprijadi
Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia
*dudung@fi.itb.ac.id
20181013_1

2. Outline
• Introduction
• Model
• Result s and discussion
• Summary
• Acknowledgments
The 4th International Biology
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13 October 2018, Surabay, Indonesia 2
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3. The 4th International Biology
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13 October 2018, Surabay, Indonesia 3
Introduction

4. Swimming snake
The 4th International Biology
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13 October 2018, Surabay, Indonesia 4
BlueWorldTV, “Sea Snake Island | JONATHAN BIRD'S BLUE WORLD”, YouTube 0rqcigdJi3o, 8 May
2014 [20181012].
t 1059 1059 1100 1101

5. Snake (Natrix) swimming
The 4th International Biology
Conference (IBOC)
13 October 2018, Surabay, Indonesia 5
Taylor G 1952 Proc. R. Soc. Lond. A 214 158.
5 cm squres, 16 fps

6. Various swimming patterns
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13 October 2018, Surabay, Indonesia 6
Graham JB, Lowell WR, Rubinoff I, Motta J 1987 J. Exp. Biol. 127 27.

7. It is a 3-d motion
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13 October 2018, Surabay, Indonesia 7
Jayne BC 1985 Copeia 1985 195.
---- water surface

8. A snake-like swimming robot
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13 October 2018, Surabay, Indonesia 8
Kamamichi N, Yamakita M, Asaka K, Luo Z-W 2006 IEEE International Conference on Robotics and
Automation, Orlando, USA, pp. 1812-1817.

9. .. with more
parts
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13 October 2018, Surabay, Indonesia 9
Crespi A, Ijspeert AJ 2008 IEEE Trans. Robot. 24 75.

10. The 4th International Biology
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13 October 2018, Surabay, Indonesia 10
Model

11. Model (in xy plane)
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..

12. Model (in xz plane)
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13 October 2018, Surabay, Indonesia 12

13. External forces: Vertical direction
• Bouyant force
• Gravitation force
The 4th International Biology
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13 October 2018, Surabay, Indonesia 13
gDF if
b
i
 3
6
1
πρ−=
gDF ii
g
i
 3
6
1
πρ=

14. External forces: Moving direction
• Viscous force
The 4th International Biology
Conference (IBOC)
13 October 2018, Surabay, Indonesia 14
( )fiif
f
i vvDF

−−3= πη

15. Internal forces: Skeletal muscle
• Spring force
with
The 4th International Biology
Conference (IBOC)
13 October 2018, Surabay, Indonesia 15
( ) ijijijij
s
ij rlrkF ˆ−−=

0=←= s
ijijij Frl


16. Simplification
• Motion only in xy plane
 2-d system)
• It can be set when
The 4th International Biology
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13 October 2018, Surabay, Indonesia 16
0=+ b
i
g
i FF


17. Molecular dynamics
• Newton II Law of motion
• Numerical integration
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13 October 2018, Surabay, Indonesia 17
ii
s
i
s
i
f
i amFFF

=++ +− 11
( ) ( ) tatvttv iii ∆+=∆+

( ) ( ) tvtrttr iii ∆+=∆+


18. The 4th International Biology
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13 October 2018, Surabay, Indonesia 18
Results and discussion

19. Problem
• How each muscle through spring force
alternates?
• It should be provided from observation
• Asumption
The 4th International Biology
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13 October 2018, Surabay, Indonesia 19








=∆ t
T
Al
b
b
π2
sin

20. Parameters
• # Environment
• GRAVFIELD 0 0 -10
• DENSITYF 1000
• VISCOSITYF 0.01
• # Simulation
• TSTEP 1E-3
• TDATA 1E-1
• # Balls
• DENSITYB 500
• DIAMETERB 0.025
• SPRINGB 100
• AMPLITB 1E-5
• PERIODB 1
• TBEG 0
• TEND 20
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21. Results: 0, 1, 4, 7, 9, 12, 14, 18.5 s
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..

22. Horizontal position vs time
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0.35
0.355
0.36
0.365
0.37
0.375
0 5 10 15 20 25
x
t

23. Vertical position vs time
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Conference (IBOC)
13 October 2018, Surabay, Indonesia 23
0.485
0.49
0.495
0.5
0.505
0.51
0 5 10 15 20 25
y
t

24. Change of position
The 4th International Biology
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13 October 2018, Surabay, Indonesia 24
0.485
0.49
0.495
0.5
0.505
0.51
0.35 0.355 0.36 0.365 0.37 0.375
y
x

25. The 4th International Biology
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13 October 2018, Surabay, Indonesia 25
Summary

26. Summary
• Simulation system for snake-like swimming
motion has been constructed
• Directional motion can be produced but not
so effective
• Further improvement, especially in change of
muscle length from observation is required.
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13 October 2018, Surabay, Indonesia 26
..

27. The 4th International Biology
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13 October 2018, Surabay, Indonesia 27
Acknowledgments

28. Acknowledgments
• P3MI ITB in presenting this work
• ITS in arranging this event
• Kemenristekdikti in calculating this work
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13 October 2018, Surabay, Indonesia 28
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29. The 4th International Biology
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13 October 2018, Surabay, Indonesia 29
Thank you

30. The 4th International Biology
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https://osf.io/43fzh/