🤖 Gudanar da rukunin mutum-mutumai Samfurin kai-tsaye
Kai ne ke gudanar da filin wani rumbu inda kusan mutum-mutumai masu motsi masu cin gashin kansu (AMR) 24 ke ɗaukar akwatuna daga hanyoyin ajiya zuwa ɗakunan cobot huɗu na shiryawa. Kowace oda tafiya ce ta 240 m — 200 m ta hanyoyin mutum-mutumai kaɗai, 40 m ta yankin haɗin gwiwa inda mutane ke aiki — da ɗauka a ɗaki. Samfurin yana lissafa layukan jira, cunkoso, kulle-juna, nisan tsayawa, makamashin batir da ƙarfin caji, da tasirin sigogin manhaja kan tsayawa, minti bayan minti, daga ƙa'idojin da aka wallafa da dabarun littattafan karatu. Samfuri ne na ƙa'idodin aiki: ba ya gudanar da manhajar mutum-mutumi, kuma lambobin na gama-gari ne, ba na wani samfur ba. Kwaikwayo ne na ilimi kawai — wurare na gaske suna bin nasu kimanta haɗari.
Abin da za ka koya
Me ya sa cajoji, ba mutum-mutumai ba, ne galibi ke zama cikas — da yadda cajin dama da caji har zuwa matakin wuta mai daidaito kawai ke tara makamashi kafin ƙololuwa.
Yadda kulle-juna ke faruwa a mahaɗai, me ya sa ajiye yankunan da ke gaba kafin shiga ke hana su, da kuma me ya sa mutum-mutumi kada ya taɓa tafiya da sauri fiye da yadda filin tsaronsa zai iya tsayar da shi inda mutane suke.
Yadda fitar canary ke kwatanta 'yan mutum-mutumai da aka sabunta da sauran rukunin, lokacin da za a mayar da baya, da kuma me ya sa ake fitar da sabuntawa a matakai.
Na'urar koyi
Lokaci 0 min
▶Yana tafiya da aiki
⚙A ɗakin cobot
⇥Yana jiran ɗaki
·Ba aiki
⚡Yana caji
⌛Yana jiran caja
↻Yana sabunta manhaja
!Ya tsaya (haɗi ko sanin wuri)
⛔A makale cikin kulle-juna
∅Caji ya ƙare, an ja shi
✓Yanki babu mutane
⚠Mutane a yankin, gudu a cikin filin
⛔Gudu ya yi yawa ga filin inda mutane suke
☺Mutum a ɗakin cobot
✕Caja ba ta aiki
Sarrafawa
Mutum-mutumai na ajiya suna farkawa daga ma'ajiya; waɗanda aka ajiye ba sa cin wuta. Kowane mutum-mutumi mai aiki yana cin awa-mutum-mutumi ɗaya a kowace awa.
An rufe yanki A ga mutane, don haka mutum-mutumai na iya gudu da sauri. Idan mutane suka shiga, dole gudun ya sake dacewa da filin gano mutane.
Mutane suna aiki a nan koyaushe. Nisan tsayawa a wannan gudun dole ya dace a cikin filin gano mutane na 1.3 m.
'Yanci: mutum-mutumai suna kauce wa juna ne kawai a wurin — da sauri, amma biyu ko fiye na iya toshe juna har abada. Ajiyar yanki: mutum-mutumi yana shiga mahaɗa ne kawai bayan an ajiye masa yankunan da ke gabansa — babu kulle-juna, ɗan jira kaɗan a kowace ketarewa.
Yana sakin dukkan mutum-mutumai da ke cikin kulle-juna yanzu. Yana cin mintuna 2 na ma'aikaci kan kowane mutum-mutumin da aka saki; ba ya hana sabbin kulle-juna faruwa.
