WIA SOOM Simulators

Ukusebenza kweqembu lamarobhothi Imodeli ephilayo

Uphethe iphansi lendlu yokugcina impahla lapho cishe amarobhothi ahambayo azimele angu-24 (ama-AMR) ethwala amabhokisi esuka emigwaqweni yokugcina eya emaseli amane e-cobot okupakisha. I-oda ngalinye liwuhambo lwama-240 m — 200 m emigwaqweni yamarobhothi kuphela, 40 m endaweni ehlanganyelwe lapho abantu besebenza khona — kanye nokukhetha (pick) eselini. Imodeli ibala imigqa yokulinda, ukuminyana, ama-deadlock, amabanga okuma, amandla ebhethri namandla amashaja, kanye nomthelela wezinguqulo zesofthiwe ekumeni, umzuzu nomzuzu, kusukela emazingeni ashicilelwe nezifomula zezincwadi zokufunda. Iyimodeli yezimiso zokusebenza: ayisebenzisi isofthiwe yerobhothi, futhi izinombolo zivamile, aziyona ezomkhiqizo othile. Ukulingisa kwezemfundo kuphela — izindawo zangempela zilandela ukuhlola kwazo ubungozi.

Okuzofunda

Isilingisi

Isikhathi 0 min
Amarobhothi asebenzayo 24 · Amabhokisi apakishiwe 360/h · Isikhathi sokulinda i-oda 0.0 min · Amarobhothi atholakalayo 100% · Indawo A (amarobhothi kuphela) 1.5 m/s · Indawo ehlanganyelwe 1.0 m/s (Δ 0.27 m) · Okukhululekile (ukugwemana endaweni), Amarobhothi abambeke ku-deadlock 0 · Amaseli e-cobot 0%, Umuntu eselini le-cobot 0 · Amashaja 0/6 (Ishaja ayisebenzi 0), Amarobhothi alinde ishaja 0 · Ukushaja okumaphakathi kwebhethri 67% · v1 24, v2.0 0, v2.1 0 · Ukuma ngehora-lerobhothi, i-build entsha kakhulu 0.0/h, Ukuma ngehora-lerobhothi, iqembu eliseleyo 0.0/h⁨24⁩ · ⁨360/h⁩ · ⁨Amarobhothi⁩························⁨✓ 1.5 m/s⁩⁨Indawo A (amarobhothi…⁨abekho abantu⁩⁨⚠ 1.0 m/s⁩ · ⁨Δ 0.27 m⁩⁨Indawo ehlanganyelwe⁩⁨⛔ 0⁩⁨Okukhululekile (ukugwemana…⁨0%⁩ · ⁨Amaseli e-cobot⁩⚙⚙⚙⚙⁨⚡ 0/6⁩ · ⁨⌛ 0⁩ · ⁨Amashaja⁩······⁨Isofthiwe: v1 · v2.0 · v2.1⁩⁨v1 24⁩ · ⁨v2.0 0⁩ · ⁨v2.1 0⁩⁨0.0/h entsha kakhulu⁩⁨0.0/h asele⁩
  • Lihamba nomsebenzi
  • Eseli le-cobot
  • Lilinde iseli
  • Alenzi lutho
  • Liyashajwa
  • Lilinde ishaja
  • Libuyekeza isofthiwe
  • Limile (ukuxhumana noma indawo)
  • Libambeke ku-deadlock
  • Liphelelwe ugesi, lidonsiwe
  • Indawo engenabantu
  • Abantu endaweni, isivinini singaphakathi kwendawo yokubona
  • Kushesha kakhulu endaweni yokubona lapho kunabantu
  • Umuntu eselini le-cobot
  • Ishaja ayisebenzi

Izilawuli

Amarobhothi angeziwe avuswa endaweni yokugcina; amarobhothi apakiwe awasebenzisi ugesi. Irobhothi ngalinye elisebenzayo libiza ihora-lerobhothi elilodwa ngehora.

Indawo A ivaliwe kubantu, ngakho amarobhothi angahamba ngesivinini esiphezulu. Uma abantu bengena kuyo, isivinini kufanele siphinde sihambisane nendawo yokubona abantu.

Abantu bahlala besebenza lapha. Ibanga lokuma kulesi sivinini kufanele lingene ngaphakathi kwendawo yokubona abantu engu-1.3 m.

