PowerPoint Presentationshai/studentlist_files/D… · PPT file · Web view · 2012-10-187 (45), April, pp.613-621. Shape Change. ... The transition from step to step is triggered

A model of Caterpillar Locomotion Based on Assur Tensegrity Structures

In the supervision of:

Prof. Shai OfferSchool of Mechanical Engineering, Faculty of engineering, Tel-Aviv University.

Dr. Ben-Hanan UriDepartment of Mechanical Engineering, Ort Braude College, Karmiel.

With collabaration of:

Prof. Ayali AmirDepartment of Zoology, Faculty of Life Sciences, Tel Aviv University.

Orki Omer

Overview

» Biological background

» Previous work

» Assur Tensegrity structure

» The caterpillar model

» Results and discussion

Biological background

Abdomen

Prolegs

Thorax

True legs

Head

Caterpillars do not have rigid segments. Instead they have soft body.

The internal pressure of the hemolymph within the body provides a hydrostatic skeleton.

The biological caterpillar has a complex musculature.

Each abdominal body segment includes around 70 discrete muscles !!

The major abdominal muscles in each segment are:1. The dorsal longitudinal muscle - DL12. The ventral longitudinal muscle - VL1

VL1

DL1

Antecostae

Eaton, J. L., 1988. Lepidopteran Anatomy. 1st edition, John Wiley, New York.



Caterpillars have a relatively simple nervous system. Yet, caterpillars are still able to perform a variety of complex movements.

Mechanical properties of the muscles are also responsible for some of the control tasks. (Woods et al., 2008)

Brain

Ganglions

Woods, W.A., Fusillo, S.J., and Trimmer, B.A., 2008. "Dynamic properties of a locomotory muscle of the tobacco hornworm Manduca sexta during strain cycling and simulated natural crawling". Journal of Experimental Biology, 211(6), March, pp. 873-82.


During motion, at least three segments are in varying states of contraction.

The primary mode of caterpillar locomotion is crawling.

Crawling is based on a wave of muscular contractions that starts at the posterior end and progresses forward to the anterior.

Previous work

A caterpillar robot that is assembled using two types of modules:

1. Joint actuation modules 2. Adhesion modules.

Wang et al. (2008)

A computer simulation of a multi-body, caterpillar like, robot. The robot was assembled using a series of actuated Stewart-platform.

Stulce (2002)Rigid bodies No softness

Wang, W., Wang, Y., Wang K., Zhang, H., and Zhang, J., 2008. “Analysis of the Kinematics of Module Climbing Caterpillar Robots”. Proceeding of 2008 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 84-89.Stulce J. R., 2002. “Conceptual Design and Simulation of a Multibody Passive-Legged Crawling Vehicle”. PhD Thesis, Virginia Polytechnic Institute and State University, Department of Mechanical Engineering

Previous work

Conventional control Methods are ineffective

Near-infinite degrees of freedom

Trimmer et al. (2006)

A caterpillar model using soft and deformable materials (silicone) and actuated using shape memory alloys wires (SMA).

The authors did not report results.

Trimmer B., Rogers C., Hake D., and Rogers D., 2006. “Caterpillar Locomotion: A New Model for Soft-Bodied Climbing and Burrowing Robots,” 7th International Symposium on Technology and the Mine Problem.

Tensegrity

Tension + Integrity

“ Islands of compression inside an ocean of tension ” (Fuller, 1975).

Definition

Air – Compressed element Envelope – Tensioned element

Fuller, R. B., 1975. Synergetics—Explorations in the Geometry of Thinking. Macmillan Publishing Co.

Tension + Integrity

Definition

Tensegrity

“ A tensegrity system is a system in a stable self-equilibrated state comprising a discontinuous set of compressed components inside a continuum of tensioned components ” (Motro, 2003).

Struts – Compressed elementsCables – Tensioned elements

Motro, R., 2003. Tensegrity: Structural Systems for the Future. Kogan Page Science.