Mutum-mutumin da ya gama aiki da wannan cajin ko ƙasa da shi zai shiga layin jiran caja. Ƙasa da haka yana amfani da ƙarin batir, amma mutum-mutumin da ya daɗe yana jira zai iya ƙarewa caji gaba ɗaya.
Cajoji suna ba da cikakken ƙarfi har kusan 70 %; sama da haka wutar lantarki tana raguwa. Tsayawa a ƙasa yana sakin caja da wuri.
Mutum-mutumai marasa aiki suna zuwa kowace caja da babu kowa maimakon zama zaune, kuma suna komawa aiki da zarar odoji suna jira kuma suna da 20 % sama da matakin tura caji.
Gudun kayan aiki lokacin da babu kowa a cikin ɗakin. Akwati mai kaya 10 yana ɗaukar 25 s a 1 m/s.
Iyakar ƙarfi da matsi: hannun da ya makale jikin akwati kada ya ji fiye da 140 N (iyakar quasi-static, da aka yi amfani da ita cikin taka-tsantsan), wanda ke ba da damar 0.67 m/s a mafi yawa a nan.
Matsar da maɓallin zamewa yana fitar da sabuwar sigar da aka wallafa zuwa wannan kason na rukunin (mutum-mutumai na farko a jere); sauran suna aiki da v1. Sigar da aka wallafa daga baya ana sanya ta ne kawai idan ka sake matsar da maɓallin zamewa. Kowane mutum-mutumi da ya canza siga yana daina aiki na mintuna 4.
Alamomi
Akwatunan da aka shirya
360/h
daidai
Lokacin isar da oda
0.0min
daidai
Mutum-mutumai da ake da su
100%
daidai
Ragowar nisan tsayawa inda mutane suke
0.27m
daidai
Odojin da ke jira
0
Ragowar gudun cobot (iyakar ƙarfi da matsi)
0.17 m/s
Matsakaicin cajin batir
67 %
Mafi ƙarancin cajin batir
42 %
Mutum-mutumai masu jiran caja
0
Mutum-mutumai masu caji
0
Mutum-mutumai da caji ya ƙare (an ja su)
0
Mutum-mutumai a makale cikin kulle-juna
0
Kulle-juna da suka faru
0
Tsayawar kewayawa (haɗi ko sanin wuri)
0
Tsayawa a kowace awa-mutum-mutumi, sabuwar siga
0.0 /h
Tsayawa a kowace awa-mutum-mutumi, sauran rukuni
0.0 /h
Rukuni a kan sabuwar siga
0 %
Rukuni a kan v2.0
0 %
Mutum-mutumai masu sabuntawa
0
Saitin gudu a yanki A
1.5 m/s
Lokacin ma'aikaci kan mutum-mutumai
0 min
Awowin mutum-mutumi da aka yi amfani
0 h
Mutum-mutumai masu aiki
24
Mutum-mutumai masu tafiya
0
Ainihin gudu a yanki A
1.50 m/s
Jira a kowace ketarewar mahaɗa
0.0 s
Wutar da rukunin ke ci
0.00 kW
Ƙarfin caji da aka bayar
0.00 kW
Ɗakunan cobot masu aiki
0 %
Yanayi
Yanayin rikici
Mataki 1 · Rabin cajoji sun lalace kafin ƙololuwar odoji
Aikin safe, mutum-mutumai 24 masu aiki, kusan odoji 3.7 a minti. Rukunin yana fara aikin da matsakaicin caji na 60 % bayan dare mai cike da aiki. A minti na 15, matsalar wutar lantarki ta lalata cajoji huɗu daga cikin shida har ƙarshen aikin. A minti na 90 ƙololuwar odoji ta fara (+25 % na awa biyu). Ka sa odoji su ci gaba da gudana, ka shiga ƙololuwar da rukuni mai caji, kada ka bar wani mutum-mutumi caji ya ƙare masa, kuma ka tsaya cikin kasafin mutum-mutumai na aikin.