Okukhululekile: amarobhothi agwemana endaweni kuphela — kuyashesha, kodwa amabili noma ngaphezulu angavimbana unomphela. Ukubhukha izindawo: irobhothi lingena empambanweni kuphela uma izindawo eziphambi kwalo sezibhukhelwe lona — awekho ama-deadlock, ukulinda okufushane ekuweleni ngakunye.

Ikhulula wonke amarobhothi abambeke ku-deadlock manje. Kubiza imizuzu ka-opharetha engu-2 ngerobhothi ngalinye elikhululiwe; akuvimbi ama-deadlock amasha ukuthi akheke.

Irobhothi eliqeda umsebenzi linalokhu kushaja noma ngaphansi lijoyina ulayini weshaja. Inani eliphansi lisebenzisa ibhethri kakhulu, kodwa irobhothi elilinda isikhathi eside kakhulu lingaphelelwa ugesi ngokuphelele.

Amashaja anikeza amandla agcwele kuze kufike cishe ku-70 %; ngaphezu kwalokho amandla kagesi ayehla kancane kancane. Ukuma kusenesikhathi kukhulula ishaja ngokushesha.

Amarobhothi angenamsebenzi aya kunoma iyiphi ishaja ekhululekile esikhundleni sokulinda engenzi lutho, futhi abuyela emsebenzini lapho ama-oda elinde futhi enokushaja okungu-20 % ngaphezu kwezinga lokuthunyelwa ukuyoshajwa.

Isivinini sethuluzi lapho kungekho muntu ngaphakathi kweseli. Ibhokisi lezinto ezingu-10 lithatha u-25 s ku-1 m/s.

Umkhawulo wamandla nomfutho: isandla esivaleleke ebhokisini akumele sizwe ngaphezu kuka-140 N (umkhawulo we-quasi-static, osetshenziswa ngokuqaphela), okuvumela isivinini esingeqi ku-0.67 m/s lapha.

Ukuhambisa isilayida kukhipha i-build entsha kakhulu eshicilelwe kuleyo ngxenye yeqembu (amarobhothi okuqala ngokulandelana); amanye asebenzisa i-v1. I-build eshicilelwa kamuva ifakwa kuphela uma uphinda uhambisa isilayida. Irobhothi ngalinye elishintsha inguqulo liba ngaphandle kokusebenza imizuzu engu-4.

Izikhombisi

Amabhokisi apakishiwe
360/h
kuvamile
Isikhathi sokulinda i-oda
0.0min
kuvamile
Amarobhothi atholakalayo
100%
kuvamile
Umkhawulo wokuma lapho kunabantu
0.27m
kuvamile
Ama-oda alindile0
Umkhawulo wesivinini se-cobot (umkhawulo wamandla nomfutho)0.17 m/s
Ukushaja okumaphakathi kwebhethri67 %
Ukushaja okuphansi kakhulu kwebhethri42 %
Amarobhothi alinde ishaja0
Amarobhothi ashajwayo0
Amarobhothi aphelelwe ugesi (adonsiwe)0
Amarobhothi abambeke ku-deadlock0
Ama-deadlock akhekile0
Ukuma kokuzulazula (ukuxhumana noma indawo)0
Ukuma ngehora-lerobhothi, i-build entsha kakhulu0.0 /h
Ukuma ngehora-lerobhothi, iqembu eliseleyo0.0 /h
Iqembu ku-build entsha kakhulu0 %
Iqembu ku-v2.00 %
Amarobhothi abuyekezwayo0
Isilungiselelo sesivinini sendawo A1.5 m/s
Isikhathi sika-opharetha esichithwe kumarobhothi0 min
Amahora-erobhothi asetshenzisiwe0 h
Amarobhothi asebenzayo24
Amarobhothi ahambayo0
Isivinini sangempela endaweni A1.50 m/s
Ukulinda ekuweleni impambano ngayinye0.0 s
Amandla asetshenziswa yiqembu0.00 kW
Amandla anikezwe amashaja0.00 kW
Amaseli e-cobot amatasa0 %

Isitayela

Amabhokisi apakishiwe: — /h6000

Izimo eziphuthumayo

Izinga 1 · Ingxenye yamashaja iyehluleka ngaphambi kwesiqongo sama-oda

Ishifu yasekuseni, amarobhothi angu-24 asebenzayo, cishe ama-oda angu-3.7 ngomzuzu. Ngemva kobusuku obumatasa, iqembu liqala ishifu lishajwe ngokwesilinganiso ngo-60 %. Ngomzuzu we-15 iphutha likagesi likhipha amashaja amane kwayisithupha ekusebenzeni ishifu yonke esele. Ngomzuzu we-90 kuqala isiqongo sama-oda (+25 % amahora amabili). Gcina ama-oda egeleza, ngena esiqongweni neqembu elishajiwe, ungavumeli irobhothi liphelelwe ugesi, futhi uhlale ngaphakathi kwesabelomali samarobhothi sale shifu.

