IMU Theory: Earth and Body Frames

Transcription

1 3/9/27 Lcu 3 N4562 umus Ssms IMU Th IMU Th: ah and d Fams X : wads NOTH Y : Twads ST Z : in h Cn f h ah b iud : ais : pich ais : ll ais b b Pf. han Munasinh Dpamn f lcnic and Tlcmmunicain ninin Facul f ninin Univsi f Mauwa 4 Inial Masumn Snss Masu inain f {} wih spc {} Od: ais,, ais pich and ais ll Oinain f {} wih spc {} is ivn b ND cnvnin d sns Fam and ah Fam Q = Sns adin acclain, vlciis.. Q = adin vhicl min w... ah fnc fam ain mai, Dicin Csin Mai DCM T Q Q

2 3/9/27 2 Od f ain is Impan : plan pichs b 9 and hn lls b 9 Plan is flin vicall upwads plan lls b 9 and hn pichs b 9 Plan is mvin hinall Cmpund ain mulipl fams, laiv and fnc C D C D {} {} {C} Scala and Vc Pduc Scala d Pduc Vc css Pduc Cmpnns css pduc pa Vc Upda quains Ls cnsid h uni vc,, aln -ais f {}. Is dscipin w... {} is im=, If {} unds a slih inain chan dcd b 3- ais d,d,d T. Th vc upda is as fllws d ain Mai Upda wih G adins Thn, vc upda quain is Simillal, d d

3 3/9/27 d d ain Mai Upda wih G adins d d d d d d d d d d d d d d Mai Upda wih G adins d d d d d d d d d wh d d and d 2ms d d bu 5H upda a is quid kp h hih d ms nliibl w hav usd fis d appimain Upda invlvs 27 muliplicains and 8 addiins, culd b implmnd n a pcss ha pvids HW supp f mai muliplicain. dspic3f4 Psvin Ohnali f Mai Th clumn vcs f hav b hnal a all ims. Numical s mak clumn vcs n-hnal Numical s accumula slwl, hus, h is im im cc maliain Cc h Mai f hnali and mali Psvin Ohnali f Mai Scala pduc indicas hw much h w uni vcs a n-hnal ach h Th n-hnal bwn and vcs f T [ ] Th adjusd hnal vcs a as fllws.5.5 3

4 3/9/27 Psvin Ohnali f Mai ppinin half ach vc ducs h hnal sinificanl und h cndiin ha bh vcs hav nal uni maniud. Th mainin vc f h mai is divd b css pduc f h w hnal vcs as fllws: f hnai, maliain is quid adjus vc maniuds uni maliain maliain f Mai Usin Tal pansin, hnal vcs can b adjusd wads uni vcs as fllws This appimain dsn hav squa and divisin invlvd: can b cmpud quickl. Finall, malid, hnal ain Mai is updad as fllws: d d d d G Dif MMS snss shw a cninuus dif a a a f a fw ds p scnd. Dif cancllain is ciicall impan. Oh inain fncs which d dif shuld b usd cninuusl cmpnsa h adin f dif. Mhd Css pduc f a fnc dicin vc wih h cspndin vc in mai DCM, indicas h. This can b fd back huh a ccin fil s ha DCM vc culd ack h fnc vc. N: Css pduc lls h anl and ais f ain ndd bin DCM vc cincid wih h f vc G Yaw Dif and Tack f ack pvids dicin hadin n h und, hus, culd b usd as a fnc. IMU DCM d DCM simad vc und cus F his fnc b usful, mus mv. Whn h vhicl is mvin hvin UV. This mhd is uslss 4

5 3/9/27 G Yaw Dif and ack f CG : Cus v Gund is ivn b h CG CG cs sin Yaw ccin anl G Yaw Dif and ack f Yaw Ccin vc sin sin CG ˆ sin ˆ uni vc Yaw dif is n - plan CG cs sin cs sin sin cs cs sin G Yaw Dif and ack f Yaw ccin anl sin sin cs cs cs cs Ccin f G Yaw Dif T cc dif, simad vc f has b ad abu is wn -ais b h anl Ccin can b b implmnd as a PI fil which aks nl h insananus anl, bu an accumulad in cn ims and aduall ach a alinmn f h hadin sima wih h und cus PI Th dif ccd sima is ivn b Slih ain abu Z ais 5

6 3/9/27 Ccin f G Yaw Dif S h ppinal ain sinificanl hih duc h quickl. ssumpin: Th vhicl is mvin in h dicin i is pinin. In UV applicains, his assumpin can b vilad du css-wind. G ll-pich Dif Ccin Usin cclms: sinl ais, h ais cclm upus pu avi vc dic inain masumn whn h snsvhicl is acclain. Whn h vhicl acclas/dclas i upus avi+acclain as h cmpnns w bd fam. ssumpin: Vhicl ds accla/dcla in fwad dicin. If i ds, i las nl bifl. u h vhicl can ak ln uns ha na lasin laal acclains. Cnifual acclain cn cclm upu = Gavi + Cnifual acclain w.. d sns fam in ND sn cn G ll-pich Dif Ccin usin cclms Wih spc bd fam assumin /p cn N: Cnifual acclain = v 2 /=ω 2 =ωv Fwad spd v v v v Gavi Vc sima fm cclm Oupu Gavi vc 2 2 sn 2 sn sn sn sn sn v sn v v 9.8 v v 6

7 3/9/27 G ll-pich Dif Ccin ll-pich Dif ll and Pich f {} fm Gavi Vc ll anl usin acclm adins ll anl fm h mai ll usin acclm cs an 2 cc ppndi, Pich {} fm Gavi Vc Pich anl fm acclm adins Pich anl fm h mai G Pich anl an 2 cc cc cc ppndi cs, sin ll and Pich Ccin Usin cclm nd, cc pich, a simad {} b pich anl abu ais cc PI cc cc Slih ain abu Y ais T cc ll, a {} b h anl abu ais PI cc cc cc cc Slih ain abu X ais cc 7

8 3/9/27 iud simain b Sns Fusin G cc cc PI CC cc PID cc cc cc cc PID cc cc cc 8