Iaoe?iiaeueia aeaaeai?y iaoe Oe?a?ie

Iaoe?iiaeueia eini?/ia aaaionoai Oe?a?ie

?inoeooo eini?/ieo aeine?aeaeaiue

E?ae TH??e Aaneeueiae/

OAeE 621.865.8

?IC?IAEA IIOEI?CAOe?EIEO IAOIAe?A AeINE?AeAEAIIss NEEAAeIEO
IAI?IOEssOe?EIEO NENOAI

01.05.04 — nenoaiiee aiae?c i oai??y iioeiaeueieo ??oaiue

aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

aeieoi?a o?ceei-iaoaiaoe/ieo iaoe

Ee?a — 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia a Ee?anueeiio oi?aa?neoao? ?iai? Oa?ana Oaa/aiea.

Iaoeiaee eiinoeueoaio — aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?
Ee?e/aiei Ieeiea Oaaei?iae/,

?inoeooo e?aa?iaoeee ?i.A.I.Aeooeiaa IAI Oe?a?ie, i?ia?aeiee
iaoeiaee niaoe?ae?no.

Io?oe?ei? iiiiaioe:

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

Aa?a’the A?eoi? ?aaaiiae/,
?inoeooo i?eeeaaeieo i?iaeai iaoai?ee ?
iaoaiaoeee ?i.ss.N.I?aeno?eaa/a IAI Oe?a?ie, caa?aeoaa/ a?aeae?eo;

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

E?oi?aiei Ai?en Ieeeoiae/,

Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea, caa?aeoaa/ eaoaae?e;

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

Iieioeei A’y/aneaa A?eai?iae/,
?inoeooo ee?oeiii? a?ieia?? oa aaiaoe/ii?
?iaeaia??? IAI Oe?a?ie, canooiiee aee?aeoi?a.

I?ia?aeia onoaiiaa — Oaeai?iaenueeee aea?aeaaiee oi?aa?neoao
I?i?noa?noaa ina?oe Oe?a?ie, iaoaiaoe/iee oaeoeueoao.

Caoeno a?aeaoaeaoueny «20» o?aaiy 1999?. i 15 aiaeei? ia
can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 26.205.01 a ?inoeooo?
eini?/ieo aeine?aeaeaiue IAIO oa IEAO, Ee?a-22, i?iniaeo Aeaaeai?ea
Aeooeiaa, 40.

C aeena?oaoe??th iiaeia iciaeiieoeny o a?o?a? ?inoeoooo eini?/ieo
aeine?aeaeaiue IAIO oa IEAO.

Aaoi?aoa?ao ?ic?neaiee «16» ea?oiy 1999?.

A/aiee nae?aoa?

niaoeiaeiciaaii? a/aii? ?aaee
I.I.Eonnoeue

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeena?oaoe?eia ?iaioa i?enay/aia ?ic?iaoe? iiaeo iaoiae?a aeine?aeaeaiiy
neeaaeieo iae?i?eieo aeeiai?/ieo aaaaoieaieiaeo iai?ioeyoe?eieo nenoai,
ye? aacothoueny ia i?aeoiaeao iaoai?ee, iaoiaeao oai??? iioeiaeueiiai
ea?oaaiiy, iioei?caoe??, e?i?eii? aeaaa?e, neiaieueieo ia?aoai?aiue oa
inaaaeiiaa?iaiue.

Aeooaeuei?noue ? nooi?iue ?ic?iaee oaiaoeee aeena?oaoe??. Iaiao?aei?noue
i?iaaaeaiiy aeine?aeaeaiue c oaiaoeee aeena?oaoe?? aeeeeeaia oe?ieei
canoinoaaiiyi, o ia?oo /a?ao, ?iaioioaoi?ee, yea aaco?oueny ia
aaaaoieaieiaeo iai?ioeyoe?eieo nenoaiao, o ??cieo aaeocyo ia?iaeiiai
ainiiaea?noaa: iaoeiiaoaeoaaii?, yaea?i?e i?iieneiaino?, eini?/i?e
oaoi?oe?, ia oe?aeeeaeo ? iaaacia/ieo ae?iaieoeoaao, ui aeiaaathoue
ye?niiai ? iaae?eiiai ooieoe?iioaaiiy, cia/ii? oaeaeeiae?? oa
aeiiii?/iino?, a oaeiae iaaeinoaoiueith ?ic?iaeith a?aeiia?aeieo
eiino?oeoeaieo oai?aoe/ieo canaae aeey aiae?co aaiiao?i-oiiieia?/ieo,
e?iaiaoe/ieo oa aeeiai?/ieo ia?aiao??a iai?ioeyoe?eieo nenoai c iaoith
iioeiaeueiiai, a?aeiinii iaaieo e?eoa???a, ?o aeai?o aeey aaoiiaoecaoe??
eiie?aoiiai ae?iaieoeoaa. Oea cia/iith i??ith aeooaeueii aeey Oe?a?ie ye
yaea?ii? oa eini?/ii? aea?aeaae c ?icaeiooith i?iieneia?noth. Oaeiai
oeio i?iaeaie aaaeei oi?iae?cothoueny, ine?eueee iio??aii iienaoe ye
ia’?eo aeine?aeaeaiiy, oae ? eiai ?iai/ee i?ino??, nieaioaaoe ae?? a
oeueiio i?inoi?? oa ?ic?aooaaoe iaiao?aei? ea?oaaiiy aeey ?oiuei?
?aae?caoe??. Aeei?enoaiiy iaaiiai oi?iae?cio iieno nenoaie iaiaaeo?oueny
?aieaie oiai eeano caaea/, ye? ca eiai aeiiiiiaith iiaeia iinoaaeoe ?
aeine?aeeoe. Iaoaiaoe/i? oi?iae?cie iieno iai?ioeyoe?eieo nenoai
cai?iiiiiaai? J.J.Uicker, J.Denavit, R.S.Hartenberg (canoinoaaiiy
iao?eoeue iaeii??aeieo eii?aeeiao), ?.I.Iiiiaei (aeei?enoaiiy aei/ieo
iao?eoeue), A.A.Ei?aiueiaei (aa?aaaoo oaa?aeeo o?e), I.Aoeia?aoiae/ai
(“neeaaeaiiy” aeaiaio?a ia’?eoo ia iniia? oi?ioe ?iae??ai) oa ?i.,
iathoue cia/io ia/enethaaeueio neeaaei?noue (e?euee?noue a?eoiaoe/ieo
iia?aoe?e, iaiao?aeio aeey ?aae?caoe??), iaaei??i?noue iieno ?
i???ioiaai?, a iniiaiiio, ia aeei?enoaiiy /enaeueieo iaoiae?a aeey
?ica’ycaiiy iinoaaeaieo caaea/. Oi?iae?cie no?oeoo?iaaiiai oa
no?oeoo?ii-ia?aiao?e/iiai iieno nenoai, cai?iiiiiaai? A.I.Aoaeeeii,
I.O.Ee?e/aieii, O.A.Aa?auaieii, aeicaieythoue aoaeoeaii iienoaaoe
nenoaio /a?ac ia?aiao?e ? no?oeoo?e i?aenenoai. I.O.Ee?e/aieii ?
O.I.Nii?iitheii ?ic?iaeai? iiae?ai? oi?iae?cie aeey nenoai c
?icaaeoaeaiiyie. A aeena?oaoe?ei?e ?iaio? aeei?enoiaothoueny oi?iae?cie,
aoaeoeai? c oi/ee ci?o i?aai?caoe?? ia/eneaiue ? i???ioiaai? ia
/enaeueii-aiae?oe/i? oa iioei?caoe?ei? iaoiaee ae??oaiiy iinoaaeaieo
caaea/.

Aeey i?iaeai ieaioaaiiy noai?a iai?ioeyoe?eieo nenoai ?c cia/iith
e?euee?noth eaiie (a?eueoa oanoe) io?eiaoe yaiee ?ica’ycie /a?ac
iaaei??i?noue ia caaaeaee iiaeeeai, oiio aeieea? iaiao?aei?noue ?ic?iaee
aoaeoeaieo iioei?caoe?eieo iaoiae?a, ye? aeicaieythoue ?ica’ycaoe oeth
caaea/o aeey aeia?eueii? nenoaie. Aaaeeeai ciaeoe anth iiiaeeio
iiaeeeaeo ?ica’yce?a c iaoith iiaoaeiae ? aiae?co aeinyaeiino? ?iai/iai
i?inoi?o ? iiaeeeaino? aeeiiaiiy iaaieo oaoiieia?/ieo iia?aoe?e.

Ca?eueoaiiy oaeaeeiae?? oa oi/iino? aeeiiaiiy caaeaieo iia?aoe?e,
ciaioaiiy aia?aaoe/ieo aeo?ao aeiaaa? aeei?enoaiiy aeeiai?/ieo
aeanoeainoae nenoaie. Iaoiaee iiaoaeiae iaoaiaoe/ieo iiaeaeae aeeiai?ee
iai?ioeyoe?eieo nenoai, ?ic?iaeai? ?.Iieii, I.Aoeia?aoiae/ai,
A.O.Aa?auaa?iei, ?.A?ooaiao?aii, O.I.Eoeaeiaei, J.M.Hollerbach, C.S.G.
Lee, M.Shahinpoor, J.Y.S.Luh, A.K.Bejczy, M.W.Walker, D.E.Orin,
C.P.Neuman, W.Schielhen, K.S.Fu oa ?ioeie a/aieie, aaciaai? ia
i?eioeeiao eeane/ii? iaoai?ee — ??aiyiiyo Iuethoiia-Aeea?a, ??aiyiiyo
Eaa?aiaea I ?iaeo, i?eioeeiao Aeaeaiaa?a, Aaonna — oaeiae cia/iith
i??ith iai?aaeai? ia ?aae?caoe?th /enaeueieie iaoiaeaie. Iaeiae, oaeee
i?aeo?ae ia aeicaiey? a?aeie?aieoe aoai iiaoaeiae ??aiyiue aeeiai?ee
a?ae aeei?enoaiiy inoaii?o o caaea/ao aiae?co ? neioaco, io?eiaoe
ia/enethaaeueio neeaaei?noue iiaoaeiae iiaeae? eiie?aoii?
iai?ioeyoe?eii? nenoaie, i?iaiae?coaaoe aieea neeaaeiaeo /anoei ??aiyiue
ia nenoaio a oe?eiio ?, oei naiei, iiaoaeoaaoe aoaeoeai? aeai?eoie
ea?oaaiiy. A oeueiio iai?yieo aaeeeee iioaioe?ae iathoue iaoiaee,
iniiaai? ia ?ic?iaoe? aai aeei?enoaii? neiaieueieo nenoai (REDUCE,
MACSYMA, MATHEMATICA oa ?io.) aeey iiaoaeiae /enaeueii-aiae?oe/ieo
i?ioeaaeo? oi?ioaaiiy ??aiyiue aeeiai?ee (I.Aoeia?aoiae/, Leu M.C.,
V.D.Tourassis, C.P.Neuman, S.Dubowsky, J.L.Grant, Khalil W., Homati N.,
Cheng P.-Y., oa ?i.). Nooo?aei iaaeie?eii oeeo iaoiae?a ? oa, ui aiie
iaaeinoaoiuei aeei?enoiaothoue niaoeeo?eo ia’?eoo aeine?aeaeaiue ?,
iacaaaeath/e ia iaaaeeeo ia/enethaaeueio neeaaei?noue, iathoue
iaaei??i?noue ia/eneaiue, oiio ?ic?iaea iaoiae?a oa aeai?eoi?a iiaoaeiae
??aiyiue ?ooo a /enaeueii-aiae?oe/i?e oi?i? c i?i?i?caoe??th ia/eneaiue
? aeooaeueiith.