Matsakaicin lokacin isar da oda yayin ƙololuwar da bayanta ≤ 3.5 min
Rukuni da aƙalla 49 % na caji a matsakaici lokacin da ƙololuwar ta fara
Babu mutum-mutumin da caji ya ƙare masa
Awowin mutum-mutumi 97 a mafi yawa don aikin
Nisan tsayawa koyaushe a cikin filin inda mutane suke
Cobot ba zai taɓa wuce iyakar ƙarfi da matsi ba idan akwai mutum a ciki
Mataki 2 · Hanya ta rufe, mutum-mutumai sun toshe juna, ƙungiya ta shiga yanki A
Kusan odoji 4.2 a minti, mutum-mutumai 24, sarrafa zirga-zirga an saita shi zuwa tuƙi na 'yanci. A minti na 10 an rufe wata hanya don sake jera shelf: mahaɗai kaɗan, ƙarin haɗuwa fuska da fuska kuma babu hanyar kewaye. A minti na 60 ƙungiyar gyara ta shiga yanki A na mutum-mutumai kaɗai na mintuna 40. Ka sa odoji su ci gaba da tafiya da ɗan lokacin ma'aikaci kaɗan, ka ajiye kowane nisan tsayawa a cikin filin tsaro inda mutane suke, kuma ka sake tafiyar da yanki A da cikakken gudu da zarar ya share.
Matsakaicin lokacin isar da oda ≤ 6 min
Yanki A ya koma ≥ 1.4 m/s a matsakaici bayan ƙungiyar ta tafi
Kulle-juna 1 a mafi yawa
Mintuna 20 na ma'aikaci a mafi yawa kan mutum-mutumai
Nisan tsayawa koyaushe a cikin filin inda mutane suke
Cobot ba zai taɓa wuce iyakar ƙarfi da matsi ba idan akwai mutum a ciki
Mataki 3 · Fitar canary ta sabuwar manhajar kewayawa
An sake jera shelf na hanyoyin a daren jiya kuma mutum-mutumai masu manhajar yanzu (v1) suna yawan rasa wurinsu a can; kowace asara tana buƙatar ma'aikaci. Siga v2.0 tana gyara hakan kuma tana aiki a kan 10 % na rukunin a matsayin canary. Ba canary isasshen lokaci don a yi mata hukunci, kwatanta ta da sauran rukunin, yanke shawarar faɗaɗa ko mayar da baya, kuma ka kai rukunin kan siga mai kyau — mataki-mataki, ba tare da cire mutum-mutumai da yawa a lokaci guda ba.
An bar canary tana aiki a mintuna 12 na farko (≥ 5 % na rukunin a kan v2.0)
An bar v2.0 mai matsala daga minti na 30 zuwa 49 (≤ 1 % na rukunin a kanta a matsakaici)
Gyaran gaggawa a kan 20 % na rukunin a mafi yawa a mintunansa 10 na farko
An fitar da gyaran gaggawa da wuri: a matsakaici ≥ 55 % na rukunin a kanta bayan an wallafa ta
Aƙalla 90 % na rukunin a kan sabuwar siga a ƙarshe
Aƙalla 60 % na mutum-mutumai a shirye koyaushe
Nisan tsayawa koyaushe a cikin filin inda mutane suke
Cobot ba zai taɓa wuce iyakar ƙarfi da matsi ba idan akwai mutum a ciki
Tushe — samfurin da ke bayan lambobin
Kowace alaƙa da na'urar koyi ke amfani da ita, tare da tushenta. Ƙayyadaddun ƙimomin da aka yi wa alama a matsayin zato daidaitawa ne na misali.
