Gabrielle Coutrot. Paper79024 0

1. 12/20/2013
Mars Exploration Rover Opportunity
Simulations of Traverses on Matijevic Hill,
Cape York, Mars
Gabrielle Coutrot
ISTVS - November 5th , 2013
1
1

2. 12/20/2013
1.1
Pressure & shear stresses – soil shear displacement
1.Terramechanics 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
From bevameter experiments: pressuresinkage equation aka Bekker-Wong-Reece
equation
q
ck 'c
bk '
n
z0
b
c cohesion, γ density, b plate
width, z0 sinkage, n pressuresinkage exponent, kc’ cohesion
modulus, kφ’ friction modulus
Conclusion
2
2

3. 12/20/2013
1.1
Pressure & shear stresses – soil shear displacement
1.Terramechanics equations
1.1 Pressure &
shear stresses –
soil shear
displacement
1.2 Drawbar pull
for a 6-wheel
rover
From experiments: shear stress-soil shear
displacement relationship for homogeneous
soil and Mohr-Coulomb criterion
2. ARTEMIS
simulation:
deformable
soil model
2.1 Terrain
assignments and
soil properties
2.2 Sensitivity
study for
deformable soil
model’s input
parameters
max
1 e
jx
kx
jx soil shear
displacement, kx
longitudinal shear
deformation modulus
Soil shear displacement jx
3. Results
Conclusion
max
c
n
tan
φ angle of internal friction, c
cohesion, and σ normal stress
3
3

4. 12/20/2013
1.2
Drawbar pull for a 6-wheel rover
1.Terramechanics equations
1.1 Pressure &
shear stresses –
soil shear
displacement
1.2 Drawbar pull
for a 6-wheel
rover
COMMANDED
ANGULAR
VELOCITIY for each
wheel
2. ARTEMIS
simulation:
deformable
soil model
2.1 Terrain
assignments and
soil properties
2.2 Sensitivity
study for
deformable soil
model’s input
parameters
THRUST
SLIP/SKID
SLOPE
SHEARING
PROPERTIES
3. Results
Conclusion
SOIL PROPERTIES
COMPACTION
RESISTANCE
4
4

5. 12/20/2013
2.1
Terrain assignment and soil properties
1.Terramechanics 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
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)
Conclusion
5
5

6. 12/20/2013
2.1
Terrain assignment and soil properties
1.Terramechanics equations
1.1 Pressure &
shear stresses –
soil shear
displacement
1.2 Drawbar pull
for a 6-wheel
rover
 Properties assigned:
Soil
properties
γ
c
φ
kc'
kφ’
n
kx
ky
Description
Soil
weight
density
Soil
cohe
-sion
Internal
friction
angle
Reece
cohesion
modulus
Reece
friction
modulus
Pressure
-sinkage
exponent
Longitudinal
shear
deformation
modulus
Lateral
shear
deformation
modulus
Unit
N m-3
kPa
Degree
/
/
/
mm
mm
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
6
6

7. 12/20/2013
2.1
Terrain assignment and soil properties
1.Terramechanics equations
1.1 Pressure &
shear stresses –
soil shear
displacement
1.2 Drawbar pull
for a 6-wheel
rover
3212
Kirkwood
(hard soil)
3101
2. ARTEMIS
simulation:
deformable
soil model
2.1 Terrain
assignments and
soil properties
2.2 Sensitivity
study for
deformable soil
model’s input
parameters
Whitewater Lake –
Broken Hammer –
Big Nickel (very
hard soil)
3090
3053
3. Results
Conclusion
50m
7
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8. 12/20/2013
2.1
Terrain assignment and soil properties
1.Terramechanics equations
1.1 Pressure &
shear stresses –
soil shear
displacement
1.2 Drawbar pull
for a 6-wheel
rover
Broken Hammer Big Nickel 3212 =
BHBN3212
Slip < 3%
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% < Slip < 10%
3. Results
Conclusion
50m
Slip < 3%
8
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9. 12/20/2013
2.1
Terrain assignment and soil properties
1.Terramechanics 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
Soil
properties
φ
kc'
kφ'
n
kx
ky
1600 4.5
38
100
800
1.1
10
10
3% < Slip < 1600 1.5
10%
38
100
800
1.1
15
15
Slip < 3%
γ
c
 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
Conclusion
9
9