  • Isikhathi sokulinda esimaphakathi phakathi nangemva kwesiqongo ≤ 3.5 min
  • Iqembu lishajwe okungenani ngo-49 % ngokwesilinganiso lapho isiqongo siqala
  • Alikho irobhothi eliphelelwa ugesi
  • Amahora-erobhothi angeqi ku-97 eshifini
  • Ibanga lokuma lihlale ngaphakathi kwendawo lapho kunabantu
  • I-cobot ayikaze isheshe ukwedlula umkhawulo wamandla nomfutho kunomuntu ngaphakathi

Izinga 2 · Umgwaqo uyavalwa, amarobhothi ayabambeka, futhi ithimba lingena endaweni A

Cishe ama-oda angu-4.2 ngomzuzu, amarobhothi angu-24, ukulawula ithrafikhi kusethwe ekushayeleni okukhululekile. Ngomzuzu we-10 umgwaqo owodwa uyavalwa ukuze kuhlelwe kabusha amashalofu: izimpambano ezimbalwa, ukuhlangana ubuso nobuso okuningi futhi azikho izindlela zokuphambuka. Ngomzuzu we-60 ithimba lokulungisa lingena endaweni A yamarobhothi kuphela imizuzu engu-40. Gcina ama-oda ehamba ngesikhathi esincane sika-opharetha, gcina wonke amabanga okuma ngaphakathi kwendawo yokuphepha lapho kunabantu, futhi uphinde usebenzise indawo A ngesivinini esigcwele uma isikhululekile.

  • Isikhathi sokulinda esimaphakathi ≤ 6 min
  • Indawo A ibuyele ku-≥ 1.4 m/s ngokwesilinganiso ngemva kokuphuma kwethimba
  • Kwakheka ama-deadlock angeqi ku-1
  • Imizuzu ka-opharetha engeqi ku-20 kumarobhothi
  • Ibanga lokuma lihlale ngaphakathi kwendawo lapho kunabantu
  • I-cobot ayikaze isheshe ukwedlula umkhawulo wamandla nomfutho kunomuntu ngaphakathi

Izinga 3 · Ukukhishwa kwe-canary kwesofthiwe entsha yokuzulazula

Amashalofu emigwaqo ahlelwe kabusha izolo ebusuku futhi amarobhothi asesofthiweni yamanje (v1) alahlekelwa yindawo yawo lapho kaningi; ukulahleka ngakunye kudinga u-opharetha. Ukukhishwa kwe-v2.0 kulungisa lokho futhi sekuvele kusebenza ku-10 % weqembu njenge-canary. Nika i-canary isikhathi esanele ukuze uyihlole, uyiqhathanise nalo lonke iqembu, unqume ukuthi uyandisa noma uyibuyisela emuva, futhi ufake iqembu ku-build enhle — ngezigaba, ngaphandle kokukhipha amarobhothi amaningi kakhulu ngesikhathi esisodwa.

  • I-canary yagcinwa isebenza emizuzwini engu-12 yokuqala (≥ 5 % weqembu ku-v2.0)
  • Iqembu lisuke ku-v2.0 enephutha kusukela ngomzuzu we-30 kuya ku-49 (≤ 1 % weqembu kuyo ngokwesilinganiso)
  • I-hotfix ingeqi ku-20 % weqembu emizuzwini yayo engu-10 yokuqala
  • I-hotfix ikhishwe ngokushesha: ngokwesilinganiso ≥ 55 % weqembu kuyo ngemva kokushicilelwa
  • Okungenani u-90 % weqembu ku-build entsha kakhulu ekugcineni
  • Okungenani u-60 % wamarobhothi atholakala ngaso sonke isikhathi
  • Ibanga lokuma lihlale ngaphakathi kwendawo lapho kunabantu
  • I-cobot ayikaze isheshe ukwedlula umkhawulo wamandla nomfutho kunomuntu ngaphakathi

Isisekelo — imodeli engemuva kwezinombolo

Wonke ubudlelwano isilingisi esibusebenzisayo, nomthombo wabo. Izinto ezihlala zingashintshi ezimakwe njengokuthathelwa yizilinganiso zesibonelo.