Aeey aiae?co e neioaco nenoai ea?oaaiiy ?ooii o ?aaeei? ?aaeueiiai /ano
aeei?enoaiiy a?aeiieo iaoiae?a aeine?aeaeaiiy nenoai ea?oaaiiy —
iioeiaeueiiai ea?oaaiiy, iae?i?eiiai ea?oaaiiy, e?iaa?ecaoe??,
aaeaioeaiiai ea?oaaiiy (?.I.Iiiia, A.N.Iaaeaaae?a, ?.?.TH?aae/,
I.Aoeia?aoiae/, ?.Iie, I.Ae.E?ooueei, O.E.*a?iionueei, A.?.Aa?a’the,
A.A.Ea??i, S.Dubowsky, A.J.Koivo, Naremdra K.S., Kelly R., Lee C.S.G.,
Luh J.Y.S., Mikhailov L.K., Sadegh N., Seraji H., C.Y.Wu, K.D.Young oa
aaaaoi ?ioeo a/aieo) — /a?ac neeaaei?noue ? iae?i?ei?noue aeeiai?ee
i?ecaiaeeoue aei cia/ieo oneeaaeiaiue. Oiio ia?niaeoeaieie ? i?aeoiaee,
iniiaai? ia ciaiiyo c o?c?ieia?? ?oo?a ethaeeie (I.I.Aa?iooaei,
I.E.Aiio?i, I.E.Oeaoe?i oa ?io.) — iaoiaee iaa/aeueiiai oeio(learning
control), eii?aeeiaoe?? (S.Arimoto, J.S.Albus, S.-R.O.Z.Bien, W.T.Miller
III, E.G.Harokopos, Kawamura S., A.I.E?oi?aiei oa ?i.), ye?
aeicaieythoue cae?enieoe ni?iuaiiy iiaeaeae, aeae?eeoe iaea?eueo nooo?a?
aeaiaioe ?ooo ? ?aae?coaaoe ea?oaaiiy a ?aaeei? ?aaeueiiai /ano.

Oaeei /eiii, ?ic?iaea iioei?caoe?eieo iaoiae?a aeine?aeaeaiiy neeaaeieo
iai?ioeyoe?eieo nenoai, iniaeeai iai?ioeyoe?eieo ?iaio?a, ? aeooaeueiith
ye c oai?aoe/ii?, oae ? c i?aeoe/ii? oi/ie ci?o.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. ?acoeueoaoe
aeine?aeaeaiue, iaaaaeai? a aeena?oaoe??, oa?eoee neeaaeiaith /anoeiith
aei i?iaeo?a AeEIO Oe?a?ie “?icaeoie eiino?oeoeaii? oai??? iiaeaethaaiiy
oa iioeiaeueiiai ea?oaaiiy neeaaeieo nenoai c iaiiaieie aeaieie” (?
1/806, 1992-1994??., ? 1.2.3/4, 1994-1996??., ? 1.4/347, 1997-1998??.),
“?ic?iaea i?iaeaiii-i???ioiaaieo iaoaiaoe/ieo ? i?ia?aiieo cania?a
iiaeaethaaiiy, aiae?co oa neioaco ea?iaieo o?ceei-iaoai?/ieo nenoai”
(?6.3/1589, 1997-1998??.). Aeena?oaoe?eia ?iaioa /anoeiai aoea
i?aeo?eiaia I?aeia?iaeiith Ni?in?anueeith i?ia?aiith a aaeoc? oi/ieo
iaoe (ISSEP), a?aio ? APU051055.

Iaoa ? caaea/? aeine?aeaeaiiy iieyaathoue o ?ic?iaoe? iioei?caoe?eieo
iinoaiiaie caaea/ ? iaoiae?a nenoaiiiai aiae?co aaiiao?i-oiiieia?/ieo
ia?aiao??a, ieaioaaiiy oa ioe?iee noai?a, iiaoaeiae iaeanoae
aeinyaeiino?, ?ic?aooieo o?a?eoi??e oa i?aai?caoe?? ?oo?a, oi?ioaaiiy
iaoaiaoe/ieo iiaeaeae a /enaeueii-aiae?oe/iiio aeaeyae? c i?i?i?caoe??th
ia/enethaaeueii? neeaaeiino?, aeeiai?ee ? ea?oaaiiy neeaaeieie
iae?i?eieie iai?ioeyoe?eieie nenoaiaie.

Iaoeiaa iiaecia. O aeena?oaoe?? iniaenoi aaoi?ii iaea?aeaii oae? iia?
?acoeueoaoe:

— aeiaaaeaii oai?aie i?i aeae?eaiiy a aeaiaioao iaoaiaoe/ieo iiaeaeae
aeeiai?ee iai?ioeyoe?eieo nenoai noaei? /anoeie, caeaaeii? a?ae
ianiiiiaioieo ia?aiao??a ? ia/enethaaii? apriori, oa ci?iii?, caeaaeii?
a?ae ocaaaeueiaieo eii?aeeiao nenoaie;

— aia?oa ?ic?iaeaii iaoiae aeaeiiiiceoe?? iai?ioeyoe?eieo nenoai ia
nenoaie ??cieo ?ici??iinoae;

— aia?oa aeiaaaeai? oai?aie i?i i?aaenoaaeaiiy aeaiaio?a ??aiyiue
aeeiai?ee iai?ioeyoe?eieo nenoai, iaeneiaeueii ca?oiiaaieo c aeae?eaiiyi
iao?eoeue niaoe?aeueiiai aeaeyaeo;

— iieacaii, ui oi?ioaaiiy aeaiaio?a ??aiyiue aeeiai?ee cae?enith?oueny
iioeiaeueiei niiniaii ? caiaeeoueny aei aeaio aaciaeo iia?aoe?e
iao?e/ieo aeiaooe?a, ye? ia/eneththoueny i?i?iaeueiith e?euee?noth
a?eoiaoe/ieo iia?aoe?e iiiaeaiiy ? aeiaeaaaiiy;

— aia?oa cae?eniaii nenoaiiee aiae?c ca e?eoa???i ia/enethaaeueii?
neeaaeiino? oe?eeo eean?a iai?ioeyoe?eieo nenoai;

— aeey caaea/ aiae?co oa iiaoaeiae iaeanoae aeinyaeiino? aeiaaaeai?
oai?aie c oiiaaie aeinyaeiino? oa eieaeueii? aeinyaeiino? noai?a
iai?ioeyoe?eieo nenoai;

— ?ic?iaeaii iioei?caoe?ei? iaoiaee aeai?o aaiiao?i-oiiieia?/ieo
ia?aiao??a iai?ioeyoe?eieo nenoai ca e?eoa??yie aeinyaeiino? iaaieo
iiiaeei oi/ie oa iaeanoae;

— cai?iiiiiaaii iia? iaoiaee ?ica’ycoaaiiy caaea/ aeine?aeaeaiiy
??aiiaaaeieo noai?a;

— ?ic?iaeaii aoaeoeai? aeai?eoie ?ica’ycaiiy caaea/ aeeiai?ee ?
iiaoaeiae i?ia?aiieo o?a?eoi??e iai?ioeyoe?eieo nenoai;

— ia iniia? ?ic?iaeaieo iioei?caoe?eieo oa /enaeueii-aiae?oe/ieo
iaoiae?a cai?iiiiiaaii aia?oa eii?aeeiaoe?eiee i?aeo?ae aei i?aai?caoe??
?oo?a iai?ioeyoe?eieo nenoai.

Oai?aoe/ia ? i?aeoe/ia oe?ii?noue iaea?aeaieo ?acoeueoao?a iieyaa? a
oiio, ui: aeey neeaaeieo aaaaoieaieiaeo iai?ioeyoe?eieo nenoai
?ic?iaeaii iiaee iaoiae iiaoaeiae iaoaiaoe/ieo iiaeaeae aeeiai?ee c
i?i?i?caoe??th ia/enethaaeueii? neeaaeiino?, yeee aeicaiey?
aeine?aeaeoaaoe a?aeii? iai?ioeyoe?ei? nenoaie oa i?iaeooaaoe iia? c
iaaieie aeanoeainoyie, aeei?enoiaoaaoe aeeiai?eo a caaea/ao aiae?co oa
neioaco nenoai ea?oaaiiy a ?aaeei? ?aaeueiiai /ano; ia iniia?
cai?iiiiiaaiiai iaoiaeo i?iaiae?ciaaii eean iai?ioeyoe?eieo nenoai c
o?noueiia nooiaiyie ?ooeeaino?, aea ?c caaaeueii? e?eueeino? 729
iiaeeeaeo e?iaiaoe/ieo noai aeae?eai? 42 noaie, ye? noaiiaeyoue
i?aeoe/iee ?ioa?an; io?eiai? ?ica’ycee caaea/ noaoeee oa ieaioaaiiy
eieaeueieo noai?a ? o?a?eoi??e ?ooo; cae?eniaii aiae?c iaeanoae
aeinyaeiino? eaiie nenoaie; cai?iiiiiaai? iaoiaee ? eiino?oeoeaieie ?
iiaeooue aaciina?aaeiuei canoiniaoaaoenue o NAI? iai?ioeyoe?eieo nenoai.