10. 12/20/2013
2.2 Sensitivity study for deformable soil model’s inputs
1.Terramechanics equations
1.1 Pressure &
shear stresses –
soil shear
displacement
1.2 Drawbar pull
for a 6-wheel
rover
γ
Soil properties
Soil properties
kx
ky
5
5
kx
ky
800
5
5
0.1
1.1
1.5
1.8
Influence of kx (bench drive)
φ
kc’
kφ’
n
kx
ky
1600
4500
c
Soil properties
1600
4500
c
1.1
n
1.1
100
Influence of c (bench drive)
φ
kc’
kφ’
kx
ky
800
5
5
Influence of φ (bench drive)
c
kc’
kφ’
kx
ky
5
5
n
1600
38
1.1
4500
1600
1.1
800
1600
γ
Soil properties
100
5
10
15
γ
Soil properties
38
Influence of n (bench drive)
φ
kc’
kφ’
γ
3. Results
Conclusion
Influence of kφ’ (bench drive)
φ
kc’
n
γ
2. ARTEMIS
simulation:
deformable
soil model
2.1 Terrain
assignments and
soil properties
2.2 Sensitivity
study for
deformable soil
model’s input
parameters
c
38
38
38
100
100
100
800
kφ’
800
900
1000
1600
n
5
10
15
c
2500
3000
4500
φ
30
32
10 35
38
10

11. 12/20/2013
2.2 Sensitivity study for deformable soil model’s inputs
1.Terramechanics 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
 kφ’, n & φ do not strongly influence rover 3D slip
11
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12. 12/20/2013
2.2 Sensitivity study for deformable soil model’s inputs
1.Terramechanics 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
12
12

13. 12/20/2013
2.2 Sensitivity study for deformable soil model’s inputs
1.Terramechanics 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
13
13

14. 12/20/2013
2.2 Sensitivity study for deformable soil model’s inputs
1.Terramechanics 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
 kx & c strongly influence rover 3D slip
 Which one is the most important?
Soil
properties
γ
1600
Soil
properties
γ
1600
Influence of kx (BHBN3212 drive)
c
φ
kc'
kφ’
n
0
30
100
800
Influence of c (BHBN3212 drive)
n
φ
kc'
kφ’
1.2
30
100
800
kx
ky
1.2
10
11
12
14
15
10
11
12
14
15
kx
ky
c
15
0
500
1000
15
14
14

15. 12/20/2013
2.2 Sensitivity study for deformable soil model’s inputs
1.Terramechanics 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
 kx controls slip and is thus adjusted; to better
approximate slip/skid once kx is modified, c is
15
adjusted
15

16. 12/20/2013
3.
Results
1.Terramechanics equations
Slip observed
1.1 Pressure &
shear stresses –
soil shear
displacement
1.2 Drawbar pull
for a 6-wheel
rover
 Average slip 7%
2. ARTEMIS
simulation:
deformable
soil model
2.1 Terrain
assignments and
soil properties
2.2 Sensitivity
study for
deformable soil
model’s input
parameters
50m
Soil
properties
Values
γ
c
φ
kc'
kφ’
n
kx
ky
1600
1.5
100
800
1.1
N m-3
kPa
/
/
/
20
(15)
mm
20
Unit
30
(38)
Degree
0
mm
distance driven (m)
10
3. Results
Conclusion
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17. 12/20/2013
3.
Results
Slip observed at the beginning,
then skid (going uphill)
 2 parts with 2 different sets of
parameters
1.Terramechanics equations
1.1 Pressure &
shear stresses –
soil shear
displacement
1.2 Drawbar pull
for a 6-wheel
rover
50m
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
Navcam of sol 3213
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18. 12/20/2013
3.
Results
1.Terramechanics equations
1.1 Pressure &
shear stresses –
soil shear
displacement
1.2 Drawbar pull
for a 6-wheel
rover
Soil
properties
1st part
γ
c
φ
kc'
kφ’
n
kx
ky
1600
800
100
800
Unit
N m-3
/
/
1.2
(1.1)
1.2
(1.1)
/
5
(10)
25
(10)
mm
5
1600
30
(38)
30
(38)
Degree
100
2nd part
1
(4.5)
1
(4.5)
kPa
0
25
mm
distance driven (m)
4
2. ARTEMIS
simulation:
deformable
soil model
2.1 Terrain
assignments and
soil properties
2.2 Sensitivity
study for
deformable soil
model’s input
parameters
BHBN3212 – 1
0
Average slip 2%
distance driven (m)
5
3. Results
Conclusion
BHBN3212 – 2
Average slip 2%
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19. 12/20/2013
3.
Results
1.Terramechanics 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
1st part on Whitewater Lake formation
3. Results
Conclusion
 2nd part on windblown sand: expect to be
19
terrain with increasing slip
19

