Mars Exploration Rover Opportunity Simulations of Traverses on Matijevic Hill, Cape York, Mars

12/20/2013

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Mars Exploration Rover Opportunity Simulations of Traverses on Matijevic Hill,

Cape York, Mars

Gabrielle Coutrot

ISTVS - November 5th , 2013

12/20/2013

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Pressure & shear stresses – soil shear displacement 1.1

1.Terramecha-nics equations

1.1 Pressure &

shear stresses – soil shear displacement

1.2 Drawbar pull for a 6-wheel rover

2. ARTEMIS simulation: deformable soil model

2.1 Terrain

assignments and soil properties

2.2 Sensitivity study for deformable soil model’s input parameters

3. Results

Conclusion

n

0''

cb

zbkckq

2

c cohesion, γ density, b plate width, z0 sinkage, n pressure-sinkage exponent, kc’ cohesion modulus, kφ’ friction modulus

From bevameter experiments: pressure-sinkage equation aka Bekker-Wong-Reece

equation

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1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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Soil shear displacement jx

x

x

k

j

max e1

jx soil shear displacement, kx longitudinal shear deformation modulus

From experiments: shear stress-soil shear displacement relationship for homogeneous

soil and Mohr-Coulomb criterion

tanmax nc φ angle of internal friction, c cohesion, and σ normal stress

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Drawbar pull for a 6-wheel rover 1.2


1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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SOIL PROPERTIES COMPACTION RESISTANCE

COMMANDED ANGULAR

VELOCITIY for each wheel

SLIP/SKID

THRUST

SHEARING PROPERTIES

SLOPE

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Terrain assignment and soil properties 2.1


1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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Terrain assignments for each three portions is done using:

• images: sinkage estimated on tracks, rover 3D slip estimated on tracks

• mobility reports from rover planners give 3D slip using Visual Odometry (VisOdom)

• geologic map (by Larry Crumpler)

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1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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Soil properties

γ c φ kc' kφ’ n kx ky

Descri-ption

Soil weight density

Soil cohe-sion

Inter-nal

friction angle

Reece cohe-sion

modulus

Reece friction

modulus

Pressure-sinkage

expo-nent

Longitu-dinal shear defor-mation

modulus

Lateral shear defor-mation

modulus

Unit N m-3 kPa Degree / / / mm mm

Properties assigned:

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1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

50m

3053

3090

3101

Kirkwood (hard soil)

Whitewater Lake – Broken Hammer – Big Nickel (very hard soil)

3212

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1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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Slip < 3%

Slip < 3%

3% < Slip < 10%

Broken Hammer Big Nickel 3212 = BHBN3212

50m

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1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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Soil properties

γ c φ kc' kφ' n kx ky

Slip < 3% 1600 4.5 38 100 800 1.1 10 10

3% < Slip < 10%

1600 1.5 38 100 800 1.1 15 15

Properties assigned for the two regions

These initial parameters are taken from Zhou et al., 2013 and are representative of a very hard surface and a less hard soil

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Sensitivity study for deformable soil model’s inputs 2.2


1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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Influence of kφ’ (bench drive)

Soil properties

γ c φ kc’ n kx ky kφ’

1600 4500 38 100 1.1 5 5

800 900

1000 1600

Influence of n (bench drive)

Soil properties

γ c φ kc’ kφ’ kx ky n

1600 4500 38 100 800 5 5

0.1

1.1

1.5

1.8

Influence of kx (bench drive)

Soil properties

γ c φ kc’ kφ’ n kx ky

1600 4500 38 100 800 1.1 5 5

10 10

15 15

Influence of c (bench drive)

Soil properties

γ n φ kc’ kφ’ kx ky c

1600 1.1 38 100 800 5 5 2500

3000

4500

Influence of φ (bench drive)

Soil properties

γ n c kc’ kφ’ kx ky φ

1600 1.1 38 100 800 5 5

30

32

35

38

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1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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kφ’, n & φ do not strongly influence rover 3D slip

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1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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kx & c strongly influence rover 3D slip

Which one is the most important?

Influence of kx (BHBN3212 drive) Soil

properties γ c φ kc' kφ’ n kx ky

1600 0 30 100 800 1.2

10 10

11 11 12 12 14 14 15 15

Influence of c (BHBN3212 drive) Soil

properties γ n φ kc' kφ’ kx ky c

1600 1.2 30 100 800 15 15

0

500 1000

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1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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kx controls slip and is thus adjusted; to better approximate slip/skid once kx is modified, c is adjusted

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Results 3.


1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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50m

Soil properties


Values 1600 1.5 30 (38)

100 800 1.1 20 (15)

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Slip observed

Average slip 7%

0 distance driven (m) 10

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Results 3.


1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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50m

Navcam of sol 3213

Slip observed at the beginning, then skid (going uphill) 2 parts with 2 different sets of parameters

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Results 3.