Ioae?eaoe?? oa iniaenoee aianie caeiaoaa/a. ?acoeueoaoe aeena?oaoe??
iioae?eiaai? o iiiia?ao??, iaa/aeueiiio iin?aieeo, 10 noaooyo o iaoeiaeo
aeo?iaeao, 7 noaooyo o ca??ieeao iaoeiaeo i?aoeue, iaoa??aeao oa oacao
12 eiioa?aioe?e. An? iniiai? ?acoeueoaoe aeena?oaoe?? iaea?aeai? aaoi?ii
iniaenoi ? aeinoaoiuei a?aeia?aaeai? a ?iaioao [1-18]. O iiiia?ao?? [1]
aaoi?ii iaienai? ia?aa?aoe 1.1, 1.3-1.5, 2.1, 2.3, 2.5, 5.1, 5.3, 5.4,
?icae?ee 4, 6; o [2] — ia?aa?aoe 1, 4, 7 ?icae?eo 1; 4, 5 ?icae?eo 2,
?icae?e 3; a ?iaioao [3,4] aaoi?o iaeaaeaoue iioei?caoe?ei? iinoaiiaee
caaea/, ?ic?iaea aeai?eoi?a oa i?ia?ai ?aae?caoe??; a [8] — ?ic?iaea
iaoiaeo iiaoaeiae i?ia?aiieo ?oo?a, a [10] — ?aea? iaoiaeo oi?ioaaiiy
??aiyiue aeeiai?ee; a ?iaioao [15],[17] — ?aea? caaaeaiiy aei
iioei?caoe?eieo caaea/ oa iaoiaee ?o ?ica’ycaiiy.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iniiai? ?acoeueoaoe ?iaioe
aeiiia?aeaeenue ? iaaiai?thaaeenue ia Nueii?e Ananithci?e eiioa?aioe??
“Oi?aaeaiea a iaoaie/aneeo nenoaiao” (Naa?aeeiane, 1990?.),
I?aeia?iae-iiio nai?ia?? “Multi-arm robot manipulators” (??eoonuee,
1991?.), neiiic?oi? ”Symposium on Optimal Control of Mechanical Systems”
(Iineaa, 1992?.), eiioa?aioe?? “Iiaeaee?iaaiea e enneaaeiaaiea
onoie/eainoe i?ioeannia” (Ee?a, 1992?.), neiiic?oi? “Ieoaiiy
iioei?caoe?? ia/eneaiue” (Ee?a, 1993?.), Ia?o?e Oe?a?inuee?e
eiioa?aioe?? c aaoiiaoe/iiai ea?oaaiiy “Aaoiiaoeea-94” (Ee?a, 1994?.),
Anaoe?a?inuee?e iaoeia?e eiioa?aioe?? “Canoinoaaiiy ia/enethaaeueii?
oaoi?ee, iaoaiaoe/iiai iiaeaethaaiiy oa iaoaiaoe/ieo iaoiae?a o iaoeiaeo
aeine?aeaeaiiyo” (Euea?a, 1995?.), Ae?oa?e Oe?a?inuee?e eiioa?aioei? c
aaoiiaoe/iiai ea?oaaiiy “Aaoiiaoeea-95” (Euea?a, 1995?.), Oe?a?inueeeo
eiioa?aioe?yo “Iiaeaethaaiiy ? aeine?aeaeaiiy no?eeino? nenoai” (Ee?a,
1994, 1996, 1997??.), Anaoe?a?inuee?e eiioa?aioe??
“Aeeoa?aioe?aeueii-ooieoe?iiaeuei? ??aiyiiy oa ?o canoinoaaiiy”
(*a?i?aoe?, 1996?.), I’yo?e Oe?a?inuee?e eiioa?aioe?? c aaoiiaoe/iiai
oi?aae?iiy “Aaoiiaoeea-98” (Ee?a, 1998?.), nai?ia?? “Aeeiai?ea oa
iioei?caoe?y ea?iaaieo nenoai” ?inoeoooo i?eeeaaeieo i?iaeai iaoai?ee ?
iaoaiaoeee IAI Oe?a?ie ?i.ss.N.I?aeno?eaa/a (ea??aiee — ae.o.-i.i.,
i?io. Aa?a’the A.?.), nai?ia?ao eaoaae?e iaoaiaoe/ieo i?iaeai ea?oaaiiy
? e?aa?iaoeee *a?i?aaoeueeiai oi?aa?neoaoo ?i. TH??y Oaaeueeiae/a
(ea??aiee — ae.o.-i.i., i?io. Nii?iithe O.I.), nai?ia?ao “Iiaeaethaaiiy
oa iioei?caoe?y nenoai” eaoaae?e iiaeaethaaiiy neeaaeieo nenoai
Ee?anueeiai oi?aa?neoaoo ?i.Oa?ana Oaa/aiea (ea??aiee — /e.-ei?. IAI
Oe?a?ie Aoaeee A.I.), nai?ia?? “Aeene?aoi? nenoaie ea?oaaiiy” ?inoeoooo
eini?/ieo aeine?aeaeaiue IAIO oa IEAO (ea??aiee — aeaaeai?e IAI Oe?a?ie
Eoioeaae/ A.I.), i?ae /an ia?aaoaaiiy ia noaaeoaaii? o E?euenueeiio
oi?aa?neoao? (New Hawen, NOA, 1998?.).

No?oeoo?a oa ianya aeena?oaoe??. Aeena?oaoe?eia ?iaioa neeaaea?oueny c?
anooio, i’yoe ?icae?e?a, aeniiae?a, nieneo aeei?enoaieo aeaea?ae, ui
ia?aoiao? 206 iaeiaioaaiue, oa aeiaeaoeo ? aeeth/a? 8 ?enoie?a oa 7
oaaeeoeue. Iiaiee ia’?i aeena?oaoe?? 260 noi??iie.

Ci?no ?iaioe

O anooi? iiaeaii caaaeueio oa?aeoa?enoeeo aeena?oaoe??: ?ice?eoi
nooi?noue oa noai iaoeiai? i?iaeaie; iaa?oioiaaii iaiao?aei?noue
i?iaaaeaiiy ? a?aecia/aii aeooaeuei?noue aeine?aeaeaiiy; noi?ioeueiaaii
iaoo ?iaioe; aiiiniaaii iiaecio iaea?aeaieo ?acoeueoao?a oa ?o
oai?aoe/ia ? i?aeoe/ia cia/aiiy.

O ia?oiio ?icae?e? a?aecia/a?oueny, ui ia’?eoii aeine?aeaeaiiy
aeena?oaoe?eii? ?iaioe ? iai?ioeyoe?ei? nenoaie, ye? neeaaeathoueny c
iiiaeei oaa?aeeo o?e, iine?aeiaii c’?aeiaieo ?aeaaeueieie ea?iaaieie
e?iaiaoe/ieie ia?aie V eeano, aea?oueny iaeyae e?oa?aoo?ieo aeaea?ae,
aea/athoueny iniiai? i?aeoiaee ? iaoiaee aeine?aeaeaiiy oaeeo nenoai,
cie?aia aeei?enoaiiy iaaieo iaoaiaoe/ieo oi?iae?ci?a iieno, iiaoaeiae
iaoaiaoe/ieo iiaeaeae aeeiai?ee oa ea?oaaiiy, aiae?cothoueny iaea?aeai?
?acoeueoaoe c ia?ae?eii ?o iaaeie?e?a, ia?aaaa ? oeyo?a iiaeaeueoiai
?icaeoeo, a oaeiae oi?ioeththoueny iniiai? caaea/? aeine?aeaeaiue.

O ae?oaiio ?icae?e? iaaiaeeoueny, iniiaaiee ia ??aiyiiyo Eaa?aiaea I
?iaeo, /enaeueii-aiae?oe/iee i?aeo?ae aei oi?ioaaiiy ??aiyiue aeeiai?ee
iai?ioeyoe?eieo nenoai o aeaeyae?

, (1)

— ianiiiiaioi? ia?aiao?e eaiie.

Aeey oeueiai ?ic?iaey?oueny iaoiae ?icae?eaiiy ia noaeo oa ci?iio
/anoeie i?e ciaoiaeaeaii? aia?aaoe/ieo oa?aeoa?enoee, a ?acoeueoao?
yeiai aoaeothoueny aeaiaioe nenoaie (1) (oai?aie 2.4-2.7) [1,5,6,10-12]:

, (2)

, (3)

, (4)

, (5)

(6)

, (7)

, (8)

Oaeei /eiii, a aeaiaioao nenoaie (1) aeae?eaia /anoeia (7), (8),
caeaaeia a?ae noaeeo aaee/ei iai?ioeyoe?eii? nenoaie ? yeo iiaeia
ia/eneeoe apriori, oa /anoeia (5), (6), caeaaeia a?ae ocaaaeueiaieo
eii?aeeiao nenoaie ? yeo o?aaa ia/enethaaoe ca eiaeii? ci?ie inoaii?o. A
ianooiieo i?ae?icae?eao aea/athoueny aeanoeaino? oa iaaiaeeoueny
aeai?eoi iiaoaeiae a yaiiio aiae?oe/iiio aeaeyae? o?eaiiiiao?e/ieo
neeaaeiaeo ??aiyiue aeeiai?ee (1).

Aeae? a aeena?oaoe?ei?e ?iaio? ?ic?iaey?oueny iaoiae aeaeiiiiceoe??
[1,12] iai?ioeyoe?eii? nenoaie, yeee aeicaiey? iiaoaeoaaoe iia?
aoaeoeai? aeai?eoie oi?ioaaiiy aeaiaio?a ??aiyiue ?ooo (1). A?i
aaco?oueny ia oiio, ui ine?eueee iai?ioeyoe?eia nenoaia iieno?oueny
iine?aeiai?noth e?iaiaoe/ieo ia?, oi, aeae?eeaoe iaaiee iaia?a?aiee
eaioetha oe??? iine?aeiaiino? ? caeeoath/enue a ?aieao oi?iae?ci?a
iieno, oaeiae iaea?aeeii iai?ioeyoe?eio nenoaio, o?eueee iaioi?
?ici??iino?.

.

. (9)

. Oiae?

. (10)

aeo?aeii? nenoaie.

, ye? aeania iio??aii ia/eneeoe, aoaeooue aeiaooee iao?eoeue

, (11)

oiae? ye ?aooa aeaiaio?a aaea ia/eneaia aeey iai?ioeyoe?eieo nenoai
iaioi? ?ici??iino?, aeae?eaieo c aaciai?.

?en. 1.

Aeaeiiiiceoe?y iai?ioeyoe?eii? nenoaie ia nenoaie iaioi? ?ici??iino?
aeicaiey? iiaoaeoaaoe aoaeoeaiee iaoiae oi?ioaaiiy aeaiaio?a nenoaie (1)
ca n e?ie?a. Eiai nooue iieyaa? a oiio, ui ia eiaeiiio e?ioe?
ia/eneththoueny o?eueee aeaiaioe nenoai a?aeiia?aeii? ?ici??iino? ? aiie
aeiaeathoueny aei aaea ia/eneaieo aeaiaio?a:

, i?e/iio aiie aoaeooue ??ciiai oeeaaeaiiy — a?ae 1-ai aei k-ai.

