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A New Configuration of Mobile A New Configuration of Mobile System of Lunar Rover and Its Drive System of Lunar Rover and Its Drive
Control Study Control Study
Harbin Institute of TechnologyHarbin Institute of Technology
Liu Dun, Liu Dun, DuDu JianJian--junjun, Zhao , Zhao ZhiZhi--ping, ping, Yuan LaoYuan Lao--huhu, Zhang , Zhang JianyingJianying
Astronautic School, Harbin Institute of TechnologyAstronautic School, Harbin Institute of TechnologyShenzhen Graduate School, Harbin Institute of TechnologyShenzhen Graduate School, Harbin Institute of Technology
1 New Configuration1 New Configuration
Harbin Institute of TechnologyHarbin Institute of Technology
Statically Determinate RoverStatically Determinate Rover
1 New Configuration1 New Configuration
Harbin Institute of TechnologyHarbin Institute of Technology
Statically Indeterminate RoverStatically Indeterminate Rover
1 New Configuration1 New Configuration
Harbin Institute of TechnologyHarbin Institute of Technology
Statically Determinate Rover Lacks of Capability Statically Determinate Rover Lacks of Capability to Traverse Ditchto Traverse Ditch
1 New Configuration1 New Configuration
Harbin Institute of TechnologyHarbin Institute of Technology
Statically Indeterminate Rover with Eight Wheels Statically Indeterminate Rover with Eight Wheels Has Capability to Traverse DitchHas Capability to Traverse Ditch
1 New Configuration1 New Configuration
Harbin Institute of TechnologyHarbin Institute of Technology
Statically Indeterminate Rover with Six Wheels Statically Indeterminate Rover with Six Wheels Lacks of Capability to Traverse DitchLacks of Capability to Traverse Ditch
(a) (a) BarycenterBarycenter being on the middle wheelbeing on the middle wheel
On the horizontal plainOn the horizontal plain On the inclineOn the incline
1 New Configuration1 New Configuration
Harbin Institute of TechnologyHarbin Institute of Technology
Statically Indeterminate Rover with Six Wheels Statically Indeterminate Rover with Six Wheels Lacks of Capability to Traverse DitchLacks of Capability to Traverse Ditch
(b) (b) BarycenterBarycenter being on the front and rear partbeing on the front and rear part
1 New Configuration1 New Configuration
Harbin Institute of TechnologyHarbin Institute of Technology
Statically Indeterminate Rover with Six Wheels of Statically Indeterminate Rover with Six Wheels of asymmetric wheel configuration to improve the asymmetric wheel configuration to improve the capability to traverse ditchcapability to traverse ditch
1 New Configuration1 New Configuration
Harbin Institute of TechnologyHarbin Institute of Technology
Statically Indeterminate Rover with Six Wheels of Statically Indeterminate Rover with Six Wheels of asymmetric wheel configuration asymmetric wheel configuration has ability to has ability to traverse ditchtraverse ditch
2 Improvement of Traction Ability2 Improvement of Traction Ability
Harbin Institute of TechnologyHarbin Institute of Technology
Traction Force Traction Force == ∑=
=n
iiiWT
1max µ
WWii -- Normal Force of Normal Force of iithth wheelwheelµµ ii -- Friction Coefficient of Lunar SoilFriction Coefficient of Lunar Soilnn -- Number of WheelsNumber of Wheels
—— Maximal friction forceMaximal friction force
To Change To Change µµ ii -- We could do nothingWe could do nothingTo Change To Change WWii -- Suggestion of this paperSuggestion of this paper
maxT
maxT
To Improve traction force, there are two ways:To Improve traction force, there are two ways:
maxTmaxTmaxTmaxT
maxT
maxT
maxT
2 Improvement of Traction Ability2 Improvement of Traction Ability
Harbin Institute of TechnologyHarbin Institute of Technology
Approach to change Approach to change WWii
KK -- Stiffness of torsion springStiffness of torsion spring
ßß i0i0, , ßß ii -- Initial and working angle of torsion springInitial and working angle of torsion spring
The easiest method to increase The easiest method to increase WWii is to change is to change ßß i0i0
( )iii KW ββ −∝ 0
2 Improvement of Traction Ability2 Improvement of Traction Ability
Harbin Institute of TechnologyHarbin Institute of Technology
Example:Example:
Two front wheels are Two front wheels are on the sandy soil and on the sandy soil and lose their traction lose their traction forces. Rover canforces. Rover can’’t go t go up. up.
Two front wheels turn Two front wheels turn up or other 4 wheels up or other 4 wheels turn down, to increase turn down, to increase traction forces on traction forces on other 4 wheels, Rover other 4 wheels, Rover continues go up. continues go up.
