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Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Terramechanics 2
• Effects of grousers • Example solutions for rolling resistance • Discussion of first steps in term project
1
© 2016 David L. Akin - All rights reserved http://spacecraft.ssl.umd.edu
Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Grousers (on Tracked Vehicle)
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Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Grousers (MSL Wheels)
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Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Mars Rover Wheels
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Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Tractive Force per Wheel (No Grousers)
A = area of contact
Cb = coe�cient of soil/wheel cohesion
� = length of contact patch
K = coe�cient of soil slips = wheel slip ratio
�b = wheel/soil friction angle
5
H = [ACb + Ww tan�b]⇤1� K
⌥
�1� e
�s⇥K
⇥⌅
s = 1� V
�r
Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Tractive Force per Wheel (With Grousers)
h = height of grouser
s = wheel slip ratio (typ. 0.02-0.05)K = coe�cient of soil slip = 1.8 cm
Cb = soil/wheel cohesion = 0.017 N/cm2
�b = wheel/soil friction angle = 35�
� = length of contact patch =D
2cos�1
�1� 2z
D
⇥
All values typical for lunar soil
A = area of contact �= b⇥
H =⇧b�Cb
⇤1 +
2h
b
⌅Ng + W tan�b
⇤1 + 0.64
h
barctan
b
h
⌅⌃ ⇧1� K
�
�1� e�
s⇥K
⇥⌃
6
Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Effect of Soil Thrust Fraction
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1
Slip Ratio
So
il T
hru
st F
ract
ion
K/l=0.10.250.512410
Soil Thrust Fraction⇤1� K
⇥
�1� e�
s⇥K
⇥⌅
7
Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Basic Equation of Vehicle Propulsion
DP = H � (Rc + Rb + Rg + Rr)
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• DP: Drawbar pull (residual drive force) • H: Maximum tractive force of wheels • Rc: Compaction resistance • Rb: Bulldozing resistance • Rg: Gravitational resistance • Rr: Rolling resistance (internal)
Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Wheel Test Apparatus• Wheel testing done at MIT Field and Space Robotics
Laboratory • Independent control of motion and wheel velocity provides
controllable slips = 1� V
�r
9
Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Wheel Torque vs. Time
ϕ=0.24
9 grousers 18 grousers
10
Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Sinkage vs. Slip Ratio
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Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Drawbar Pull vs. Slip Ratio
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Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Motor Torque vs. Slip Ratio
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Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Example: Wheelbarrow (Single) Wheel
0
100
200
300
400
500
600
0 200 400 600 800 1000
Wheel Weight (N)
Dra
wb
ar
Resi
stan
ce (
N)
Dry SandSandy LoamClayLunarMER-B Sandy LoamMER-B Slope Soil
b=0.1 mD=0.3 m
R = (kc + k�b)�1
2n+1 W2(n+1)2n+1
1n + 1
�3
3� n
⇥ 2(n+1)2n+1
D�(n+1)2n+1
Com
pact
ion
Res
ista
nce
(N)
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Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Effects of Wheel Parameters
0
20
40
60
80
100
120
140
160
180
200
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Wheel Diameter (m)
Dra
wb
ar
Resi
stan
ce (
N)
b=0.1b=0.25b=0.5
W=500 N
Com
pact
ion
Res
ista
nce
(N)
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Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Effect of Soil “Spring Constant” on R/W
0.1
1
10
100
1000
10000
1 10 100 1000 10000
Soil "k" value (N/m)
Resi
stan
ce/
Weig
ht
n=0n=0.5n=1
Wheel 1 m diameter x 0.2 m width
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Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Soil Type and Wheel Load
1
10
100
1000
10000
100000
1000000
10 100 1000 10000Weight on Wheel (N)
Dra
wb
ar
Resi
stan
ce (
N)
ClayDry SandSnow
Wheel 1 m diameter x 0.2 m width
Com
pact
ion
Res
ista
nce
(N)
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Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Soil Type and Specific Resistance
0.1
1
10
10 100 1000
Weight on Wheel (N)
Resi
stan
ce/
Weig
ht
ClayDry SandSnow
Wheel 1 m diameter x 0.2 m width
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Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Effect of Wheel Diameter and Width
100
1000
10000
0.01 0.1 1
Wheel Width (m)
Resi
stan
ce (
N)
D=1 mD=2 mD=4 m
100
1000
10000
0.01 0.1 1
Wheel Width (m)
Resi
stan
ce (
N)
D=1 mD=2 mD=4 mDualQuad
Wheel Load = 1000 N
Com
pact
ion
Res
ista
nce
(N)
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Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Effect of Slope
-600
-400
-200
0
200
400
600
-100 -50 0 50 100
Slope (deg)
Dra
wb
ar
Resi
stan
ce (
N)
Gra
vita
tiona
l Res
ista
nce
(N)
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Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Bulldozing Resistance (Reminder)
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Rb =b sin (↵+ �)
2 sin↵ cos�
�2zcKc + �z2K�
�
General case:
For tracked vehicles, only the first term applies:
Rb =b sin (↵+ �)
2 sin↵ cos�
�2zcKc + �z2K�
�
`o
= z tan2✓⇡
4� �
2
◆+`3o
�
3
⇣⇡2� �
⌘+ c`2
o
1 + tan
✓⇡
4+
�
2
◆�
All angles in radians!
