Table of Contents
1. Gabatarwa
Robotics da tsarin mulkin kai suna ƙara dogaro da haɗaɗɗun na'urori masu auna bayanai da yawa, musamman haɗa bayanan gani daga kyamarori tare da ingantattun bayanan lissafi daga na'urorin auna nisa na laser (LRFs). Na'urar auna nisa ta laser 2D, saboda tsada da amincinta, ita ce babbar kayan aiki a cikin robotics mai motsi. Duk da haka, haɗa bayananta da hotunan kyamara yana buƙatar sanin daidaiton matsayinsu na dangi—wata matsala da aka sani da kwatance na waje. Babban ƙalubalen da aka magance a cikin wannan takarda shi ne cewa filin dubawa na na'urar auna nisa ta laser 2D ba a iya gani ga kyamara ta al'ada, wanda ke sa daidaiton fasalin kai tsaye ya zama ba zai yiwu ba. Wannan aikin yana gabatar da sabuwar mafita, mafi ƙarancin amfani da kallo ɗaya na manufa da aka ƙera ta musamman mai siffar V.
2. Hanyar Aiki
2.1 Tsarin Matsala
Manufar ita ce a nemo canjin ƙarfi $T = \{R, t\}$, inda $R$ keɓaɓɓen matrix na juyawa 3x3 ne kuma $t$ shine vector na fassara 3x1, wanda ke nuna maki daga tsarin daidaitawa na LRF $L$ zuwa tsarin daidaitawa na kyamara $C$. Ba tare da daidaiton kai tsaye tsakanin maki na laser da pixels ba, matsalar ba ta da ƙayyadaddun ƙa'idodi ta amfani da hanyoyin PnP na gargajiya.
2.2 Manufar Kwatance Mai Siffar V
Manufar kwatance da aka gabatar, wacce aka nuna a Hoto na 1 na PDF, ta ƙunshi filaye biyu na triangular waɗanda ba su da layi ɗaya an jera su cikin siffar V, kowannensu an ƙawata shi da tsarin allon duba. Allon duba yana sauƙaƙa ingantaccen ƙididdige matsayi na kowane fili dangane da kyamara. Filin dubawa na LRF yana haɗuwa da wannan siffar V, yana samar da sassan layi biyu akan filayen triangular biyu.
2.3 Ƙayyadaddun Aya-zuwa-Fil
Babban ƙirƙira yana cikin amfani da ƙayyadaddun aya-zuwa-fil maimakon aya-zuwa-aya ko aya-zuwa-layi. Kowane aya na laser $p^L$ da ke kan sanannen fili $\Pi$ a cikin tsarin kyamara dole ne ya gamsar da lissafin fili: $n^T (R p^L + t) + d = 0$, inda $n$ shine naúrar al'ada ta fili kuma $d$ shine nisanta daga asali. Kallo ɗaya yana ba da ƙayyadaddun irin wannan da yawa daga maki akan triangles biyu.
3. Mafita ta Nazari
3.1 Cirewar Lissafi
Marubutan sun nuna cewa ƙayyadaddun daga kallon siffar V ɗaya za a iya tsara su cikin tsarin lissafi. Ta hanyar haɗa ƙayyadaddun daga maki akan filaye biyu da dabara, sun kawar da vector na fassara $t$ da farko, suna rage matsalar zuwa warware juyawa $R$ daga lissafin quadratic. Da zarar an ƙayyade $R$, ana iya lissafin $t$ a layi daya. Hanyar mafita tana guje wa rashin fahimta da ke cikin hanyoyi kamar Vasconcelos et al. [6] da Zhou [7].
3.2 Hujjar Keɓancewa
Babbar gudummawa ita ce hujja ta yau da kullun cewa ƙayyadaddun da aka gabatar daga kallon siffar V ɗaya suna ba da mafita ta musamman don sigogin waje, ban da tsarin lalacewa (misali, filin LRF yana layi daya da layin haɗuwa na filayen manufa biyu). Wannan yana kawar da buƙatar lura da yawa ko zato na farko, wanda ya kasance babban aibi a cikin fasahar da ta gabata.
4. Gwaje-gwaje da Sakamako
4.1 Gwaje-gwajen Ƙirƙira
An gudanar da gwaje-gwajen ƙirƙira tare da matakan daban-daban na hayaniyar Gaussian da aka ƙara zuwa maki na laser da ganowa na kusurwar hoto. Hanyar da aka gabatar ta ci gaba da samun ƙarancin kuskure a cikin ƙididdige juyawa da fassara idan aka kwatanta da hanyoyin tushe [5, 6, 7], musamman a ƙarƙashin yanayin hayaniya mafi girma, yana nuna ƙarfinta.