Aei caae?yieo ia oeueiio e?ioe? /eai?a iao?eoe? nee ?ia?oe??
aeiaeathoueny oae? aeaiaioe: aeey ae?aaiiaeueieo

(12)

aeey iaae?aaiiaeueieo

(13)

Oaeei /eiii, iaaaaeaiee iaoiae aea? iiaeeea?noue ca n e?ie?a iaea?aeaoe
/eaie iao?eoe? nee ?ia?oe?? iai?ioeyoe?eii? nenoaie ?ici??iino? n.
Eiaeiee /eai oi?io?oueny ?oa?aoe?eiei niiniaii, ui iaaaaaoi ni?iuo?
aiae?c ? a?oioaaiiy aeaiaio?a. Ia eiaeiiio e?ioe? o?aaa ia/eneeoe
o?eueee iaiao?aeio /anoeio aeiaooe?a, a e?euee?noue /eai?a, oe?eeii
ciaeaeaieo ia e?ioe?, aei??aith? iiia?o e?ieo.

Ia iniia? iaoiaeo aeaeiiiiceoe?? o o?aoueiio ?icae?e? ?ic?iaey?oueny
iaoiaeeea ? aeiaiaeyoueny a?aeiia?aei? oai?aie i?i oi?ioaaiiy ??aiyiue o
no?oeoo?iaaiiio ? iaeneiaeueii ca?oiiaaiiio aeaeyae?.

(1), o a?aeiia?aeiino? aei iaoiaeo aeaeiiiiceoe??, aoaeothoueny ca
ianooiieie oi?ioeaie

(14)

(15)

(16)

Oai?aia 3.2. Iaae?aaiiaeuei? aeaiaioe iao?eoe? nee ?ia?oe?? aoaeothoueny
ca ianooiieie oi?ioeaie

(17)

(18)

(19)

(20)

(21)

(22)

(23)

iao?eoeue a?aeoeaio?iaeo nee ni?aaaaeeeai

(24)

(25)

(26)

(27)

(28)

(29)

iao?eoe? a?aeoeaio?iaeo nee iai?ioeyoe?eii? nenoaie (1) aoaeothoueny
ca ianooiieie ni?aa?aeiioaiiyie

(30)

(31)

(32)

(33)

(34)

(35)

— iao?eoe? niaoe?aeueiiai aeaeyaeo, o yeeo o?eueee aeaa aeaiaioe
aei??aiththoue iaeeieoe?, ?aooa — ioeth.

, ni?aaaaeeea? ianooii?

. (36)

(37)

(38)

.

Oai?aia 3.8. Aeaiaioe aaeoi?a a?aa?oaoe?eieo nee ia/eneththoueny ca
oi?ioeaie

, (39)

,

(40)

(41)

. I?i?i?caoe?y e?eueeino? ia/eneaiue aeinyaa?oueny i?e ciaoiaeaeaii?
iia?aoe?? ne?aeo c o?aooaaiiyi aeaeyaeo iao?eoeue ? ia/eneaii? aaciaeo
aeiaooe?a iao?eoeue i?i?iaeueiith e?euee?noth a?eoiaoe/ieo iia?aoe?e
iiiaeaiiy ? aeiaeaaaiiy.

A ianooiiiio i?ae?icae?e? ?icae?eo 3 aeine?aeaeo?oueny ? aiae?co?oueny
ia/enethaaeueia neeaaei?noue oi?ioaaiiy ??aiyiue aeeiai?ee (1) aeey
iai?ioeyoe?eieo ?iaio?a o /enaeueii-aiae?oe/iiio aeaeyae? ia iniia?
iaoiaeo aeaeiiiiceoe?? [16,18]. Ine?eueee ia/enethaaeueia neeaaei?noue
oi?ioaaiiy ??aiyiue aeeiai?ee cai?iiiiiaaiei iaoiaeii caeaaeeoue a?ae
eiie?aoii? e?iaiaoe/ii? noaie iai?ioeyoi?a ? eiai ianiiiiaioieo
ia?aiao??a, oi ca iniiao aea?aii eean iai?ioeyoe?eieo ?iaio?a c
o?noueiia ? iaioa nooiaiyie ?ooeeaino?. Iaiaaeeiiny eeanii e?iaiaoe/ieo
noai o?eueee c iiai?ioieie c’?aeiaiiyie ? iicia/eii oeeo?ith 1 iaa?oaiiy
eaiee iaaeiei in? IO, oeeo?ith 2 — iaaeiei in? IO, oeeo?ith 3 — iaaeiei
in? OZ ?, oaeei /eiii, e?iaiaoe/io noaio iai?ioeyoi?a aoaeaii caienoaaoe
iine?aeiai?noth oeeo? — 1,2 /e 3. Aeey oanoeeaieiaeo iai?ioeyoi??a
caaaeueia e?euee?noue e?iaiaoe/ieo noai a oeueiio eean? aoaea 36=729.
Ine?eueee, ye i?aaeei, aeey iai?ioeyoe?eieo ?iaio?a ia?oa ? inoaiiy
eaiee iaa?oathoueny iaaeiei in? IO ? ca oiiae, ui i?ye? o?e eaiee
i?ae?yae ia iiaeooue iaoe iaeiaeiaiai nooiaiy ?ooeeaino?, io?eia?ii 42
noaie, aeei?enoaiiy yeeo ia? i?aeoe/iee ?ioa?an. Aeey oeeo noai
iiaoaeo?ii ??aiyiiy aeeiai?ee (1) a /enaeueii-aiae?oe/iiio aeaeyae? ?
aeine?aeeii ?oith ia/enethaaeueio neeaaei?noue (aeea. oaae.1).

?c aiae?co ?acoeueoao?a oaae.1, aeieeaa? ua iaeia iiaa nooo?aa
aeanoea?noue ??aiyiue aeeiai?ee, a naia: e?iaiaoe/i? noaie, neiao?e/i?
a?aeiinii iiai?io?a iaaeiei inae OY i OZ, iathoue iaeiaeiao
ia/enethaaeueio neeaaei?noue. Oiaoi c oi/ee ci?o aiae?co
ia/enethaaeueii? neeaaeiino? cai?iiiiiaaiei /enaeueii-aiae?oe/iei
iaoiaeii aeineoue aeine?aeeoe o?eueee 21 e?iaiaoe/i? noaie
iai?ioeyoe?eieo nenoai, a oea oe?eeii ?aaeueia ? cae?eniaiia caaea/a.

Oaaeeoey 1. Ia/enethaaeueia neeaaei?noue oi?ioaaiiy ??aiyiue aeeia-

i?ee aeey oanoeeaieiaeo iai?ioeyoi??a (+ -aeiaeaaaiiy, * —
iiiaeaiiy).

MP-6 + * MP-6 + *

112131 169 173 113121 169 173

112231 167 153 113321 167 153

112331 178 155 113221 178 155

112321 204 200 113231 204 200

112311 165 154 113211 165 154

121131 196 198 131121 196 198

121331 247 251 131221 247 251

121311 239 253 131211 239 253

121321 283 308 131231 283 308

121231 283 308 131321 283 308

122311 232 224 133211 232 224

122321 278 283 133231 278 283

122131 243 256 133121 243 256

123121 306 334 132131 306 334

123131 306 334 132121 306 334

123211 290 295 132311 290 295

123311 246 219 132211 246 219

122331 240 216 133221 240 216

123231 341 362 132321 341 362

123221 293 285 132331 293 285

123321 287 271 132231 287 271

A ?iaio? aeey oeeo e?iaiaoe/ieo noai aea?oueny ia/enethaaeueia
neeaaei?noue iiaoaeiae eiaeii? neeaaeiai? ??aiyiue (1). Iieacaii, ui
aeecueei aeaio o?aoei caeiathoue ia/eneaiiy ei??ie?niaeo nee, iaeaea
iieiaeio — ?ia?oe?ei? neee. sseui eaiee iai?ioeyoi?a ? neiao?eciaaieie
o?eaie, oi ia/enethaaeueia neeaaei?noue ciaioeoueny i?eaeecii ia
o?aoeio. A?aecia/a?oueny, ui ia/enethaaeueia neeaaei?noue
i?iaiae?ciaaieo e?iaiaoe/ieo noai aaciina?aaeiuei caeaaeeoue a?ae oeio
e?iaiaoe/ieo ia? c’?aeiaiiy oa?i???a ? ?icoaooaaiiy iaeiaeiaeo nooiai?a
?ooeeaino? a e?iaiaoe/i?e noai? iai?ioeyoe?eiiai ?iaioa. Ia
ia/enethaaeueio neeaaei?noue o cia/i?e i??? aieeaathoue ianiiiiaioi?
ia?aiao?e eaiee.

*aoaa?oee ?icae?e aeena?oaoe?eii? ?iaioe i?enay/aii ?ic?iaoe?
iioei?caoe?eieo iaoiae?a aaiiao?i-noaoe/iiai aiae?co ? neioaco neeaaeieo
iai?ioeyoe?eieo nenoai.

caaeathoue caeii ?ooo n-oi? eaiee iai?ioeyoe?eii? nenoaie. Oe?
ooieoe?? caeaaeaoue a?ae ocaaaeueiaieo eii?aeeiao oae, ui

(42)

— nooue ?ica’ycee caaea/ Eio?

(43)

(44)

. (45)

Ciaeaeaii /anoeii? iio?aei? ocaaaeueiaieo eii?aeeiao, nei?enoaa-oenue
aeey oeueiai nenoaiith ni?yaeaieo ??aiyiue:

aea ((i) — iao?eoe?, ui caaeiaieueiythoue nenoai?:

C (42), aeey aeeoa?aioe?eiaieo ooieoe?e aeieeaa?, ui

, (46)

? aaeoi?aie noaio oa e?iaiaoe/ii? noaie iai?ioeyoe?eii? nenoaie. Aeey
e?iaiaoe/ieo noai c iaaei??i?noth, aeey ciaoiaeaeaiiy ?ica’yceo caaea/?
iaa?iaiiai ieaioaaiiy noai?a aeei?enoiao?oueny iaoiae aeeiai?/iiai
i?ia?aioaaiiy.

Aeey iaoaiaoe/ii? iinoaiiaee caaea/? ciaoiaeaeaiiy iioeiaeueieo
aaiiao?i-oiiieia?/ieo ia?aiao??a iai?ioeyoe?eii? nenoaie
ni?aa?aeii-oaiiy (43)-(45) ia?aieoaii o oaeiio aeaeyae? [1,17]:

, (47)

(48)

(49)

. (50)

caaeaia /enei.

iiaeia aoaeoaaoe ??ci? e?iaiaoe/i? noaie nenoaie. Aaaaeaii ooieoe?iiae

, (51)

.