3 Parameter Identification in Drive Control3 Parameter Identification in Drive Control
Harbin Institute of TechnologyHarbin Institute of Technology
Two parameters under identification:Two parameters under identification:Wheel slip Wheel slip uuii and instantaneous rotary center angle and instantaneous rotary center angle ?? ii
ddii ,, dd -- Ideal and real instantaneous rotary centerIdeal and real instantaneous rotary center?? -- SinkageSinkage of soilof soilVVixix, , VVixix
** -- Ideal and real velocity along rover longitudinal axis Ideal and real velocity along rover longitudinal axis VVii
** -- Real Velocity of wheel centerReal Velocity of wheel centerOO ii -- Angular velocity of wheelAngular velocity of wheel
di
The ideal wheel:The ideal wheel: The real wheel:The real wheel:iiix rV Ω= iiiiix urV −Ω= ψcos*
Figure 7. The Real Wheel.
iΩ iBiv∗
ixv∗x
iψdrd
id'id
∆ibixv iΩ
iB
ib
ir
3 Parameter Identification in Drive Control3 Parameter Identification in Drive Control
Harbin Institute of TechnologyHarbin Institute of Technology
VVi i , , VVcc -- Velocity of wheel center Velocity of wheel center bbi i and rover mass and rover mass center round circle center round circle center center OO
ωρρ == ccii VV
niVV iiix ,,2,1,cos L=∆= ξ
c
O
x
bi
? ? i
G0
?vi
vix
? i
? c
vc
?? -- SinkageSinkage of soilof soil
?? -- Angular velocity of rover Angular velocity of rover round circle center round circle center OO
-- Radius of curvature Radius of curvature of wheel center bi and of wheel center bi and rover mass center rover mass center CC
The planar movement of L.R.The planar movement of L.R.
iρ
,i cρ ρ
3 Parameter Identification in Drive Control3 Parameter Identification in Drive ControlHarbin Institute of TechnologyHarbin Institute of Technology
WhereWhere
After After nn measurements, we can write for estimationsmeasurements, we can write for estimations::iiii uxx == 21 ˆ,cosˆ ψ
6,2,1),()(ˆ)( L==− innn iiin δω XA
[ ][ ]
T1 2
1
T
T
ˆ ˆ ˆ( ) [ ( ) ( )]
(1) (1)(2) (2)
( ) , ( ) ( ) /[ ( ) cos ( )]( ) [ ( ) cos ( )]
( ) ( )
( ) (1) (2) ( )
( ) (1) (2) ( )
i i i
i i
i ii i i i i i
i i ii i
i i i i
X n x n x n
a ba b
A n a k O k r k ? kb k k ? k
a n b n
n n
n n
ρρ
ω ω ω ω
δ δ δ δ
−
=
− − = = ∆
= ∆ −
=
=
M M
L
L
3 Parameter Identification in Drive Control3 Parameter Identification in Drive Control
Harbin Institute of TechnologyHarbin Institute of Technology
The optimal estimations of and The optimal estimations of and for minimal quadratic sum of for minimal quadratic sum of dd ii((nn))
)()()]()([)(ˆ 1 nnAnAnAnX Tii
Tii ω−=
1ˆix 2ˆix
3 Parameter Identification in Drive Control3 Parameter Identification in Drive Control
Harbin Institute of TechnologyHarbin Institute of Technology
For real time application, we suggest the following For real time application, we suggest the following calculation sequence: To obtain the calculation sequence: To obtain the kk+1+1thth estimations estimations
through through kkthth estimations and estimations and kk+1+1thth
measurementsmeasurementsbyby
)1(ˆ +kxi )(ˆ kxi])1()1([)1( +−+=+ kbkak iiα
)](ˆ)1()1()[1()(ˆ)1(ˆ1 kXkkkPkXkX i
Tkii +−+++=+ + αωα
[ ]
11
( 1)[1 ( 1) ( 1)] ( 1)[ ( ) ( )]
( 1) ( 1), ( 1)
T T Tk k k k k
Tk i i
i i
P P P k k P k k PP A k A k
k a k b k
α α α α
α
+−
= − + + + + + = + = + − +
WhereWhere
4 Conclusion4 Conclusion
Harbin Institute of TechnologyHarbin Institute of Technology
1)1) A new asymmetrical configuration of statically A new asymmetrical configuration of statically indeterminate rover with 6 wheels is proposed. It has indeterminate rover with 6 wheels is proposed. It has better ability to traverse ditch.better ability to traverse ditch.
2)2) A MethodA Method to change the normal forces of wheels to change the normal forces of wheels through changing initial angles and/or stiffness of through changing initial angles and/or stiffness of suspension devices for improving traction ability is suspension devices for improving traction ability is suggested.suggested.
3)3) A real time identification method to determine the A real time identification method to determine the wheel slips and angles of instantaneous rotary centers wheel slips and angles of instantaneous rotary centers for more accurate rover drive is given.for more accurate rover drive is given.