DAGE-MTI Excel Series Instrukcja Użytkownika Pobierz pdf (Strona 18)



 DocumentMT0100P.N

©XsensTechnologiesB.V. MTiandMTxUserManualandTechnicalDocumentation

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4.3.1 Quaternionorientationoutputmode

Aunitquaternionvectorcanbeinterpretedtorepresentsarotationaboutaunitvectornthroughanangleα.



((), ()

qcossin)

(,,,)qqqqq=



qq=−

†

(, , , )

= n



Aunitquaternionitselfhasunitmagnitude,andcanbewritteninthefollowingvectorformat;



0123GS

1q =



Quaternionsareanefficient,non‐singulardescriptionof3Dorientationandaquaternionisuniqueuptosign:



Analternativerepresentationofaquaternionisasavectorwithacomplexpart,therealcomponentisthefirst

one,q

.



Theinverse(q

)isdefinedbythecomplexconjugate(†)ofq

.Thecomplexconjugateiseasilycalculated;



0123GS SG

qqqqqq

=−−−=

†

qq qq==xx x



Asdefined here



rotatesavectorinthesensorco‐ordinatesystem(S)totheglobalreferenceco‐ordinate

system(G).



GS GS GS SGGS S



Hence,q

rotatesavectorintheglobalreferenceco‐ordinatesystem(G)tothesensorco‐ordinatesystem(S),

whereq

SG

isthecomplexconjugateofq

.



4.3.2 Euleranglesorientationoutputmode

Thedefinition used for'Euler‐angles'here is equivalentto'roll, pitch, yaw/heading' (also known asCardan).

TheEuler‐anglesareof XYZEarthfixedtype(subsequentrotationaroundglobalX,YandZaxis,alsoknownas

aerospacesequence).



Theoutputdefinitioninquaternionoutputmodeis:



MTData DATA = 

MID50(0x32)



All data elements in DATA field are FLOATS (4 bytes) , unless specified otherwise by modifying the

OutputSettingDataFormatfield.



q3q2q1q0

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