Umthetho kaLittle: wonke ama-oda angakapakishwa — alindile noma asevele ethwelwe yirobhothi — ahlukaniswe ngesilinganiso amabhokisi apakishwa ngaso ngempela, kunikeza isikhathi sokulinda i-oda.
lead time W = L / X, L = orders waiting + orders on a robot, X = totes packed per minute (smoothed, τ = 10 min)[5]
Isivinini siyehla njengoba amarobhothi amaningi ehlanganyela imigwaqo (ubudlelwano obuqondile besivinini–ubuningi buka-Greenshields).
v_eff = v · max(0.1, 1 − n_moving / N_jam), N_jam = 120 robots (80 with an aisle closed)[7][9]Amanani okubonisa, hhayi awendawo yangempela noma womkhiqizo wangempela. Izindawo zangempela zisetha izindawo zokubona, izivinini nemikhawulo ngokuhlola kwazo ubungozi nangedatha yomkhiqizi.
Ngaphandle kokubhukha, amarobhothi amabili angalinda ngalinye isikhala esibanjwe elinye — ukulinda okujikelezayo. Ukuhlangana kukhula ngesikwele senani lamarobhothi ahambayo.
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]Amanani okubonisa, hhayi awendawo yangempela noma womkhiqizo wangempela. Izindawo zangempela zisetha izindawo zokubona, izivinini nemikhawulo ngokuhlola kwazo ubungozi nangedatha yomkhiqizi.
Ukubhukha izindawo: irobhothi lingena kuphela uma izindawo eziphambi kwalo sezibhukhelwe lona (zonke ngesikhathi esisodwa, ngokulandelana okungaguquki), okususa ukulindana okuyindilinga; impambano ngayinye ibe isiziphatha njengolayini onomsizi oyedwa onesikhathi sokuwela esingaguquki.
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]Amanani okubonisa, hhayi awendawo yangempela noma womkhiqizo wangempela. Izindawo zangempela zisetha izindawo zokubona, izivinini nemikhawulo ngokuhlola kwazo ubungozi nangedatha yomkhiqizi.
Lapho abantu bengaba khona, ibanga lokuma — ibanga lokusabela kanye nokubhuleka — kufanele lingene ngaphakathi kwendawo yokubona abantu.
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]Amanani okubonisa, hhayi awendawo yangempela noma womkhiqizo wangempela. Izindawo zangempela zisetha izindawo zokubona, izivinini nemikhawulo ngokuhlola kwazo ubungozi nangedatha yomkhiqizi.
Umkhawulo wamandla nomfutho: isivinini esiphezulu lapho ukuthintana nesandla kuhlala ngaphansi komfutho ovunyelwe, kubalwa kusukela esisindweni esincishisiwe (reduced mass) sesandla nerobhothi kanye nokuqina kwesandla. Umkhawulo we-quasi-static usetshenziswa ngisho nasekuthintaneni okufushane, okuwukuqaphela.
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]Amanani okubonisa, hhayi awendawo yangempela noma womkhiqizo wangempela. Izindawo zangempela zisetha izindawo zokubona, izivinini nemikhawulo ngokuhlola kwazo ubungozi nangedatha yomkhiqizi.
Ibhokisi lezimpahla lithatha isikhathi sokubamba kanye nokwelula okubili ngempahla ngayinye; uma kunomuntu ngaphakathi, i-cobot isebenza ngesivinini sokusebenzisana. Amarobhothi asizwa ngokulandelana kokufika kwawo emaseli, umzuzwana ngomzuzwana phakathi komzuzu ngamunye.
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]Amanani okubonisa, hhayi awendawo yangempela noma womkhiqizo wangempela. Izindawo zangempela zisetha izindawo zokubona, izivinini nemikhawulo ngokuhlola kwazo ubungozi nangedatha yomkhiqizi.
Amandla okuhamba: umthwalo ongaguquki we-elekthronikhi, ukumelana kokugingqika, namandla okubhuleka alahleka lapho kumiswa futhi kuhanjwa.
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]Amanani okubonisa, hhayi awendawo yangempela noma womkhiqizo wangempela. Izindawo zangempela zisetha izindawo zokubona, izivinini nemikhawulo ngokuhlola kwazo ubungozi nangedatha yomkhiqizi.
Amashaja anikeza amandla agcwele kuze kufike cishe ku-70 % wokushaja, bese amandla kagesi ehla kancane kancane (i-current engaguquki, bese i-voltage engaguquki).
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]Amanani okubonisa, hhayi awendawo yangempela noma womkhiqizo wangempela. Izindawo zangempela zisetha izindawo zokubona, izivinini nemikhawulo ngokuhlola kwazo ubungozi nangedatha yomkhiqizi.
Irobhothi liyama lapho ukuxhumana nomphathi weqembu kuthula isikhathi eside kune-watchdog yalo; i-watchdog emfushane ibamba ukuphazamiseka okufushane kwe-Wi-Fi okuningi kakhulu.
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]Amanani okubonisa, hhayi awendawo yangempela noma womkhiqizo wangempela. Izindawo zangempela zisetha izindawo zokubona, izivinini nemikhawulo ngokuhlola kwazo ubungozi nangedatha yomkhiqizi.
Ukuqhathanisa kwe-canary: ukuma ngehora-lerobhothi kwamarobhothi aku-build entsha kakhulu kuqhathaniswa nalo lonke iqembu eliseleyo.
stops per robot-hour, canary vs control: 60·stops / robots (smoothed τ = 10 min); update or rollback = 4 min out of service[13]
Ezinye izinto ezingaguquki zale modeli
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-minAmanani okubonisa, hhayi awendawo yangempela noma womkhiqizo wangempela. Izindawo zangempela zisetha izindawo zokubona, izivinini nemikhawulo ngokuhlola kwazo ubungozi nangedatha yomkhiqizi.