Oiae? caaaeueio caaea/o ciaoiaeaeaiiy iioeiaeueieo ia?aiao??a
iai?ioeyoe?eii? nenoaie, ye? iaenei?cothoue ?ici?? ?iai/i? iaeano? a
caaeaieo iai?yieao ? aeicaieythoue aeoiaeeoe a caaeai? oi/ee aeaii?
iaeano?, iiaeia noi?ioethaaoe oae: ciaeoe

(52)

ca iaiaaeaiue (47)-(49).

Aeey ciaoiaeaeaiiy iioeiaeueieo cia/aiue ia?aiao??a iai?ioeyoe?eii?
nenoaie aeei?enoiaothoueny iioei?caoe?ei? i?ioeaaeo?e.

A i?ae?icae?e? 4.3, aeei?enoiaoth/e iiiyooy oai??? iioeiaeueiiai
ea?oaaiiy, iaaiaeyoueny aeaye? i?aeoiaee aei aiae?co oa iiaoaeiae
iaeanoae aeinyaeiino? iai?ioeyoe?eieo nenoai [1-3].

n-oi? eaiee iai?ioeyoe?eii? nenoaie iacaaii aeinyaeiei, yeui eiai
iiaeia ?aae?coaaoe ca iaaieo cia/aiue ocaaaeueiaieo eii?aeeiao.

oe??? eaiee aeinyaeiee.

.

? oe?eeii aeinyaeiee.

aaeoi? i?aeoiaeo iiaeia ci?ithaaoe, caeeoath/e i?e oeueiio aac ci?i
aaeoi?e iieiaeaiiy oa i???ioaoe??.

Aeey aeine?aeaeaiiy iaeanoae aeinyaeiino? ?icaeyaeathoueny iine?aeiaii
eiai non?aei? c’?aeiaiiy (j-1) oa (j), j=1,n. Aeiaaaeaia ianooiia

(53)

j-? eaiee iai?ioeyoe?eii? nenoaie aoaea aeinyaeiei.

.

, iaiao?aeii e aeineoue aeeiiaiiy oiiae

,

? ?ica’yceaie caaea/? (43).

Aeey eiie?aoii? iai?ioeyoe?eii? nenoaie ?icaeyaeathoueny oiiae
aeinyaeiino?, oe?eeii aeinyaeiino? oa eieaeueii? aeinyaeiino?, a oaeiae
aeine?aeaeothoueny iaai? eieaeuei? aeanoeaino? e?iaiaoe/ieo noai, ye?
aeaee a ciiao aeai?eoi?coaaoe aiae?c oa iiaoaeiao iaeanoae aeinyaeiino?.

Iio??aii ca a?aeiieie: e?iaiaoe/ieie caeaaeiinoyie

(54)

, ?acoeueoaoaie aei???a eii?aeeiao noai?a nenoaie

, (55)

.

?ica’ycaiiy caaea/? (54),(55) caaaeaii aei ?ica’ycaiiy a?aeiieo caaea/
ioe?ithaaiiy ia?aiao??a, ?ic?iaeaieo o no/ani?e oai??? ea?oaaiiy.

, ye? iaiao?aei? aeey aecia/aiiy oeueiai noaio, a oaeiae ae?th/?
ciai?oi? neee. A caeaaeiino? a?ae oiai ye? ia?aiao?e a?aeii?, a ye?
iio??aii aecia/eoe, aeae?eeii o?e caaea/? noaoeee.

;

2) neea oa iiiaio nee, ui
i?eeeaaeai? aei n-oi? eaiee iai?ioeyoe?eii? nenoaie f=(R,Q).

.

;

.

Ciaeoe: neeo oa iiiaio nee f=(R,Q).

;

2) neea oa iiiaio nee f=(R,Q).

.

Oai?aia 4.8. Nenoaia ??aiyiue

(56)

aea A((, p) — iao?eoey n(6 c aeaiaioaie:

(57)

a h((, p)- aaeoi? n(1 c aeaiaioaie:

, (58)

aea

iieno? noaoe/io iiaeaeue iai?ioeyoe?eiiai ?iaioa.

ia?aiao?e, ye? aecia/athoueny no?oeoo?iaaiei i?aeoiaeii.

Nie?ath/enue ia i?aaenoaaeaiiy (56) ??aiyiue noaoeee, i?iiiiothoueny
?ica’ycee caaea/ 1-3. Ia?oa caaea/a — i?yia caaea/a noaoeee ? iaea?eueo
i?inoith: ?? ?ica’ycie — aaeoi? ocaaaeueiaieo nee — iaeiicia/ii
aecia/a?oueny ca o?eniaaiei iieiaeaiiyi oa i?eeeaaeaiei coneeeyi ca
oi?ioeaie (56)-(58).

Caaea/a 2. Iao?eoey A((, p), a caaaeueiiio aeiaaeeo, ? i?yiieooiith
iao?eoeath ?ici??iino? n(6. Iaoae n = 6 , oiaoi iai?ioeyoe?eia nenoaia
ia? o?noue nooiai?a ?ooeeaino?. Aeey ciaoiaeaeaiiy neee oa iiiaioa nee
?ica’yaeaii nenoaio (56) a?aeiinii f. sseui det A((, p) ( 0, oi ca
a?aeiiei aaeoi?ii ocaaaeueiaieo eii?aeeiao ( oa ocaaaeueiaieo nee u
iaeiicia/ii aecia/a?oueny aaeoi? f:

(59)

sseui det A((, p)=0, oi iiaeeea? aeaa aeiaaeee:

A. Aeey caaeaieo u ? ( aaeoi? f ciaoiaeeoueny iaiaeiicia/ii, oiaoi
?nio? oe?ea iiiaeeia aaeoi??a f, ye? caaeiaieueiythoue (56). Oiio
noaaeoueny caaea/a ciaoiaeaeaiiy f c oiia:

. (60)

?ica’yceii (60) aoaea:

, (61)

— inaaaeiiaa?iaia iao?eoey.

A. Aeey caaeaieo u ? ( ?ica’yce?a ia ?nio?. Oea icia/a?, ui aeey ieo
ia iiaeeeaee noaoe/ii-??aiiaaaeiee noai nenoaie.

aoaea i?yiieooiith, ? aeey ciaoiaeaeaiiy neee oa iiiaioa nee, ui
i?eeeaaeai? aei iai?ioeyoe?eii? nenoaie, iaiao?aeii aeei?enoiaoaaoe
iaoiaee inaaaeiiaa?iaiiy.

— caaeaia neea oa iiiaio neee. Aaeoi? ocaaaeueiaieo eii?aeeiao aoaeaii
ciaoiaeeoe c oiia i?i?ioia ooieoe?iiaea:

(62)

— iiiaeeia aioo??oi?o iaiaaeaiue ia ocaaaeueiai? eii?aeeiaoe

— caaeai? cia/aiiy.

Aeey ciaoiaeaeaiiy aaeoi?a ocaaaeueiaieo eii?aeeiao canoiniao?oueny
a?aae??ioia i?ioeaaeo?a

,

.

Aeey ciaoiaeaeaiiy /anoeiieo iio?aeieo ia?ii:

.

Oaeei /eiii, iiaoaeiaai? eiino?oeoeai? iaoiaee ?ica’ycaiiy caaea/
noaoeee 1-3.

O i’yoiio ?icae?e? aeena?oaoe?eii? ?iaioe iaaiaeyoueny iia? iaoiaee
?ica’ycaiiy caaea/ aeeiai?ee, iiaoaeiae i?ia?aiieo ?oo?a oa i?aai?caoe??
ea?oaaiiy iai?ioeyoe?eieo nenoai.

Aeei?enoiaoth/e ?ic?iaeaiee o ae?oaiio ?icae?e? iaoiae oi?ioaaiiy
aeaiaio?a ??aiyiue (1), ?ica’ycothoueny caaea/? aeeiai?ee
iai?ioeyoe?eieo nenoai, a naia: i?yia oa iaa?iaia caaea/? aeeiai?ee ?
ciaoiaeaeaiiy aoaeoeaieo iiiaio?a ?ia?oe?? [1,5].

Aiaeia?/ii iaoiaeo oeeaaeaiiy aeaiaio?a, i?iiiio?oueny aeai?eoi aeey
ciaoiaeaeaiiy aaeoi?a ocaaaeueiaieo nee o i?ioean? oi?ioaaiiy oeeo
aeaiaio?a. Aeey i?inoioe iaaaaeaii aeai?eoi ia/eneaiiy ia?oiai aeiaeaieo
a (1).

, ye? iaaeathoue a?aeiia?aei? oeeaaeaiiy ocaaaeueiaieo nee

(63)

.

aioeththoueny.

. Aiaeia?/ii iiaeia iiaoaeoaaoe aeai?eoie ?ic?aooieo a?aeoeaio?iaeo,
ei??ie?niaeo oa a?aa?oaoe?eieo nee.

.

iiaeia caienaoe oae

aoaea

(64)

.

.

.

.

Oiae? aoaeoeai? iiiaioe ia/eneththoueny ca oi?ioeaie

(65)

.

A i?ae?icae?e? 5.3 ?icaeyaea?oueny caaea/a iiaoaeiae i?ia?aiieo ?oo?a
aeey aaaeeeaiai a i?eeeaaeieo canoinoaaiiyo eeano ?oo?a, eiee caaeai?
cia/aiiy ooieoe?? ? ia?oeo iio?aeieo o aoceao [1,2,8]:

(66)

(67)

(68)

Nieaei aoaeaii ooeaoe o aeaeyae? iie?iiia

. (69)

oiia c? (66)-(68). O?e oiiae, ui caeeoeeenue, caaeathoueny a
caeaaeiino? a?ae eiie?aoii? caaea/?:

A. Caaeai? oaeaeeino? ia iaio e?ioeyo ?ioa?aaeo ? i?enei?aiiy ia iaeiiio
c ieo:

(70)

A. Caaeai? oaeaee?noue aai i?enei?aiiy ia iaeiiio c e?ioe?a ? oiiaa
ieaaiino? ia anueiio ?ioa?aae?:

(71)

A. Caaeai? oaeaee?noue aai i?enei?aiiy ia iaeiiio c e?ioe?a ? oiiaa
i?i?ioio aia?a??:

(72)

aeey iaaaaeaieo aeua aeiaaee?a.