20. 12/20/2013
3.
Results
1.Terramechanics 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
Resistances
Drive
Average
thrust Compaction Slope
Resistance Rc
(N)
angle
(N)
wtsinθs
Total
Drawbar
Pull (N)
Fd = F∑RR
Kirkwood
238
88.3
13° 156.24 245
BHBN3212
(1)
BHBN3212
(2)
253
94.4
12°
139.5
153
106
4°
50.22 156.2 3.22
234
7
19
Drawbar pull close to 0
Simulations accurate
Conclusion
20
20

21. 12/20/2013
3.
Results
Other model tested: contact model, based
on Coulomb’s law of friction
1.Terramechanics equations
1.1 Pressure &
shear stresses –
soil shear
displacement
1.2 Drawbar pull
for a 6-wheel
rover
Ff < μFn
50m
Soil properties
2. ARTEMIS
simulation:
deformable
soil model
2.1 Terrain
assignments and
soil properties
2.2 Sensitivity
study for
deformable soil
model’s input
parameters
μs
μd
STV
FTV
Initial
Final
Unit
0.781
0.625
/
0.577
0.577
/
0.003
0.003
m/s
0.005
0.005
m/s
50m
Skid observed
 Average skid -3.3%
3. Results
Conclusion
0
distance driven (m)
21
15
21

22. 12/20/2013
Conclusion
1.Terramechanics 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
 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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22

23. 12/20/2013
Conclusion
1.Terramechanics 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
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23

24. 12/20/2013
Thank You!
24

25. 12/20/2013
BACK UP SLIDES
25
25

26. 12/20/2013
BACK UP SLIDES
W
ζ
R
θr
Td
θ
ω
V
θf
soil
X
τ
δ angle between σn
normal stress and p(θ)
resultant between σn
and τ shear stress
ξ angle between p and XT
η angle between XT
and Rω
Rω
ζ
η
V
δ σn
q'
H T
p
ξ
θ
ζ direction of the
resultant force
between the effective
driving force Td and
the axle load W
q‘(θ) component of p(θ)
to the direction of angle
ζ to vertical axis
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26

27. 12/20/2013
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
W
ζ
 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
Td
X
V
q'
H
Rω
T
p
ζ
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27

28. 12/20/2013
BACK UP SLIDES
 Hence:
X
θf
d(θ) = XH dθ
θ
β
H
Rω
T
θf
= XT cosβ dθ
θ
V
ζ
X
θf
= XT cos (90 – (θ + ζ + η)) dθ
θ
=
Rω
β
H
T
θf
XT sin (θ + ζ + η) dθ
V
τ
η
ζ
σn
θ
θ
28
28

29. 12/20/2013
BACK UP SLIDES
θf
d(θ) =
XT sin (θ + ζ + η) dθ
θ
θf
= R
(1 i ) 2
2(1 i ) cos
1 sin(θ + ζ + η) dθ
Vcosθ
θ
 What is η?
Vsinθ
V sin
tan (η) =
R
V cos
And
Thus:
V = Rω(1 – i)
tan (η) =
Vsinθ
V
η
θ
Rω
V
σn
q
(1 i ) sin
1 (1 i ) cos
29
29

30. 12/20/2013
BACK UP SLIDES
XT 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.
30
30

31. 12/20/2013
BACK UP SLIDES
The length driven by the wheel at point F is thus
Thus
31
31

32. 12/20/2013
BACK UP SLIDES
Hence:
32
32

33. 12/20/2013
BACK UP SLIDES
The soil deformation is thus:
And
33
33

34. 12/20/2013
BACK UP SLIDES
So
For skid:
34
34

35. 12/20/2013
BACK UP SLIDES
 The soil deformation d(θ) is thus for a wheel slipping
through soil:
f
d( )
(1 i) 2
R
2(1 i) cos
1 sin
tan
1
(1 i) sin
1 (1 i) cos
 For a wheel skidding:
f
d( )
R
1
1 is
2
2
1
1 is
cos
1 sin
tan
1
sin
1 i s cos
35
35

36. 12/20/2013
1.1
Pressure & shear stresses – soil shear displacement
1.Terramechanics equations
1.1 Pressure &
shear stresses –
soil shear
displacement
1.2 Drawbar pull
for a 6-wheel
rover
ω
R
θr θ
V
θf
soil
X θ Vcosθ
V
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
Rω
V
Rω
Vs
V longitudinal speed
ω angular velocity
jx
Vs slip velocity point X
jx soil shear displacement
R radius of the wheel
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36

37. 12/20/2013
BACK UP SLIDES
V longitudinal velocity
Ra
Rc
Fd
F
Rν
wt
θs
Fd drawbar pull
Rν motion resistance
F thrust
Ra aerodynamic resistance
wt weight
Rc compaction resistance
θs slop angle
37
37