Tensegrity structures are usually statically indeterminate structures

Tensegrity

(a) Human spine (b) Cytoskeleton

In Nature

Ingber, D.E., 1998. "The Architecture of life", Scientific American, 278(1), January ,pp. 48-57.

Previous work

Rieffel et al. (2010)

A 15-strut, highly indeterminate tensegrity model, inspired by the caterpillar structure.

Using of Artificial Neurons Networks (ANNs) for control. Locomotion does not resemble caterpillar crawling.

Conventional control methods are ineffective

Indeterminate structure

Rieffel J.A., Valero-Cuevas, F. J., and Lipson, H., 2010. "Morphological communication: exploiting coupled dynamics in a complex mechanical structure to achieve locomotion". Journal of the Royal Society interface, 7(45), April, pp.613-621.

Shape Change Self-stress forces must be maintained during motion

Sultan C. and Skelton R. E., 2003 "Deployment of tensegrity structures“, International Journal of Solids and Structures, 40(18), September, pp. 4637–4657.van de Wijdeven J. and de Jager B., 2005 "Shape change of tensegrity structures: design and control“, in American Control Conference.

Equilibrium manifoldFinal configuration

Initial configurationEquilibrium path

(b)(a)

Sultan and skeleton (2003)

The method is based on the identification of an equilibrium manifold.

Van de Wijdeven and de Jager (2005)

The nodal positions of the tensegrity structure are found at every sub-shape by solving a constrained optimization problem.

Motion is divided into many steps

Assur Trusses

Definition

Assur truss Not an Assur truss

An Assur truss is a determinate truss, in which applying an external force at any joint, results in forces in all the rods of the truss.

√ X

Assur Trusses In general - determinate trusses cannot have self-stress

Assur trusses have a configuration in which there is:

1. An infinitesimal mechanism 2. A single self-stress in all elements.

This configuration is termed singular configuration (Servatius et al., 2010)

BC

A

O1 O2O3

BC

A

O2

O3O1

Singular configuration Generic configuration

Servatius, B., Shai, O., and Whiteley, W.,2010. “Geometric properties of Assur graphs”. European Journal of Combinatorics, 31(4), May, pp. 1105-1120.

Assur Tensegrity

Tensioned elements Compressed elements

CablesStruts

Assur Tensegrity structure is a statically determinate structure

Assur truss in a singular configuration can turn into tensegrity structure.

Shape change of Assur Tensegrity

it is possible to make any Assur truss configuration into a singular one simply by changing the length of any one of its ground elements

Shai O., 2010. "Topological Synthesis of All 2D Mechanisms through Assur Graphs" in Proceedings of the ASME Design Engineering Technical Conferences.

Shape change of Assur Tensegrity

The algorithm:(Bronfeld, 2010)

Bronfeld A., 2010 "Shape change algorithm for a tensegrity device," M.S. thesis, Tel-Aviv University, Tel-Aviv, Israel.

Activate the device controllers.

One ground element is defined a the force-controlled element. All other elements are position-controlled elements.

For the force-controlled element select a desired force in. For the position controlled elements generate a desired trajectory.

Caterpillar model

CablesStrut

Bars

Each caterpillar segment is represented by a 2D tensegrity triad consisting of two bars connected by two cables and a strut.

Leg

Caterpillar model

Parameters of each segment:

Mass : 0.182 (g)Height : 5 (mm)Length : 4.55 (mm) (in rest)

The complete model consists of eight segments connected in series.

Caterpillar model

Caterpillar Model Biological caterpillarUpper cable DL1

Strut Hydrostatic skeletonLower cable VL1

Bar Antecostae

VL1

DL1

Area conservation

The internal air cavity that can be emptied constitutes 3-10% of body volume (Lin et al., 2011)

Lin H. T., Slate D. J., Paetsch C. R., Dorfmann A. L. and Trimmer B. A., 2011 "Scaling of caterpillar body properties and its biomechanical implications for the use of hydrostatic skeleton“, The Journal of Experimental Biology, 214(7), April , pp. 1194-1204.

g

g

𝜑𝐵 𝜑𝑆

Bending Shearing

Area conservation

Lin H. T., Slate D. J., Paetsch C. R., Dorfmann A. L. and Trimmer B. A., 2011 "Scaling of caterpillar body properties and its biomechanical implications for the use of hydrostatic skeleton“, The Journal of Experimental Biology, 214(7), April , pp. 1194-1204.