Aeae? a aeena?oaoe?? iieaco?oueny, ui ?ic?iaeai? a iiia?aaei?o ?icae?eao
iaoaiaoe/i? iaoiaee aeicaieythoue cae?enieoe eii?aeeiiaaiee ?oo
iai?ioeyoe?eii? nenoaie [1,13,14]. Eii?aeeiaoe?y c oi/ee ci?o o?c?ieia??
?oo?a ? iiaeieaiiyi iaaei??iino? nenoaie aeey aeinyaiaiiy iinoaaeaii?
oe?e?. Iiaeieaiiy iaaei??ii? e?eueeino? ocaaaeueiaieo eii?aeeiao
(aaiiao?e/ia eii?aeeiaoe?y), ye? ia?aaiaeyoue nenoaio a oe?eueiaee noai
iieyaa? o aecia/aii? oeo ?c ieo, ui aiinyoue iaea?eueoee aianie o ?oo,
?iaey/e i?e oeueiio oe?eueiaee noai aeinyaeiei. Oea cae?enith?oueny ca
aeiiiiiaith iioei?caoe?eieo i?ioeaaeo? ieaioaaiiy noai?a. E?iaiaoe/ia
eii?aeeiaoe?y ?ooo aecia/a?oueny ciaoiaeaeaiiyi oaeeo ci?i ocaaaeueiaieo
eii?aeeiao ye ooieoe?e /ano, ca yeeo aca?iicaeaaei?noue (iae?i?eia) i?ae
ieie aoaea ciaioaia. Eii?aeeiaoe?y ia ??ai? aeeiai?ee (aeeiai?/ia
eii?aeeiaoe?y) nenoaie iiaeyaa? o ciaoiaeaeaii? oeo neeaaeiaeo aeaiaio?a
??aiyiue ?ooo, ye? aiinyoue iaea?eueoee (aeii?iaioiee) aeeaae o eiai
?aae?caoe?th.

C iaeyaeo ia io?eiai? ?acoeueoaoe iiaeia cae?enithaaoe eii?aeeiaoe?th
?ooo iai?ioeyoe?eii? nenoaie oeyoii iine?aeiaiiai ?ica’ycoaaiiy ?
ei?aeoe?? oaee?o iaiao?aeieo caaea/:

1. Caaeaoe ii/aoeiaee noai nenoaie (aaeoi? ocaaaeueiaieo eii?aeeiao).

2. Caaeaoe oe?eueiaee noai nenoaie.

3. Cae?enieoe aaiiao?e/io eii?aeeiaoe?th.

4. Aecia/eoe ?ioa?aae /ano.

5. Cae?enieoe e?iaiaoe/io eii?aeeiaoe?th.

6. Ia?aa??eoe iaiaaeaiiy ia iieiaeaiiy, oaeaee?noue oa i?enei?aiiy ii
eiaei?e ?c ocaaaeueiaieo eii?aeeiao. sseui ? ii?ooaiiy, oi ca?eueoeoe
?ioa?aae /ano ? ia?aeoe ia i. 5.

7. Noi?ioaaoe ??aiyiiy ?ooo (1).

8. Ia?aa??eoe iaiaaeaiiy ia ocaaaeueiai? ea?oth/? neee. sseui ?
ii?ooaiiy, oi ca?eueoeoe ?ioa?aae /ano ? ia?aeoe ia i. 5.

9. Cae?enieoe aeeiai?/io eii?aeeiaoe?th.

Oaeei /eiii, o ?acoeueoao? ?iaioe aeai?eoio aoaea ciaeaeaii a?ae??cie
/ano aeeiiaiiy caaeaiiai ?ooo aac ii?ooaiiy iaiaaeaiue ia ocaaaeueiai?
eii?aeeiaoe, oaeaeeino?, i?enei?aiiy oa ocaaaeueiai? ea?oth/? neee, a
oaeiae iaa?? no?oeoo? ?c ??aiyiue aeeiai?ee, ye? ?aae?ciaothoue oeae
?oo. Ioaea, i?ioeaaeo?a i?aai?caoe?? eii?aeeiiaaii ?ooo oe?eeii
eiino?oeoeaia ? ?? iiaeia ?aae?coaaoe apriori, i?ney /iai aeey caaeaiiai
?ooo caa??aaoe iaiao?aeiee iaa?? aeaiaio?a ??aiyiue aeeiai?ee.

Aeniiaee

I?iaaaeai? a aeena?oaoe?ei?e ?iaio? aeine?aeaeaiiy ? iaea?aeai?
?acoeueoaoe na?ae/aoue, ui ?ic?iaea iioei?caoe?eieo iaoiae?a nenoaiiiai
aeine?aeaeaiiy neeaaeieo iae?i?eieo iai?ioeyoe?eieo nenoai ? aaaeeeaith
? aeooaeueiith. Oaeee i?aeo?ae aeicaiey? cae?enithaaoe iinoaiiaee iiaeo
caaea/ ? ?ic?iaeyoe eiino?oeoeai? iaoiaee ?o ?ica’ycaiiy.

?ic?iaeaii iiaee iaoiae oi?ioaaiiy iaoaiaoe/ieo iiaeaeae aeeiai?ee
iai?ioeyoe?eieo nenoai o /enaeueii-aiae?oe/iiio aeaeyae? c
i?i?i?caoe??th ia/enethaaeueii? neeaaeiino?, yeee iniiao?oueny ia
ianooiieo io?eiaieo iiaeo ?acoeueoaoao.

1. Io?eiai? oai?aie i?i i?aaenoaaeaiiy aeaiaio?a e?iaoe/ii? oa
iioaioe?aeueii? aia?a?e a iaeneiaeueii ca?oiiaai?e oi?i? c aeae?eaiiyi
/anoei, caeaaeieo a?ae ianiiiiaioieo ia?aiao??a ? /anoei, caeaaeieo a?ae
ocaaaeueiaieo eii?aeeiao nenoaie. A ia?oo /anoeio aoiaeyoue ia?aiao?e
ia/enethaai? apriori, a ia a i?ioean? aeania iiaoaeiae ??aiyiue ?ooo,
ye? iaaeae? aaaaeathoueny iaaieie noaeeie aaee/eiaie, ui cia/ii ciaioo?
e?euee?noue ia/eneaiue. Aeine?aeaeai? ? iaea?aeai? iia? aeanoeaino? ?
iiaoaeiaai? aoaeoeai? aeai?eoie oi?ioaaiiy a yaiiio aiae?oe/iiio
aeaeyae? /anoei, caeaaeieo a?ae o?eaiiiiao?e/ieo ooieoe?e ocaaaeueiaieo
eii?aeeiao.

Aeiaaaeai? oai?aie i?i ni?aaaaeeea?noue oaeiai i?aaenoaaeaiiy ? aeey
aeaiaio?a ??aiyiue aeeiai?ee iai?ioeyoe?eieo nenoai.

2. Aia?oa aeey oi?ioaaiiy iaoaiaoe/ieo iiaeaeae iai?ioeyoe?eieo nenoai
aeiaaaeai? oai?aie i?i aeaeiiiiceoe?th aeo?aeii? nenoaie ia nenoaie
iaioi? ?ici??iino?. Ia iniia? oeeo oai?ai cai?iiiiiaaii iaoiae
oeeaaeaiue aeey iiaoaeiae ??aiyiue aeeiai?ee. Aeei?enoaiiy oeueiai
iaoiaeo, c o?aooaaiiyi ?icae?eaiiy ia /anoeie, aeicaieeei iaea?aeaoe
i?aaenoaaeaiiy aeey aeaiaio?a iao?eoeue ?ia?oe?eieo, a?aeoeaio?iaeo,
ei??ie?niaeo ? aaeoi?a a?aa?oaoe?eieo nee ??aiyiue ?ooo o no?oeoo?iaai?e
? ca?oiiaai?e oi?i? c aeae?eaiiyi iao?eoeue niaoe?aeueiiai aeaeyaeo.
Iaea?aeai? i?aaenoaaeaiiy ii noo? ? eiino?oeoeaiei aeai?eoiii oi?ioaaiiy
aeaiaio?a ??aiyiue ?ooo, yeee caiaeeoueny aei canoinoaaiiy aeaio aaciaeo
iia?aoe?e iiiaeaiiy iao?eoeue ? ia/eneth?oueny i?i?iaeueiith e?euee?noth
a?eoiaoe/ieo iia?aoe?e.

Cae?eniaii nenoaiiee aiae?c ca e?eoa???i ia/enethaaeueii? neeaaeiino?
oe?eiai eeano e?iaiaoe/ieo noai iai?ioeyoe?eieo ?iaio?a. Ine?eueee a
?aieao ?ic?iaeaiiai iaoiaeo eiaeia iai?ioeyoe?eia nenoaia aoaea
oa?aeoa?ecoaaoeny aeaniith e?euee?noth a?eoiaoe/ieo iia?aoe?e oi?ioaaiiy
??aiyiue ?ooo, oi aeine?aeaeaii caeaaei?noue ia/enethaaeueii?
neeaaeiino? nenoaie a?ae oei?a c’?aeiaiue, iine?aeiaiino? c’?aeiaiue
e?iaiaoe/ieo ia?, ia’?aeiaiue eaioetha?a eaiie o a?aeiia?aeieo noaiao.
Iieacaii, ui ?c 729 iiaeeeaeo e?iaiaoe/ieo noai oanoeeaieiaeo
iai?ioeyoe?eieo ?iaio?a o?eueee 42 noaiiaeyoue i?aeoe/iee ?ioa?an. Aeey
oeeo noai cae?eniaii aiae?c ? iaaaaeaii ia/enethaaeuei? neeaaeiino?
iiaoaeiae eiaeii? neeaaeiai? ??aiyiue ?ooo.

?ic?iaeaiee iaoiae oaeiae aeicaiey? cae?enithaaoe iia?aoe?? cai?ie
(anoaaee) eaiie (eaioetha?a eaiie) o nenoai?, i?e/iio ia/eneththoueny
o?eueee o? aeaiaioe, ye? aaciina?aaeiuei iia’ycai? c oe??th eaieith
(eaioethaaie eaiie), a ia oi?ioaaiiy an?o aeaiaio?a nenoaie, ui aaaeeeai
a NAI? iai?ioeyoe?eieo nenoai.

Io?eiaii caaaeueiee ?ica’ycie caaea/? iaa?iaiiai ieaioaaiiy noai?a
iai?ioeyoe?eieo nenoai. Iaaaaeaia iioei?caoe?eia iinoaiiaea caaea/?
aeai?o aaiiao?i-oiiieia?/ieo ia?aiao??a e?iaiaoe/ieo noai
iai?ioeyoe?eieo nenoai oeyoii aaaaeaiiy ooieoe?iiae?a, ye?
oa?aeoa?ecothoue ?iai/ee i?ino?? nenoaie. Ciaeaeai? iioeiaeuei? ioe?iee
? aiinoa??i?i? iiiaeeie cia/aiue aaiiao?e/ieo ia?aiao??a, noi?ioeueiaai?
e?eoa??? aeinyaeiino? noai?a iai?ioeyoe?eieo nenoai ? aeine?aeaeai?
eieaeuei? aeanoeaino? e?iaiaoe/ieo ia?, ye? aeicaieythoue nooo?ai
ni?inoeoe aiae?c oa iiaoaeiao iaeanoae aeinyaeiino?.