`o
⌘ soil disruption depth, and is not the same as contact length `
Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Bulldozing Resistance (Rb)
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Symbol Description Value
Angle of internal friction 30-40 degrees for Lunar Regolith
γ Soil density 0.002595 N/cm3 for Lunar Regolith
Co Cohesive strength of soil 0.017 N/cm2 for Lunar RegolithLo
(degrees)Distance of rupture
Kc (degrees)
Modulus of cohesion of soil deformation
Kγ (degrees)
Modulus of density of soil deformation
Nc (radians)
Coefficient of passive earth pressure
α(degrees)
Angle of approach of the wheel
Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Bulldozing Example (1)
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� = 33o = 0.576 rad
↵ = cos
�1
✓1� 2z
d
◆= cos
�1
✓1� 2(1.812)
81.2
◆= 17.18o = 0.2999 rad
Nq =
e(1.5⇡��) tan�
2 cos
2⇣
⇡4 +
�2
⌘= 32.23
`o
= z1 tan2
✓⇡
2� �
4
◆= 0.5341
Nc =Nq � 1
tan�= 48.09
Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Bulldozing Example (2)
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N� =2(Nq + 1) tan�
1 + 0.4 sin 4�= 33.27
Kc = (Nc � tan�) cos2 � = 33.37
K� =
✓2N�
tan�+ 1
◆cos
2 � = 72.77
� = 0.002595N
cm3; c
o
= 0.017N
cm2
` =d
2
cos
�1
✓1� 2z
d
◆= 12.18 cm
Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Terzhagi Parameters
25
Red lines represent values calculated for this example
Terramechanics 2 ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Bulldozing Example (3)
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Rb =b sin (↵+ �)
2 sin↵ cos�
�2zcKc + �z2K�
�
+`3o
�
3
⇣⇡2� �
⌘+ c`2
o
1 + tan
✓⇡
4+
�
2
◆�
hRbi = cm
✓cm
N
cm2+
N
cm3cm2
◆+ cm3 N
cm3+
N
cm2cm2
Rb = 94.98 + 0.000131 + 0.014 = 95.00 N per leading wheel
Rb,total
= 190.0 N
Course Overview ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
AAR Design Project Statement• Perform a detailed design of a small astronaut
assistance rover, emphasizing mobility systems– Chassis systems (e.g., wheels, steering, suspension…)– Support systems (e.g., energy storage)– Navigation and guidance system (e.g., sensors,
algorithms...)
• Design for Moon, then assess feasibility of systems for Mars, and conversion to Earth analogue rover
• This is not a hardware project - focus is on detailed design (but may be built later!)
27
Course Overview ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Objectives for Design Project (1)• UMd SSL is proposing to do month-long
simulations of lunar/Mars science exploration missions to examine impact of robotics
• Primary missions would be held at HI-SEAS in Hawaii
• Rover design should facilitate shipping to/from Hawaii– Minimal size and mass– Modular construction for packing (ideally each less than
50 lbs with packaging)
28
Course Overview ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Aerial View of HI-SEAS Site
29
Course Overview ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Sample HI-SEAS Terrain
30
24° slope
Course Overview ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Sample HI-SEAS Terrain
31
Course Overview ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Sample HI-SEAS Terrain
32
Course Overview ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Sample HI-SEAS Terrain
33
Course Overview ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
Sample HI-SEAS Terrain
34
Course Overview ENAE 788X - Planetary Surface Robotics
U N I V E R S I T Y O FMARYLAND
First Steps in Rover Design• Assume a vehicle gross weight• Examine rolling resistance for design parameters
– Number of wheels– Diameter of wheels– Width of wheels
• Calculate torque transfer to ground– Required torque for climbing maximum slope– Design of grousers for required torque
• Next step: chassis design
35