𝑀 𝑖=−𝑐 ∙𝜑𝑆

Ф2Ф1

M M

Internal toque:

The internal torque enables a small (but not negligible) shear angle

The internal air cavity that can be emptied constitutes 3-10% of body volume (Lin et al., 2011)

Control Scheme

Level 1Central Control

Level 2 localized control

Leg Controllers

Cable Controllers

Strut controllersGr

ound

co

ntac

t se

nsor

High level control

Low level control

Brain

Hydrostatic pressure

Ganglia

Muscle behavior

Leg behavior

Low Level Control

Impedance Control:

The biological caterpillar muscles have large, nonlinear, deformation range and display viscoelastic behavior (Woods et al., 2008)

Cables Controller Muscles behavior

𝐹 0 ,𝑘𝑙 ,𝑣 𝑇 𝑐𝑎𝑏𝑙𝑒

𝑇 𝑐𝑎𝑏𝑙𝑒=−𝐹 0

2+𝑘 ( 𝑙−𝑙0 ) −𝑏𝑣

Initial tensionStatic term

Damping term

Output tension



Low Level Control

Cable controller𝑙 ,𝑣 𝑇 cable

High Level Command (0 - 1)

00.10.20.30.40.50.60.70.80.91.0 So

ft an

d re

laxe

d ca

ble

Stiff and shrunken cable

Nerve Stimulation

High Level Command


Cable controller𝑙 ,𝑣 𝑇 cable

Low pass filter

Low Level Control

High Level Command (0 - 1)

The caterpillar muscles develop force slowly (Woods et al., 2008)

Causes slower cable reaction


Low Level Control

The internal pressure in caterpillars is not isobarometric and the fluid pressure changes do not correlate well with movement (Lin et al., 2011)

𝐹 𝑠𝑡𝑟𝑢𝑡=𝐹 0−𝑏𝑣

Initial forceDamping term

Output force

.

Strut Controller Internal pressure

Lin H.T., Slate D. J., Paetsch C. R., Dorfmann A. L. and Trimmer B. A., 2011. “Scaling of caterpillar body properties and its biomechanical implications for the use of hydrostatic skeleton”. The Journal of Experimental Biology, 214(7), April, pp. 1194-1204.

𝑇 𝑐𝑎𝑏𝑙𝑒=𝐹 0

2+𝑘 (𝑙− 𝑙0 ) −𝑏𝑣

Shape change Without external forces

the cables assume exactly the virtual lengths :

𝑙1=𝑙0 ,1 ,𝑙2=𝑙0 ,2

𝜑𝑏=sin−1( 𝑙0 , 1− 𝑙0 , 2

2h ) ,𝑙𝑠=𝑙0 , 1+ 𝑙0 , 2

2

describing the shape of the triad by and :

Shape change Softness

𝐹 𝑒

𝑙𝑠𝜑𝐵𝑙𝑠𝐹 𝑒

𝜑𝐵𝑙𝑠

𝑀 𝑒

Axial force Bending torque Bending force

As long as the external load is within its limits, the initial force within the segment doesn’t influence segment stiffness

Low Level ControlLeg Controller Leg behavior

Caterpillar legs are used as support rather than levers. When a leg touches the ground it cannot be lifted until it is actively

unhooked and retracted.(Lin and Trimmer, 2010)

Leg controller

Leg position

High Level Command (0 , 1)

Trigger when touching the ground

Ground contact sensorLeg locking

Lin H. T. and Trimmer B. A., 2010. "The substrate as a skeleton: ground reaction forces from a soft-bodied legged animal“, The Journal of Experimental Biology, 213(7), April, pp. 1133-1142.