1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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Soil properties


1st part 1600 1 (4.5)

30 (38)

100 800 1.2 (1.1)

5 (10)

5

2nd part 1600 1 (4.5)

30 (38)

100 800 1.2 (1.1)

25 (10)

25


BHBN3212 – 1 Average slip 2%

BHBN3212 – 2 Average slip 2%



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Results 3.


1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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1st part on Whitewater Lake formation

2nd part on windblown sand: expect to be terrain with increasing slip

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Results 3.


1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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Drive Average thrust

(N)

Resistances Drawbar Pull (N)

Fd = F-∑RR

Compaction Resistance Rc

(N)

Slope angle

wtsinθs Total

Kirkwood 238 88.3 13° 156.24 245 7 BHBN3212

(1) 253 94.4 12° 139.5 234 19

BHBN3212 (2)

153 106 4° 50.22 156.2 3.22

Drawbar pull close to 0

Simulations accurate

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Results 3.


1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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50m

Skid observed Average skid -3.3%


Soil properties μs μd STV FTV

Initial 0.781 0.577 0.003 0.005

Final 0.625 0.577 0.003 0.005

Unit / / m/s m/s

50m

Other model tested: contact model, based on Coulomb’s law of friction

Ff < μFn

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Conclusion


1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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For most cases the deformable soil model can reproduce accurately the actual drives if not on bedrock It can thus be used as a tool for path planning as well as understanding difficult situation the rover might encounters However, it cannot reproduce extremes cases such as drive with high sinkage. Hence an ongoing research to develop a Discrete Element Model that would simulate all kind of drive on deformable soil For drives on bedrock the contact model, based on Coulomb’s law of friction, is a useful too that can be used as well

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Conclusion


1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

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Thank You!

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BACK UP SLIDES

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BACK UP SLIDES

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q'

δ angle between σn

normal stress and p(θ) resultant between σn

and τ shear stress

ζ direction of the resultant force between the effective driving force Td and the axle load W

η angle between XT and Rω

θr θ

θ

θf

ω

Rω

V R

soil

X

V

σn

p

τ

δ

ξ

ζ

ζ

η

W

Td

ξ angle between p and XT

T H

q‘(θ) component of p(θ) to the direction of angle ζ to vertical axis

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BACK UP SLIDES

The soil deformation d(θ) is the length of the trajectory l(θ) in the direction of q’(θ), component of p(θ) to direction of angle ζ to vertical

XT is an elemental length of trajectory of l(θ) directed in the same direction as the resultant velocity vector of the vehicle velocity V and the circumferential speed Rω

XH is the component of XT in the direction of the angle of effective torque to vertical axis

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Rω

X V

ζ

T

H

q'

p

ζ

W

Td

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BACK UP SLIDES

Hence:

d(θ) = XH dθ = XT cosβ dθ = XT cos (90 – (θ + ζ + η)) dθ = XT sin (θ + ζ + η) dθ

θ

θf

θ

θf

θ

θf

θ

θf

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Rω

X V

ζ

T

H

β

θ

Rω

X V

σn

τ

ζ η

T

H

β

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BACK UP SLIDES

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d(θ) = XT sin (θ + ζ + η) dθ

= R sin(θ + ζ + η) dθ What is η?

tan (η) = And V = Rω(1 – i) Thus: tan (η) =

1cos)1(2)1(2

ii

θ

θf

cosVR

sinV

θ

θf

θ

Rω

V

σn

q

η

Vcosθ

V Vsinθ

Vsinθ

cos)1(1

sin)1(

i

i

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BACK UP SLIDES

is an elemental length of trajectory of l(θ). Let F(X, Y) be the location of an arbitrary point on the wheel, which drives l(θ) in a plane (X, Y) as defined in Figure 6. dX and dY are thus elemental displacement in the X and Y direction of the driven wheel.

XT

30

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BACK UP SLIDES

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The length driven by the wheel at point F is thus

Thus

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BACK UP SLIDES

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Hence:

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BACK UP SLIDES

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The soil deformation is thus:

And

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BACK UP SLIDES

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So

For skid:

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BACK UP SLIDES

The soil deformation d(θ) is thus for a wheel slipping through soil:

For a wheel skidding:

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f

cos)i1(1

sin)i1(tansin1cos)i1(2)i1(R)(d

12

f

cosi1

sintansin1cos

i1

12

i1

1R)(d

s

1

s

2

s

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1.1 Pressure &




2.1 Terrain



3. Results

Conclusion

θr θ

θ

θf

Vcosθ

ω

Rω

V R

Vs

jx

soil

X

V

V Rω

R radius of the wheel

Vs slip velocity point X

jx soil shear displacement

ω angular velocity

V longitudinal speed

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BACK UP SLIDES

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θs

Fd

F

wt

Ra

V longitudinal velocity

Rc

Rν

Rc compaction resistance

Ra aerodynamic resistance F thrust

Rν motion resistance

wt weight

θs slop angle

Fd drawbar pull

Mars Exploration Rover Opportunity Simulations of Traverses on Matijevic Hill, Cape York, Mars

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Transcript of Mars Exploration Rover Opportunity Simulations of Traverses on Matijevic Hill, Cape York, Mars