a new configuration of mobile system of lunar rover and...

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


Statically Determinate RoverStatically Determinate Rover



Statically Indeterminate RoverStatically Indeterminate Rover



Statically Determinate Rover Lacks of Capability Statically Determinate Rover Lacks of Capability to Traverse Ditchto Traverse Ditch



Statically Indeterminate Rover with Eight Wheels Statically Indeterminate Rover with Eight Wheels Has Capability to Traverse DitchHas Capability to Traverse Ditch



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



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



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



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


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



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



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


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



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



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



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


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.


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