High Level ControlLevel 1 control Brain (CPG)

H8 H7 H6 H5 H4 H3 H2 H1

Crawling direction

Posterior side

Anterior side

Step 3

Step 4

Step 2

Step 1

Step 5

Step 6

Step 9

Step 7

Step 8

» coordinates motion» activate relevant segments in each step

Swing phaseStance phase

High Level Control

H8 H7 H6 H5 H4 H3 H2 H1 Posterior side

Anterior side

» A new stride starts before the previous stride ends.

» The transition from step to step is triggered by the contact of the legs with the ground.

» In each step, several segments are in various stages of contraction

» Each stride issues the same set of step commands.

L8 L7 L6 L5 L4 L3 L2 L1 L0

Level 1 control Brain (CPG)

High Level ControlLevel 2 control Ganglia

responsible for fitting motion to the terrain shape:

Mode I: Adjusting a segment in stance phase to the terrain shape

Mode II: Adjusting a segment in swing phase to the terrain shape

Mode I:

ࢻ ࢻࢼ�� ࢼ��ࢻ

ࢼ��

High Level ControlLevel 2 control Ganglia

Mode II:

0.7

0.7 0

0.4

+ =

0.9

0.5

Level 1 commands

Stance commands

Output commands

responsible for fitting motion to the terrain shape:

Mode I: Adjusting a segment in stance phase to the terrain shape

Mode II: Adjusting a segment in swing phase to the terrain shape

Results

Stage 1.Stage 2.

Stage 3.𝑳𝟎

𝑯𝟏𝑯 𝟒

𝑳𝟖

Crawling stages

Results Segment length

5 6 7 8 9 10 11 12 13 14 15

3

4

5H8

5 6 7 8 9 10 11 12 13 14 15

3

4

5H7

5 6 7 8 9 10 11 12 13 14 15

3

4

5H6

5 6 7 8 9 10 11 12 13 14 15

3

4

5H5

5 6 7 8 9 10 11 12 13 14 15

3

4

5H4

5 6 7 8 9 10 11 12 13 14 15

3

4

5H3

5 6 7 8 9 10 11 12 13 14 15

3

4

5H2

5 6 7 8 9 10 11 12 13 14 15

3

4

5H1

Seg

men

t len

gth

(mm

)

Time (s)

Time (s)

Segm

ent l

engt

h (m

m) H1

H2

H3

H4

H5

H6

H7

H8

SegmentStance Length (mm)

Min length (mm)

Length change

)%(Stance time (s)

Swing time (s)

Step time (s)

Duty factor)%(

H1 4.55 3.07 32 1.40 0.76 2.16 35H2 4.64 3.08 34 1.26 0.90 2.16 41H3 4.38 3.06 30 1.17 0.99 2.16 46H4 4.42 3.06 31 1.15 1.01 2.16 47H5 4.65 3.05 34 1.20 0.96 2.16 44H6 4.24 3.05 28 1.10 1.06 2.16 49H7 4.36 3.06 30 1.14 1.02 2.16 47H8 4.35 3.07 29 0.97 1.19 2.16 55

Average 4.45 3.06 31 1.17 0.99 2.16 46

Results Crawling parameters

Stride Length (mm)

Duration of one crawl (s)

Velocity (mm/s)

Biological caterpillar 8.52 2.78 3.03

Model caterpillar 4.64 2.71 1.93

-50 -48 -46 -44 -42 -400

1

2

3

4

5

6

C.M. positoin - X axis (cm)

C.M

. pos

ition

- Y

axi

s (c

m)

C.M positionStart of phase 1Start of phase 2Start of phase 3End of stride

Start of phase 3of the i th stride

Start of phase 1of the i+1 th stride

Start of phase 2of the i+1 th stride

(In blue circle)

End of stride i(In red square)

Stride

Stride

Crawling direction

Results Dynamics

Tetanic stimulus of a caterpillar muscle

Caterpillar Model Biological caterpillar

Activation of a model cable

0.27 s 50% of peak force 0.26 s0.41 s 80% of peak force 0.56 s


Results Dynamics

The maximum change in cable forces is only 13.8% relative to resting force

5 6 7 8 9 10 11 12 13 14 150

10

20

30

40

50

60

70

Time (s)