Dokar Little: duk odar da ba a kammala shiryawa ba tukuna — mai jira ko wadda ke kan mutum-mutumi — idan aka raba da saurin da ake shirya akwatuna a zahiri, za a sami lokacin isar da oda.
lead time W = L / X, L = orders waiting + orders on a robot, X = totes packed per minute (smoothed, τ = 10 min)[5]
Gudu yana raguwa yayin da ƙarin mutum-mutumai ke raba hanyoyin (dangantakar layi ta gudu–yawa ta Greenshields).
v_eff = v · max(0.1, 1 − n_moving / N_jam), N_jam = 120 robots (80 with an aisle closed)[7][9]Ƙimomin misali ne, ba na wani ainihin wuri ko samfur ba. Ainihin wurare suna saita filaye, gudu da iyakoki daga nasu kimanta haɗari da bayanan mai ƙera.
Ba tare da ajiya ba, mutum-mutumai biyu na iya kowanne jiran wurin da ɗayan ke riƙe — jira mai zagaye. Haɗuwa tana ƙaruwa da murabba'in yawan mutum-mutumai masu tafiya.
free traffic: P(new deadlock in a minute) = 1 − e^(−κ·n_moving²/n_I), κ = 0.00001 (× 300 with an aisle closed, n_I = 6 → 4); a robot behind joins with p = 0.5 (≤ 8); the fleet manager re-plans with p = 0.2/min (0.03/min with no detour)[8][10]Ƙimomin misali ne, ba na wani ainihin wuri ko samfur ba. Ainihin wurare suna saita filaye, gudu da iyakoki daga nasu kimanta haɗari da bayanan mai ƙera.
Ajiyar yanki: mutum-mutumi yana shiga ne kawai idan an ajiye masa yankunan da ke gabansa (gaba ɗaya a lokaci guda, a tsayayyen jeri), wanda ke kawar da jiran da'ira; daga nan kowace mahaɗa tana aiki kamar layin jira mai mai hidima ɗaya da tsayayyen lokacin ketarewa.
zone reservation: a robot enters only when the zones ahead are granted to it → no circular wait; each crossing W = ρτ / (2(1 − ρ)), ρ = λ_I·τ, τ = 2 s, 6 crossings per task[8][6][9]Ƙimomin misali ne, ba na wani ainihin wuri ko samfur ba. Ainihin wurare suna saita filaye, gudu da iyakoki daga nasu kimanta haɗari da bayanan mai ƙera.
Inda mutane za su iya kasancewa, nisan tsayawa — tafiyar lokacin martani tare da birki — dole ya dace a cikin filin gano mutane.
d_stop = v·t_r + v²/(2a) + C ≤ F (t_r = 0.3 s, a = 0.8 m/s², C = 0.1 m, F = 1.3 m ⇒ v ≤ 1.17 m/s where people can be)[1][2]Ƙimomin misali ne, ba na wani ainihin wuri ko samfur ba. Ainihin wurare suna saita filaye, gudu da iyakoki daga nasu kimanta haɗari da bayanan mai ƙera.
Iyakar ƙarfi da matsi: mafi girman gudun da taɓawa da hannu ke kasancewa ƙasa da matsin da aka yarda, wanda aka lissafa daga rage nauyin hannu da mutum-mutumi da taurin hannun. Ana amfani da iyakar quasi-static har ma don taɓawa ta ɗan lokaci, wanda ke nufin taka-tsantsan.
v ≤ F / √(μ·k), μ = (1/m_H + 1/m_R)⁻¹, m_R = M/2 + m_L; hand: F = 140 N (quasi-static limit, used conservatively), k = 75 N/mm, m_H = 0.6 kg; M = 24 kg, m_L = 3 kg ⇒ v ≤ 0.67 m/s[3][4]Ƙimomin misali ne, ba na wani ainihin wuri ko samfur ba. Ainihin wurare suna saita filaye, gudu da iyakoki daga nasu kimanta haɗari da bayanan mai ƙera.