Ukungahleliwe: i-generator ye-mulberry32 enembewu; ukusabalalisa okusetshenzisiwe — uniform, exponential (inverse CDF), normal (Box–Muller), Poisson (Knuth). Imbewu iyabonisa futhi ingabelwana.

Imithombo

  1. ISO 3691-4:2023 Industrial trucks — Safety requirements and verification — Part 4: Driverless industrial trucks and their systems (personnel detection, zones, speed) — ISO/TC 110/SC 2, 2023
  2. ISO 13855:2024 Safety of machinery — Positioning of safeguards with respect to the approach of the human body (minimum distance S = K·T + C; replaces the 2010 edition) — ISO/TC 199, 2024
  3. ISO/TS 15066:2016 Robots and robotic devices — Collaborative robots (Annex A: body-region limits; transient contact speed v = F/√(μk), μ = (1/m_H + 1/m_R)⁻¹, m_R = M/2 + m_L) — ISO/TC 299, 2016
  4. ISO 10218-2:2025 Robotics — Safety requirements — Part 2: Industrial robot applications and robot cells (collaborative applications; takes over the ISO/TS 15066 body-region data) — ISO/TC 299, 2025
  5. J. D. C. Little — A Proof for the Queuing Formula: L = λW — Operations Research 9(3):383–387, 1961
  6. M. Harchol-Balter — Performance Modeling and Design of Computer Systems (M/G/1 Pollaczek–Khinchine mean wait; M/D/1) — Cambridge University Press, 2013
  7. B. D. Greenshields — A Study of Traffic Capacity (linear speed–density relation) — Highway Research Board Proceedings 14:448–477, 1935
  8. E. G. Coffman, M. Elphick, A. Shoshani — System Deadlocks (the four necessary conditions; prevention by ordered resource allocation) — ACM Computing Surveys 3(2):67–78, 1971
  9. I. F. A. Vis — Survey of research in the design and control of automated guided vehicle systems (fleet sizing, zone control, deadlocks, battery management) — European Journal of Operational Research 170(3):677–709, 2006
  10. M. De Ryck, M. Versteyhe, F. Debrouwere — Automated guided vehicle systems, state-of-the-art control algorithms and techniques (traffic, deadlock avoidance, battery charging strategies) — Journal of Manufacturing Systems 54:152–173, 2020
  11. BU-409: Charging Lithium-ion (constant current to about 70 % state of charge, then constant voltage while the current tapers) — Battery University
  12. T. D. Gillespie — Fundamentals of Vehicle Dynamics (rolling resistance F = C_rr·m·g; kinetic energy lost in braking) — SAE International, 1992
  13. The Site Reliability Workbook — Ch. 16 Canarying Releases (canary vs control, multi-stage rollout, rollback) — Beyer, Murphy, Rensin, Kawahara, Thorne (eds.), O'Reilly, 2018

Obani abenza lokhu ukuze baziphilise

Imodeli yemfundo — hhayi yezinqumo zokusebenza. Izindawo zangempela zilinganisa yonke into ehlala ingashintshi kumishini nedatha yazo.