Cab

les'

For

ce (m

N)

Cable 1 Cable 2 Resting Force Min/Max Forces

Maximum change of cableforces relative to the restingforce is 13.8%

The change of cable forces in H3 while crawling

Results Area conservation

5 10 15 200

50

100

150

200

Time (s)

Cat

erpi

llar a

rea

(mm

2 )

Min area = 157.3 mm2

The change in caterpillar area is 6.14%

Max Area = 167.6 mm2

g is only 6.14%

Minimum:

Maximum:

Time

Cate

rpill

ar a

rea

(mm

2 )

The change in caterpillar area while crawling 6.14%

Internal pressure

The model was tested with various levels of internal pressure. As long as is above a certain threshold, crawling is independent of the magnitude of internal pressure

Results Different terrains

Discussion Assur tensegrity + Impedance control

» Stabilityself-stress of the tensegrity structure is always maintained.

» SoftnessTensegrity structures have natural high compliance (softness).Using impedance control, this degree of “softness” can be changed and controlled.

» SimplicityStatically determinate structure & Independent controllers createssimple and intuitive shape change.

Discussion Assur tensegrity + Impedance control

Soft robot Rigid robot

Assur tensegrity

Discussion

The model exhibits several characteristics which are analogous to those of the biological caterpillar:

» Internal PressureDuring growth, body mass is increased 10,000-fold while internal pressure remains constant. In the same way, our model is able to maintain near constant internal forces regardless of size.

» Simple nerve systemMechanical properties of the muscles are also responsible for some of the control tasks. Our model shows that using impedance control for each cable also simplifies the high level control.

» Crawl StagesThe model has demonstrated that effective crawling requires three different stages. Trimmer et al. found kinematic differences between three anatomic parts of the caterpillar.

Discussion

The model exhibits several characteristics which are analogous to those of the biological caterpillar:

» Stride LengthThere is a discrepancy between the stride length of the model and that of the biological caterpillar.

» Stride DurationThe duration of one stride are comparable in both the model and the biological caterpillar.

» Slow Muscle reactionThe caterpillar muscle develop force slowly. Our model show that adding the LP filter, which makes the cable to react slower, ease the high level control and makes the motion smoother

Discussion

The model suggests some characteristics of the biological caterpillar:

» Locomotion energyThe model shows that cables’ force doesn’t significantly change while the caterpillar is in motion. It suggests that Caterpillars don’t invest considerably more energy while crawling than while resting.

» Ground reactionsThe model schedule the motion using signals from the legs when they touch the ground. It suggests that the biological caterpillar also uses ground reaction to coordinate its movements.

Future Research

» Improving the existing model

» Expanding the model to a three dimensional model.

» Building a mechanical model.

Future research can be made in three directions:

Thank You!

potential energy of the system: Δ𝑈=−∫𝑙0

𝑙 𝑓

𝐹 (𝑙 )𝑑𝑙

Choosing triad configuration

If the system is in stable equilibrium, the potential energy function is at its minimum point.

Therefore,to get a stable system, any shift from equilibrium must result in cable lengthening and\or strut shortening.

(a) (b)

Two options:

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ݒ

ݒ

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�critical � �ෝ��

real � �ෝ��

� Ȁ�ݐƸ

� �ෝ��

�ଵǡ��ଶǡ��ଷ

� Ȁ� �ෝ��ݐƸ

4 bar mechanism(In rigid lines)

𝑪 𝑩 𝑨

Tested element(In dashed line) 𝜔

𝑶𝟏𝑶𝟑 𝑶𝟐


� Ȁ�ݐƸ

lengthen

shorten

�ଵǡ��ଶǡ��ଷreal � �ෝ�� critical � �ෝ��

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�ݐƸ

𝑪 𝑩 𝑨

𝜔𝑶𝟏𝑶𝟑 𝑶𝟐


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PowerPoint Presentationshai/studentlist_files/D… · PPT file · Web view · 2012-10-187 (45), April, pp.613-621. Shape Change. ... The transition from step to step is triggered