Akwatin kayayyaki yana ɗaukar lokacin kamawa tare da miƙa hannu sau biyu ga kowane kaya; idan akwai mutum a ciki, cobot yana aiki da gudun haɗin gwiwa. Ana yi wa mutum-mutumai hidima bisa tsarin isowarsu ɗakunan, daƙiƙa bayan daƙiƙa a cikin kowane minti.
tote time = 10 items × (1.5 s + 2 × 0.5 m / v_cobot); v_cobot = collaborative speed while a person is in the cell; 4 cells, served in order of arrival within the minute[3]Ƙimomin misali ne, ba na wani ainihin wuri ko samfur ba. Ainihin wurare suna saita filaye, gudu da iyakoki daga nasu kimanta haɗari da bayanan mai ƙera.
Ƙarfin tafiya: nauyin lantarki tsayayye, juriyar birgima, da makamashin birki da ke ɓacewa a kowace tsayawa da tashi.
P = 60 W + C_rr·m·g·v/η + 0.03/m · v · ½mv²·(1 − r)/η (C_rr = 0.012, m = 500 kg, η = 0.75, r = 0.5)[12]Ƙimomin misali ne, ba na wani ainihin wuri ko samfur ba. Ainihin wurare suna saita filaye, gudu da iyakoki daga nasu kimanta haɗari da bayanan mai ƙera.
Cajoji suna ba da cikakken ƙarfi har kusan 70 % caji, sannan wutar tana raguwa (wuta mai daidaito, sannan ƙarfin lantarki mai daidaito).
P_charge = 0.8 kW up to 70 % SoC, then × (1 − 0.9·(SoC − 70)/30); battery 0.8 kWh; stranded at 1 %[11][10]Ƙimomin misali ne, ba na wani ainihin wuri ko samfur ba. Ainihin wurare suna saita filaye, gudu da iyakoki daga nasu kimanta haɗari da bayanan mai ƙera.
Mutum-mutumi yana tsayawa idan haɗinsa da manajan rukuni ya yi shiru fiye da lokacin watchdog ɗinsa; gajeren watchdog yana kama ƙarin gajerun katsewar Wi-Fi da yawa.
P(link silent > W in a robot-minute) = 0.224·e^(−W/0.1 s); watchdog W: v1 0.5 s, v2.0 0.15 s, v2.1 0.5 s; stop 2 min[13]Ƙimomin misali ne, ba na wani ainihin wuri ko samfur ba. Ainihin wurare suna saita filaye, gudu da iyakoki daga nasu kimanta haɗari da bayanan mai ƙera.
Kwatancen canary: tsayawa a kowace awa-mutum-mutumi na mutum-mutumai da ke kan sabuwar siga idan aka kwatanta da sauran rukunin.
stops per robot-hour, canary vs control: 60·stops / robots (smoothed τ = 10 min); update or rollback = 4 min out of service[13]
Sauran ƙayyadaddun ƙimomin wannan samfuri
task 200 m in zone A + 40 m in the shared area · 6 intersections · 4 cobot cells, a person inside 25 % of minutes · 6 chargers · shift-start charge stratified over mean ± 27.5 % · v1 mislocalises 0.6 % per driving minute in re-racked aisles (others 0.04 %), 6-min stop + 3 operator-min · clearing a deadlock 2 operator-min per robot · tow 15 operator-minƘimomin misali ne, ba na wani ainihin wuri ko samfur ba. Ainihin wurare suna saita filaye, gudu da iyakoki daga nasu kimanta haɗari da bayanan mai ƙera.
Rashin tsari: mai samar da mulberry32 mai iri; rarrabawar da aka yi amfani da su — uniform, exponential (inverse CDF), normal (Box–Muller), Poisson (Knuth). Ana nuna iri kuma ana iya raba shi.
M. Harchol-Balter — Performance Modeling and Design of Computer Systems (M/G/1 Pollaczek–Khinchine mean wait; M/D/1) — Cambridge University Press, 2013
B. D. Greenshields — A Study of Traffic Capacity (linear speed–density relation) — Highway Research Board Proceedings 14:448–477, 1935