Download - 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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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
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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.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
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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.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
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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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Terrain assignment and soil properties 2.1
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
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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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Terrain assignment and soil properties 2.1
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
50m
3053
3090
3101
Kirkwood (hard soil)
Whitewater Lake – Broken Hammer – Big Nickel (very hard soil)
3212
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Terrain assignment and soil properties 2.1
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
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Slip < 3%
Slip < 3%
3% < Slip < 10%
Broken Hammer Big Nickel 3212 = BHBN3212
50m
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Terrain assignment and soil properties 2.1
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
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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.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
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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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Sensitivity study for deformable soil model’s inputs 2.2
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
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kφ’, n & φ do not strongly influence rover 3D slip
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Sensitivity study for deformable soil model’s inputs 2.2
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
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Sensitivity study for deformable soil model’s inputs 2.2
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
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Sensitivity study for deformable soil model’s inputs 2.2
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
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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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Sensitivity study for deformable soil model’s inputs 2.2
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
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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.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
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50m
Soil properties
γ c φ kc' kφ’ n kx ky
Values 1600 1.5 30 (38)
100 800 1.1 20 (15)
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Unit N m-3 kPa Degree / / / mm mm
Slip observed
Average slip 7%
0 distance driven (m) 10
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Results 3.
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
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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.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
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Soil properties
γ c φ kc' kφ’ n kx ky
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)
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Unit N m-3 kPa Degree / / / mm mm
BHBN3212 – 1 Average slip 2%
BHBN3212 – 2 Average slip 2%
0 distance driven (m) 4
0 distance driven (m) 5
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Results 3.
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
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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.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
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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.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
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50m
Skid observed Average skid -3.3%
0 distance driven (m) 15
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.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
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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.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
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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
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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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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
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