4.2 Gwaje-gwajen Duniya ta Ainihi
An yi amfani da na'ura ta zahiri tare da Hokuyo UTM-30LX LRF da kyamara mai stereo (ta amfani da kyamara ɗaya kawai don kwatance). Hanyar da aka gabatar ta sami matsakaicin kuskuren sake zanen maki na laser akan hoton kyamara na kusan pixels 0.3, wanda ya fi na Zhang da Pless [5].
4.3 Kwatanta da Hanyoyin Da suka Gabata
Takardar tana ba da cikakken nazari na kwatanta:
- Zhang & Pless [5] (Maki-a-kan-Fili): Yana buƙatar lura da >20, yana ƙuntata 2 DoF kawai a kowane lura.
- Vasconcelos et al. [6] (P3P): Yana buƙatar lura da ≥3, yana fama da lalacewa (gangar jikin haɗari).
- Hanyar da aka Gabatar: Yana buƙatar lura ɗaya kawai (mafi ƙarancin), yana ba da mafita ta nazari ta musamman, kuma ba shi da lahani ga lalacewar da aka ambata.
5. Nazarin Fasaha & Sharhin Kwararru
Babban Fahimta
Wannan takarda ba wani ci gaba ne kawai ba; canji ne na asali wajen warware matsala mai dorewa ta haɗaɗɗun na'urori masu auna bayanai. Marubutan sun gano daidai cewa tushen matsalar a cikin aikin da ya gabata shine rashin fahimta na asali. Hanyoyi kamar [6] da [7] a zahiri suna ƙoƙarin warware matsalar da ba ta da kyau tare da ƙarin bayanai, wanda ba shi da inganci a lissafi kuma ba shi da aminci. Babban fahimta shine yin amfani da lissafin jiki na 3D na manufa ɗaya, wanda aka ƙera da wayo don shigar da isassun ƙayyadaddun ƙa'idodi don sanya matsalar ta zama mai kyau tun daga farko. Wannan yayi daidai da falsafar da ke bayan nasarar mafita mafi ƙanƙanta a cikin hangen nesa na kwamfuta, kamar waɗanda ke da alaƙa da tsari-daga-motsi, inda kyawun yake cikin samun matsakaicin bayanai daga mafi ƙarancin bayanai.
Kwararar Hankali
Hujjar tana da ƙarfi sosai: 1) Rashin ganin filin laser yana buƙatar ƙayyadaddun ƙa'idodi kai tsaye. 2) Hanyoyin da suka gabata sun yi amfani da ƙayyadaddun ƙa'idodi waɗanda ba su isa ba a kowane lura, wanda ya haifar da rashin fahimta. 3) Manufa mai siffar V tana haifar da filaye biyu daban-daban, waɗanda ba su da layi ɗaya tare da zanen laser. 4) Ƙayyadaddun aya-zuwa-fil daga maki da yawa akan waɗannan filaye biyu yana haifar da tsarin lissafi tare da mafita ta musamman don canjin 6-DoF. Hujjar keɓancewa ita ce maɓalli wanda ya ɗaga wannan daga dabara zuwa hanyar da ta dace.
Ƙarfi & Aibobi
Ƙarfi: Bukatar bayanai mafi ƙarancin (hoton ɗaya) babbar fa'ida ce mai amfani ga kwatance a filin. Mafita ta Nazari tana tabbatar da haɗuwa da sauri, tana guje wa faduwar ingantaccen daidaitawa. Ingantaccen gwaji yana da cikakke, yana rufe duka nazarin hayaniyar ƙirƙira da aikin duniya ta ainihi.
Aibobi & Faɗakarwa: Ƙafar Achilles na hanyar shine tsarin lalacewa. Idan filin dubawa na laser yana layi daya da layin haɗuwa na filayen manufa biyu, ƙayyadaddun ƙa'idodi suna rushewa kuma mafita ta gaza. A aikace, wannan yana buƙatar sanyawa mai kyau yayin kwatance—ƙaramin amma ƙa'ida mai mahimmanci na aiki. Bugu da ƙari, daidaito yana dogara ne akan ingantaccen ƙira da ƙididdige matsayi na manufar V. Duk wani kuskure a cikin daidaita lissafin jiki na manufar (matsayin allon duba) yana yaɗuwa kai tsaye cikin sigogin waje.
