【導(dǎo)讀】運(yùn)動(dòng)學(xué)模型由于操作器得到發(fā)展,它們關(guān)系到基坐標(biāo)和工件。工件姿態(tài)是從實(shí)驗(yàn)測(cè)量中引出的討論,同樣地是識(shí)別方法學(xué)。完全模擬實(shí)驗(yàn)已經(jīng)實(shí)現(xiàn)。實(shí)驗(yàn)工作的目的是描寫參數(shù)辨認(rèn)和精確確認(rèn)。的那方法能得到在重復(fù)時(shí)近連續(xù)地校準(zhǔn)機(jī)器人。機(jī)器手有合理的重復(fù)精度()而知名,但仍有不好的精確性(毫米)。為了實(shí)現(xiàn)機(jī)器手精確性，機(jī)器人可能要校準(zhǔn)也是好理解。在標(biāo)定過程中，幾個(gè)。作為結(jié)果的模型是定義基于廠商的運(yùn)動(dòng)學(xué)參數(shù)設(shè)置錯(cuò)誤量,和識(shí)別未知。一個(gè)接近完成辨認(rèn)由分析不同中間姿態(tài)變量P和運(yùn)動(dòng)學(xué)參數(shù)K的微分關(guān)系決。這是標(biāo)準(zhǔn)優(yōu)化問題和可能解決用的眾所周知的。為了標(biāo)度過程到進(jìn)行。它是三軸的，棱鏡測(cè)量系統(tǒng)達(dá)到。560，放置接近于CMM，特殊的操作裝置能到達(dá)邊緣。系相一致時(shí)，它們將被書寫成矩陣元素實(shí)現(xiàn)運(yùn)動(dòng)學(xué)參數(shù)功能的矩陣形狀。優(yōu)化程序使用命名為ZXSSO，和標(biāo)準(zhǔn)庫功能的IMSL。

　　

【正文】 A. 3. Calculate the pose of the PUMA endeffector. 4 . M e a s u r e t h e a c t u a l p o s e o f t h e P U M A e n d e f f e c t o r f o r t h e s a me s e t o f j o i n t a n g l e s . I n g e n e r a l , t h e me a s u r e d a n d predicted pose will be different. 5 . M o d i f y t h e ki n e ma ti c p a r a me t e r s i n a n o r d e r l y ma n n e r i n o r d e r t o b e s t f i t ( i n a l e a s t s q u a r e s s e n s e ) t h e m e a s u r e d pose to the predicted pose. T he pro cess is a pplied not to a si n gle se t o f joi nt a ngles b ut to a n u mb e r o f j o i n t a n gl e s . T he to ta l n u mb e r o f j o i n t a n gl e s e t s r e q u i r e d , w h i c h a l s o e q u a l s t h e n u m b e r o f p h y s i c a l measurement made, must satisfy K p i s t h e n u mb e r o f k i n e ma t i c p a r a me t e r s t o b e i d e n t i f i e d N i s t h e n u m b e r o f m e a s u r e m e n t s ( p o s e s ) t a k e n D r r e p r e s e n t s t h e n u mb e r o f d e g r e e s o f f r e e d o m p r e s e n t i n each measurement. In the s ys te m d esc rib ed i n thi s pa per, the numb e r o f d e gr ee s of freedom is given by since full pose is meas ure d. In prac tice, ma ny more meas ure me nts s h o u l d b e t a k e n t o o f f s e t t h e e f f e c t o f n o i s e i n t h e e xp e r i me n t a l me a s u r e me n t s . T h e o p ti mi s a ti o n p r o c e d ur e u s e d i s kno w n a s ZX S S O , a nd i s a s ta nd a r d l i b r ar y f u nc ti o n i n t he IMSL package . Pose Measurement It i s ap p are nt fr o m the a b ov e tha t a me a ns to de ter mi ne the f u l l p o s e o f t h e P U M A i s r e q u i r e d i n o r d e r t o p e r f o r m t h e c a l i b r a ti o n. T hi s me t ho d w i l l no w b e d e s c r i b e d i n d e ta i l . T he e nd e ffe c to r c o nsi s ts o f a n a rr a nge me nt o f fi v e p re ci si o nto o li ng b a l l s a s s h o w n i n F i g . 5 . C o n s i d e r t h e c o o r d i n a t e s o f t he c e n tr e o f e a c h b a l l e x p r e s s e d i n te r ms o f t he t o o l fr a me ( F i g. 5 ) a n d t he w o r l d c o o r d i na te fr a me , a s s ho w n i n F i g . 6 . T h e r e l a t i o n s h i p b e t w e e n t h e s e c o o r d i n a t e s ma y b e w r i t t e n as: w h e r e P i 39。 i s t h e 4 x 1 c o l u mn v e c t o r o f t h e c o o r d i n a t e s o f t he i t h b a l l e xp r e s s e d w i t h r e s p e c t to t he w o r l d fr a me , P ~ i s t h e 4 x 1 c o l u m n v e c t o r o f t h e c o o r d i n a t e s o f t h e i t h b a l l expressed with respect to the tool frame, and T is the 4 ? 4 h o m o g e n i o u s t r a n s f o r m f r o m t h e w o r l d f r a m e t o t h e t o o l frame. T he n ma y b e fo u nd , a nd us e d a s t he me a s ur e d p o s e i n t he c a l ib r a ti o n p r o c es s . It i s no t q ui te t ha t s i mp l e , ho w e v e r, si nc e i t i s n o t p o s s i b l e t o i n v e r t e q u a t i o n ( 11 ) t o o b t a i n T. T h e a b o v e p r o c e s s i s p e r fo r me d f o r t h e fo u r b a l l s , A , B , C a n d D, and the positions ordered as: or in the form: S i n c e P 39。 , T a n d P a r e a l l n o w s q u a r e , t h e p o s e ma t r i x ma y be obtained by inversion: I n p r a c ti c e i t ma y b e d i ff i c u l t f o r t h e C M M t o a c c e s s f o u r b a i l s t o d e t e r mi n e P ~ w h e n t h e P U M A i s p l a c e d i n c e r t a i n c o nfi g ur a ti o ns . T hr e e b a l l s a r e a c tua l l y me a s ur e d a nd a fo ur t h ball i s fi c ti tio usl y l oca ted ac cor di ng to the ve c tor cr oss p rod uc t: R e g a r d i n g t h e d e t e r m i n a t i o n o f t h e c o o r d i n a t e s o f t h e c e n t r e o f a b a l l b a s e d o n me a s u r e d p o i n t s o n i t s s u r f a c e , n o a n a l y t i c a l p r o c e d u r e s a r e a v a i l a b l e . A n o t h e r n u me r i c a l o p ti mi s a ti o n s c he me w a s u s e d f o r t hi s p ur p o s e s uc h t h a t t he penalty function: w a s mi n i mi s e d , w h e r e ( u , v, w ) a r e t h e c o o r d i n a t e s o f t h e c e n t r e o f t h e b a l l t o h e d e t e r mi n e d , ( x / , y ~ , z ~ ) a r e t h e c o o r d i na te s o f t he i t h p o i n t o n t he s ur fa c e o f t he b a l l a nd r i s t h e b a l l d i a me t e r . I n t h e t e s t s p e r f o r me d , i t w a s f o u n d s u ffi c i e n t to me a s ur e o nl y f o ur p o i n ts ( i = 4 ) o n t he s ur fa c e to determine the ball centre