Noi?ioeueiaai? o?e caaea/? aeine?aeaeaiiy ??aiiaaaeieo noai?a,
aeiaaaeaia oai?aia i?i i?aaenoaaeaiiy iiaeae? noaoeee o aeaeyae?
e?i?eii? nenoaie. Caaaeuei? ?ica’ycee iinoaaeaieo caaea/ io?eiaii ia
iniia? iaoiae?a inaaaeiiaa?iaiiy oa i?i?i?caoe?? ooieoe?iiae?a.

Ia aac? ?ic?iaeaiiai iaoiaeo oi?ioaaiiy ??aiyiue aeeiai?ee iiaoaeiaai?
iia? aoaeoeai? aeai?eoie ?ica’ycaiiy i?yii? ? iaa?iaii? caaea/
aeeiai?ee, ciaoiaeaeaiiy aoaeoeaieo iiiaio?a ?ia?oe??. Iaaaaeaii iaoiae
iiaoaeiae i?ia?aiieo ?oo?a iai?ioeyoe?eieo nenoai o aeaeyae? a?i?oiaeo
nieaei?a /aoaa?oiai ii?yaeeo, ye? caaacia/othoue i?ioiaeaeaiiy /a?ac
caaeai? aocee ?c caaeaieie oaeaeeinoyie.

Io?eiai? a aeena?oaoe?ei?e ?iaio? iaoiaee ?ica’ycoaaiiy caaea/
ieaioaaiiy noai?a ? o?a?eoi??e oa iiaoaeiae ??aiyiue aeeiai?ee aeaee
iiaeeea?noue ?ic?iaeoe iiaee i?aeo?ae aei i?aai?caoe?? ea?oaaiiy ?ooii,
yeee aeicaiey? aeine?aeeoe i?e?iaeo i?ioean?a ea?oaaiiy ?ooii c iaoith
ni?iuaiiy ? aeae?eaiiy iaeaaaii?oeo aeaiaio?a ? ?o aeei?enoaiiy a
oaoi?/ieo ??oaiiyo iiaoaeiae oaeeo nenoai ea?oaaiiy. Aaaaeai? iiiyooy
aaiiao?e/ii?, e?iaiaoe/ii? ? aeeiai?/ii? eii?aeeiaoe??, ia iniia? yeeo
aoaeothoueny aeai?eoi eii?aeeiaoe?? ?oo?a ye niin?a ciaoiaeaeaiiy
aeiaaeueiiai ea?oaaiiy.

Aaoi? aeneiaeth? ue?o iiaeyeo nai?io iaoeiaiio eiinoeueoaioia? aeieoi?o
o?ceei-iaoaiaoe/ieo iaoe, i?ioani?o Ieeie? Oaaei?iae/o Ee?e/aieo ca
iinoaiiaeo oa iaaiai?aiiy i?iaeai aeaii? aaeoc? aeine?aeaeaiue oa
iino?eio oaaao aei ?iaioe.

Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaai? a oaeeo ?iaioao:

1.Ee?e/aiei I.O.,E?ae TH.A.,Ni?iea ?.I.Iioei?caoe?y iai?ioeyoe?eieo
?iaio?a. — Ee?a.: Eea?aeue.- 1990. — 144 n.

2.Ee?e/aiei I.O., Ni?iea ?.A., E?ae TH.A. Iaieioeyoeeiiiua ?iaiou.
Aeai?eoie/aneia e i?ia?aiiiia iaania/aiea n?aaenoa oi?aaeaiey
aeaeaeaieai. — Eeaa: EAO, 1987. — 84 n.

3.Ee?e/aiei I.O., E?ae TH.A., Ni?iea ?.A. Iaoaiaoe/aneia iiaeaee?i-aaiea
iaoaieee e i?ioeannia oi?aaeaiey iaieioeyoeeiiiuie ?iaioaie //Ecaanoey
AI NNN?. Oaoi. eeaa?iaoeea. — 1987. — ? 3. — N. 147-155.

4.Ee?e/aiei I.O., E?ae TH.A., Ni?iea ?.A. Iiaeaee?iaaiea, iioeieca-oeey
e aaeaioaoeey iaieioeyoeeiiiuo ?iaioia //Eeaa?iaoeea e au/ene. oaoieea.
— 1987, Aui.73. — N.90-93.

5.E?ae TH.A. E oi?ie?iaaieth o?aaiaiee aeeiaieee iaieioeyoeeiiiuo
?iaioia i?eiaieoaeueii e caaea/ai oi?aaeaiey aeaeaeaieai // Aaoiiaoeea.
— 1988. — ?4. — N.89-93.

6.E?ae TH.A. Iioeiecaoeey au/eneaiee i?e oi?ie?iaaiee o?aaiaiee
aeaeaeaiey iaieioeyoeeiiiuo ?iaioia// Aeieeaaeu AI ONN?. Na?.A. -1988. —
? 9. — N.74-78.

7.E?ae TH.A. Enneaaeiaaiea iaoaiaoe/aneeo iiaeaeae e eioi?iaoeeiiiuo
i?ioeannia a nenoaiao oi?aaeaiey iaieioeyoeeiiiuie ?iaioaie // Aanoi.
Eeaa. oi-oa .Iiaeaee e nenoaiu ia?aaioee eioi?iaoeee. — 1989, Aui.8. —
N.58-63.

8.Ni?iea ?.A., E?ae TH.A. Iino?iaiea i?ia?aiiiuo aeaeaeaiee
iaieio-eyoeeiiiuo ?iaioia a aeaea nieaeiia /aoaa?oiai ii?yaeea.
//Au/ene. e i?eee. iaoaiaoeea. — 1989, Aui.68. — N.114-120.

9.E?ae TH.A. Eniieueciaaiea iaoaiaoe/aneeo iiaeaeae a nenoaiao
oi?aaeaiey aeaeaeaieai iaieioeyoeeiiiuo ?iaioia// Aanoi. Eeaa. oi-oa.
Iiaeaee?iaaiea e iioeiecaoeey neiae. nenoai. — 1989, Aui.8. — N.51-54.

10.E?ae TH.A. Ia iaeiii iiaeoiaea e aiaeeoe/aneiio iino?iaieth o?aaiaiee
aeaeaeaiey iaieioeyoeeiiiuo ?iaioia //Au/ene. e i?eee. iaoaiaoeea. —
1990, Aui.72. — N.82-88.

11.Aoaeee A.I., E?ae TH.A., Naiaithe TH.A. E oi?ie?iaaieth o?aaiaiee
aeaeaeaiey iaieioeyoi?a a /eneaiii-aiaeeoe/aneii aeaea// Aeieeaaeu AI
ONN?. Na?.A. — 1990. — ? 11. — N.59-62.

12. E?ae TH.A. Iaoiae iino?iaiey o?aaiaiee aeeiaieee iaieioey-oeeiiiuo
?iaioia a /eneaiii-aiaeeoe/aneii aeaea// Ecaanoey ?AI. Oaoie/aneay
eeaa?iaoeea. — 1993. — ?1. — C. 137-141.

13.E?ae TH.A. Eii?aeeiaoeeiiiue iiaeoiae e i?aaiecaoeee aeaeaeaiee
iaieioeyoeeiiiuo ?iaioia//I?iaeaiu oi?aaeaiey e eioi?iaoeee. -1995. -N4.
— C.120-128.

14. Krak Yu.V. On the construction of coordinated motions for a
manipulator // Cybernetics and computing technology. Complex control
systems. — 1998. — N 107. — P.43-50.

15. Kirichenko N.F., Krak Yu.V. Structural representation and solution
of problems of statiks for manipulating systems// Cybernetics and
computing technology. Complex control systems. — 1998. — N 111. —
P.15-23.

16.E?ae TH.A. Aeeiaieea iaieioeyoeeiiiuo ?iaioia:
/eneaiii-aiaee-oe/aneee iaoiae iino?iaiey e enneaaeiaaiea
au/eneeoaeueiie neiaeiinoe //I?iaeaiu oi?aaeaiey e eioi?iaoeee. -1998. —
N2. — C.142-151.

17.Kirichenko N.F., Krak Yu.V. The optimization problems in
investigation of geometric-topological parameters of a manipulator //
Cybernetics and computing technology. Discrete control systems — 1998. —
N 109. — P.82-95.

18.E?ae TH.A. Iioei?caoe?ei? caaea/? a ?iaioioaoi?oe?// I?aoe? i’yoi?
oe?a?inueei? eiioa?aioe?? c aaoiiaoe/iiai oi?aae?iiy “Aaoiiaoeea-98”
i?enay/aii? 100-??//th Ee?anueeiai iie?oaoi?/iiai ?inoeoooo. — *anoeia
1. — E.: — 1998. — N.244-253.

E?ae TH.A. ?ic?iaea iioei?caoe?eieo iaoiae?a aeine?aeaeaiiy neeaaeieo
iai?ioeyoe?eieo nenoai. — ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy aeieoi?a o?ceei-iaoaiaoe/ieo
iaoe ca niaoe?aeuei?noth 01.05.04 — nenoaiiee aiae?c i oai??y
iioeiaeueieo ??oaiue. — ?inoeooo eini?/ieo aeine?aeaeaiue IAI Oe?a?ie ?
IEAO, Ee?a, 1999.

Aeena?oaoe?y i?enay/aia ?ic?iaoe? iiaeo iaoiae?a aeine?aeaeaiiy
neeaaeieo iae?i?eieo aeeiai?/ieo aaaaoieaieiaeo iai?ioeyoe?eieo nenoai,
ye? aacothoueny ia i?aeoiaeao iaoai?ee, iaoiaeao oai??? iioeiaeueiiai
ea?oaaiiy, iioei?caoe??, e?i?eii? aeaaa?e, neiaieueieo ia?aoai?aiue oa
inaaaeiiaa?iaiue. Cai?iiiiiaai? iioei?caoe?ei? iinoaiiaee caaea/ ?
?ic?iaeai? iaoiaee nenoaiiiai aiae?co aaiiao?i-oiiieia?/ieo ia?aiao??a,
ieaioaaiiy oa ioe?iee noai?a, aeine?aeaeaiiy oa iiaoaeiae iaeanoae
aeinyaeiino?, ?ic?aooieo o?a?eoi??e oa i?aai?caoe?? ?oo?a, oi?ioaaiiy
iaoaiaoe/ieo iiaeaeae a /enaeueii-aiae?oe/iiio aeaeyae? c i?i?i?caoe??th
ia/enethaaeueii? neeaaeiino?, aeeiai?ee ? ea?oaaiiy neeaaeieie
iai?ioeyoe?eieie nenoaiaie. Cae?eniaii nenoaiiee aiae?c ca e?eoa???i
ia/enethaaeueii? neeaaeiino? oe?eeo eean?a iai?ioeyoe?eieo ?iaio?a.