Fahimta Mai Aiki
Ga masu aiki: Yi amfani da wannan hanyar don saurin kwatance, a cikin filin sabbin dandamali na mutum-mutumi. Yanayinta na harbi ɗaya ya sa ya dace don tabbatar da kwatance bayan kulawa ko tasiri. Duk da haka, koyaushe a tabbatar da hanyar ta biyu, mai maimaitawa (misali, auna maɓallan nisa da hannu) don karewa daga tsarin lalacewa. Ga masu bincike: Wannan aikin yana buɗe kofa don bincika sauran lissafin jiki na manufa mafi ƙanƙanta. Shin tetrahedron ko fili mai lanƙwasa zai iya ba da ƙarin ƙayyadaddun ƙa'idodi masu ƙarfi? Ƙa'idar amfani da manyan kayan aiki na lissafi (filaye akan layi/maki) don samar da ƙayyadaddun ƙa'idodi shine samfuri mai ƙarfi don sauran matsalolin kwatance na tsaka-tsaki, kamar radar-kyamara ko haɗaɗɗun kyamara mai zafi, waɗanda ke samun karbuwa a cikin binciken tuƙi mai cin gashin kansa a cibiyoyi kamar Cibiyar Robotics ta Carnegie Mellon.
6. Cikakkun Bayanai na Fasaha
6.1 Tsarin Lissafi
Bari aya a cikin tsarin LRF ta zama $p^L = (x^L, y^L, 0)^T$ (tunda yana kan filin z=0 na LRF). Matsayinsa a cikin tsarin kyamara shine $p^C = R p^L + t$. Idan wannan aya yana kan fili a cikin tsarin kyamara tare da sigogi $\pi = (n^T, d)^T$ inda $\|n\|=1$, nisan aya-zuwa-fil shine sifili: $$ n^T (R p^L + t) + d = 0 $$ Ga $N$ maki akan fili ɗaya, wannan yana samar da tsarin: $$ n^T R P^L + n^T t \cdot \mathbf{1}^T + d \cdot \mathbf{1}^T = \mathbf{0}^T $$ inda $P^L$ matrix ne na tarin vectors $p^L$. Dabarar mafita ta haɗa da amfani da maki daga filaye biyu don kawar da $t$ da warware $R$ da farko.
6.2 Lissafin Jiki na Manufar Kwatance
Manufar V an bayyana ta ta hanyar lissafin fili biyu, $\Pi_1: (n_1, d_1)$ da $\Pi_2: (n_2, d_2)$. Layin haɗuwa na waɗannan filaye wani muhimmin abu ne. Layin duban laser $L$ yana haɗuwa da $\Pi_1$ a sashin $S_1$ da $\Pi_2$ a sashin $S_2$. Ana san daidaitawar 3D na maki akan $S_1$ da $S_2$ a cikin tsarin LRF daga dubawa, kuma ana san ainihin filayen da suka dace daga lissafin jiki na haɗuwa.
7. Sakamakon Gwaje-gwaje & Jaridu
Takardar ta haɗa da sakamako na ƙididdiga wanda aka taƙaita shi kamar haka:
Kuskuren Juyawa (Ƙirƙira)
Hanyar da aka Gabatar: ~0.05° - 0.15° a cikin matakan hayaniya.
Hanyar [6]: ~0.1° - 0.4°, babban bambanci.
Hanyar [7]: Sau da yawa ta gaza ko ta samar da kuskure >1° a cikin tsarin kama da lalacewa.
Kuskuren Fassara (Ƙirƙira)
Hanyar da aka Gabatar: ~1-3 mm.
Hanyar [5]: >10 mm, tana buƙatar kallo 20+ don kusanci irin wannan daidaito.
Kuskuren Sake Zanen Duniya ta Ainihi
Hanyar da aka Gabatar: pixels 0.3 (matsakaici).
Hanyar [5]: 0.5 - 0.8 pixels.
Ƙarancin kuskuren sake zanen yana nuna ingantaccen haɗaɗɗun bayanan laser cikin hangen nesa na kyamara.
Lura: Hoto na 1 na takardar yana kwatanta na'urar kwatance da manufar V a zahiri. Hotuna masu zuwa suna yiwuwa suna zana kuskuren juyawa/fassara vs. matakin hayaniya, suna nuna ingantaccen kwanciyar hankali na hanyar da aka gabatar.
8. Tsarin Nazari: Misalin Hali
Yanayi: Mutum-mutumin hidima a asibiti yana buƙatar sake daidaita LRF da kyamararsa bayan maye gurbin ruwan tabarau.
- Hanyar Gargajiya ([5]): Kwararren fasaha dole ne ya ɗauki hotuna 20+ na allon duba a wurare daban-daban, yana tabbatar da cewa layin laser ya ratsa shi kowane lokaci. Tsarin yana ɗaukar mintuna 15-20, yana da saukin yin kuskure ta hanyar bambancin kallo.
- Hanyar da aka Gabatar: Kwararren fasaha yana sanya manufar V a cikin hangen mutum-mutumin. Ana ɗaukar hoton ɗaya inda laser ya bugi fukaɗun manufar biyu a sarari. Software yana lissafin sabon kwatance cikin daƙiƙa.
Fahimtar Tsarin: Ribar inganci ba ta layi daya ba ce; yana da ƙarfi dangane da shirye-shiryen aiki da rage lokacin kashe aiki saboda kwatance. Wannan tsarin yana ba da fifiko ga ƙaramin juzu'in aiki da fitarwa mai ƙayyadaddun ƙa'ida, waɗanda ke da mahimmanci don turawa a duniya ta ainihi.
9. Aikace-aikace na Gaba & Jagorori
- Kwatance Mai Ƙarfi: Shin za a iya faɗaɗa ƙa'idar don aiwatar da kwatance mai ci gaba, kan layi don lissafin karkatar na'urar auna bayanai saboda zafin jiki ko girgiza, ta amfani da tsarin jiki mai kama da V a cikin muhalli?
- Cibiyoyin Sadarwar Na'urori Masu Auna Bayanai Da Yawa: Daidaita cibiyoyin sadarwar na'urori masu auna bayanai da yawa, iri-iri (misali, na'urorin auna nisa na laser da yawa da kyamarori akan motar cin gashin kanta ɗaya) ta amfani da raba lura da manufa.
- Haɗawa tare da Koyo Mai Zurfi: Duk da yake hanyoyin nazari suna da ƙarfi, hanyar haɗaɗɗiya za ta iya amfani da hanyar sadarwar jijiyoyi (wacce aka horar da ita akan bayanan ƙirƙira da aka samar ta amfani da ƙa'idodin wannan hanyar) don ba da zato na farko don daidaitawa a cikin yanayin hayaniya mai tsanani, kama da yadda DeepLabCut ya sauya ƙididdige matsayi.
- Daidaitawa: Wannan hanyar manufar V tana da yuwuwar zama ma'auni ko ka'ida don kwatance na na'urar auna nisa ta laser 2D da kyamara, kamar yadda allon duba yake don kwatance na ciki, saboda ƙarancinsa da bayyananniyar nazari.
10. Nassoshi
- Thrun, S., et al. (2005). Robotics: Hanyoyin Yiwuwa. MIT Press.
- Geiger, A., et al. (2012). Daidaita kyamara da na'urar auna nisa ta atomatik ta amfani da harbi ɗaya. ICRA.
- Pusztai, Z., & Hajder, L. (2017). Ingantaccen kwatance na tsarin LiDAR-kyamara ta amfani da akwatuna na yau da kullun. ICCV Workshops.
- Lepetit, V., et al. (2009). EPnP: Mafita Mai Daidai O(n) ga Matsalar PnP. IJCV.
- Zhang, Q., & Pless, R. (2004). Kwatance na waje na kyamara da na'urar auna nisa ta laser. IROS.
- Vasconcelos, F., et al. (2012). Mafita mafi ƙarancin don kwatance na waje na kyamara da na'urar auna nisa ta laser. TPAMI.
- Zhou, L. (2014). Sabuwar mafita mafi ƙarancin don kwatance na waje na LIDAR 2D da kyamara ta amfani da daidaiton fili-layi uku. IEEE Sensors Journal.
- Kassir, A., & Peynot, T. (2010). Kwatance na atomatik na amintacce na kyamara-laser. ACRA.
- Moghadam, P., et al. (2013). Kwatance na waje na layi na na'urorin auna nisa da hoto. ICRA.
- Dong, W., & Isler, V. (2018). Sabuwar Hanyar don Kwatance na Waje na Na'urar Auna Nisa ta Laser 2D da Kyamara. IEEE Transactions on Robotics. (Wannan takarda).