Eeth/ia? neiaa: iai?ioeyoe?eia nenoaia, iioei?caoe?y,
/enaeueii-aiae?oe/i? iaoiaee, aeeiai?ea, inaaaeiiaa?iaiiy,
ia/enethaaeueia neeaaei?noue, iai?ioeyoe?ei? ?iaioe.

E?ae TH.A. ?ac?aaioea iioeiecaoeeiiiuo iaoiaeia enneaaeiaaiey neiaeiuo
iaieioeyoeeiiiuo nenoai. — ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie aeieoi?a oeceei-iaoaiaoe/aneeo
iaoe ii niaoeeaeueiinoe 01.05.04 — nenoaiiue aiaeec e oai?ey
iioeiaeueiuo ?aoaiee. — Einoeooo einie/aneeo enneaaeiaaiee IAI Oe?aeiu e
IEAO, Eeaa, 1999.

Aeenna?oaoeey iinayuaia ?ac?aaioea iiauo iaoiaeia enneaaeiaaiey neiaeiuo
iaeeiaeiuo aeeiaie/aneeo iiiaicaaiiuo iaieioeyoeeiiiuo nenoai, eioi?ua
aace?othony ia iiaeoiaeao iaoaieee, iaoiaeao oai?ee iioeiaeueiiai
oi?aaeaiey, iioeiecaoeee, eeiaeiie aeaaa?u, neiaieueiuo i?aia?aciaaiee e
inaaaeiia?auaieyo. I?aaeeiaeaiu iioeiecaoeeiiiua iinoaiiaee caaea/ e
?ac?aaioaiu iaoiaeu nenoaiiiai aiaeeca aaiiao?i-oiiieiae/aneeo
ia?aiao?ia, ieaie?iaaiey e ioeaiee ninoiyiee, enneaaeiaaiey e iino?iaiey
iaeanoae aeinoeaeeiinoe, ?ann/aoa o?aaeoi?ee e i?aaiecaoeee aeaeaeaiee,
oi?ie?iaaiey iaoaiaoe/aneeo iiaeaeae a /eneaiii-aiaeeoe/aneii aeaea n
ieieiecaoeeae au/eneeoaeueiie neiaeiinoe, aeeiaieee e oi?aaeaiey
neiaeiuie iaieioeyoeeiiiuie nenoaiaie. Inouanoaeai nenoaiiue aiaeec ii
e?eoa?eth au/eneeoaeueiie neiaeiinoe oeaeuo eeannia iaieioeyoeeiiiuo
?iaioia.

Aeenna?oaoeey ninoieo ec aaaaeaiey, iyoe aeaa, caeeth/aiey, nienea
eeoa?aoo?u e aeiiieiaiey.

Ai aaaaeaiee aeaii iauoth oa?aeoa?enoeeo ?aaiou, i?iaiaeece?iaaii
ninoiyiea iao/iie i?iaeaiu, iainiiaaii iaiaoiaeeiinoue i?iaaaeaiey e
ioia/aii aeooaeueiinoue enneaaeiaaiee, noi?ioee?iaaii oeaeue ?aaiou,
iiaecio iieo/aiiuo ?acoeueoaoia, eo oai?aoe/aneia e i?aeoe/aneia
cia/aiea.

A ia?aii ?acaeaea aeaaony iaic?aiea eeoa?aoo?iuo enoi/ieeia, eco/athony
iniiaiua iiaeoiaeu e iaoiaeu enneaaeiaaiey oaeeo nenoai.

Ai aoi?ii ?acaeaea i?eaiaeeony, iniiaaiiue ia o?aaiaieyo Eaa?aiaea I
?iaea, /eneaiii-aiaeeoe/aneee iiaeoiae e oi?ie?iaaieth o?aaiaiee
aeeiaieee iaieioeyoeeiiiuo nenoai. Aeey yoiai ?ac?aaioai iaoiae
?acaeaeaiey ia iinoiyiioth e ia?aiaiioth /anoe a yeaiaioao o?aaiaiee
aeaeaeaiey. Enneaaeiaaiu naienoaa e ?ac?aaioai aeai?eoi iino?iaiey a
yaiii aiaeeoe/aneii aeaea ninoaaeythueo o?aaiaiee aeaeaeaiey, eioi?ua
caaenyo io iaiauaiiuo eii?aeeiao iaieioeyoeeiiiie nenoaiu. Aeaeaa a
?aaioa ?ac?aaioai iaoiae aeaeiiiiceoeee iaieioeyoeeiiiie nenoaiu ia
nenoaiu iaiueoae ?acia?iinoe.

Ia iniiaaiee iaoiaea aeaeiiiiceoeee iaieioeyoeeiiiuo nenoai, a o?aoueai
?acaeaea ?ac?aaioaia iaoiaeeea e aeieacaiu oai?aiu i oi?ie?iaaiee
yeaiaioia o?aaiaiee a no?oeoo?e?iaaiiii e iaeneiaeueii na?oiie?iaaiiii
aeaea. Ieieiecaoeey au/eneaiee aeinoeaaaony ca n/ao iaoiaeaeaiey
iia?aoeee neaaea n o/aoii aeaea iao?eoe e au/eneaiey aaceniuo
i?iecaaaeaiee ieieiaeueiui /eneii a?eoiaoe/aneeo iia?aoeee. A
iiae?acaeaea 3.3 enneaaeoaony au/eneeoaeueiay neiaeiinoue iino?iaiey
o?aaiaiee aeaeaeaiey aeey oeaeuo eeannia iaieioeyoeeiiiuo ?iaioia aei
oanoe noaiaiae naiaiaeu. Ec 729 aiciiaeiuo eeiaiaoe/aneeo noai
oanoecaaiiuo iaieioeyoeeiiiuo ?iaioia auaeaeaiu 42, eioi?ua
i?aaenoaaeytho i?aeoe/aneee eioa?an, i?e/ai oieueei 21 ec ieo eiatho
?acee/iua neiaeiinoe. Iieacaii, /oi au/eneeoaeueiay neiaeiinoue caaeneo
io oeia eeiaiaoe/aneeo ia? e ianniiiiaioiuo ia?aiao?ia caaiueaa.

A /aoaa?oii ?acaeaea ?ac?aaioaiu iioeiecaoeeiiiua iaoiaeu
aaiiao?i-noaoe/aneiai aiaeeca e neioaca neiaeiuo iaieioeyoeeiiiuo
nenoai. ?aoaiu caaea/e ia?aoiiai ieaie?iaaiey eieaeueiuo ninoiyiee,
iaoiaeaeaiey iioeiaeueiuo aaiiao?i-oiiieiae/aneeo ia?aiao?ia, aiaeeca e
iino?iaiey iaeanoae aeinoeaeeiinoe, ioeaiee ia?aiao?ia caaiueaa
iaieioeyoeeiiiuo nenoai. Iinoaaeaiu e ?aoaiu, eniieuecoy iaoiaeu
iioeiecaoeee e inaaaeiia?auaiee, o?e caaea/e enneaaeiaaiey ?aaiiaaniuo
ninoiyiee nenoaiu.

A iyoii ?acaeaea i?eaaaeaiu iiaua iaoiaeu ?aoaiey caaea/ aeeiaieee,
ieaie?iaaiey aeaeaeaiee a aeaea y?ieoiauo nieaeiia /aoaa?oiai ii?yaeea,
i?aaiecaoeee eii?aeeie?iaaiiiai oi?aaeaiey aeaeaeaieai iaieioeyoeeiiiuo
nenoai.

Oaeei ia?acii, a aeenna?oaoeeiiiie ?aaioa iieo/aiu neaaeothuea iniiaiua
?acoeueoaou:

— aeieacaiu oai?aiu i ?acaeaeaiee a yeaiaioao o?aaiaiee aeaeaeaiey
iinoiyiiie e ia?aiaiiie /anoae;

— aia?aua ?ac?aaioai iaoiae aeaeiiiiceoeee iaieioeyoeeiiiuo nenoai;

— aia?aua aeiaaaeaiu oai?aiu i i?aaenoaaeaiee yeaiaioia o?aaiaiee
aeaeaeaiey a iaeneiaeueii na?oiie?iaaiiii n auaeaeaieai niaoeeaeueiuo
iao?eoe aeaea;

— aia?aua inouanoaeai nenoaiiue aiaeec au/eneeoaeueiie neiaeiinoe oeaeuo
eeannia iaieioeyoeeiiiuo ?iaioia;

— ?ac?aaioaiu iaoiaeu aiaeeca e iino?iaiey iaeanoae aeinoeaeeiinoe,
ii?aaeaeaiey iioeiaeueiuo aaiiao?i-oiiieiae/aneeo ia?aiao?ia, ?aoaiey
caaea/ noaoeee;

— ia iniiaaiee ?ac?aaioaiiuo iaoiaeia, aia?aua i?aaeeiaeaii
iioeiecaoeeiiue iiaeoiae e i?aaiecaoeee aeaeaeaiee iaieioeyoeeiiiuo
nenoai.

Eeth/aaua neiaa: iaieioeyoeeiiiay nenoaia, iioeiecaoeey,
/eneaiii-aiaeeoe/aneea iaoiaeu, aeeiaieea, inaaaeiia?auaiea,
au/eneeoaeueiay neiaeiinoue, iaieioeyoeeiiiua ?iaiou.

Krak Yu.V. Development of the optimization methods for investigation of
complex manipulation systems. — Manuscript.

Thesis for the Degree of Doctor of Physical and Mathematical sciences by
the Speciality 01.05.04 — system analysis and theory of optimal
solution. — The Institute of Space Research of National Academy of
Sciences of the Ukraine and National Space Agency of the Ukraine, Eyiv,
1999.

The dissertation is devoted to the development of new methods of
investigation of complex nonlinear dynamic multilink manipulation
systems, based on mechanics approaches, methods of optimal control
theory, optimizations, of linear algebra, symbolic calculations and
pseudoinversions. Optimization problems statements are proposed and
methods of systems analysis for geometrical and topological parameters,
positions planning and estimation, investigation and construction
reachable spheres, trajectory planning and movement organizations,
formation of mathematical models in numerical-analytical form with
computational complexity minimization, dynamics and control of complex
manipulation systems are created. Systems analysis by computational
complexity criterion of whole sets of manipulation robots is realized.

Keywords: manipulation system, optimization, numerical-analytical
methods, dynamics, pseudo-inversion, computational complexity,
manipulation robots.

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