{"id":48687,"date":"2025-08-31T10:11:15","date_gmt":"2025-08-31T08:11:15","guid":{"rendered":"https:\/\/www.derivaty.sk\/?p=48687"},"modified":"2025-08-31T10:11:15","modified_gmt":"2025-08-31T08:11:15","slug":"reaktivne-planovanie-trajektorii-implementacia-predikcie-dynamickych-prekazok-v-realnom-case","status":"publish","type":"post","link":"https:\/\/www.vrtulniky.sk\/news\/reaktivne-planovanie-trajektorii-implementacia-predikcie-dynamickych-prekazok-v-realnom-case\/","title":{"rendered":"Reakt\u00edvne pl\u00e1novanie trajekt\u00f3ri\u00ed: Implement\u00e1cia predikcie dynamick\u00fdch prek\u00e1\u017eok v re\u00e1lnom \u010dase"},"content":{"rendered":"<h2>Pre\u010do predikova\u0165 dynamick\u00e9 prek\u00e1\u017eky<\/h2>\n<p>Auton\u00f3mne UAV operuj\u00face v komplexn\u00fdch prostrediach (mest\u00e1, priemyseln\u00e9 are\u00e1ly, n\u00edzka letov\u00e1 hladina) sa stret\u00e1vaj\u00fa s dynamick\u00fdmi prek\u00e1\u017ekami: in\u00e9 drony, vt\u00e1ctvo, helikopt\u00e9ry, vozidl\u00e1, \u017eeriavy \u010di \u013eudia. Klasick\u00e9 pl\u00e1novanie s fixa\u010dnou mapou (static map) vedie k suboptim\u00e1lnym alebo nebezpe\u010dn\u00fdm trajekt\u00f3ri\u00e1m. <em>Predikcia pohybu<\/em> \u2013 od kr\u00e1tkodob\u00fdch extrapol\u00e1ci\u00ed po <em>intent-aware<\/em> modely \u2013 umo\u017e\u0148uje pl\u00e1nova\u0165 trajekt\u00f3rie, ktor\u00e9 s\u00fa nielen bezkol\u00edzne, ale aj plynul\u00e9, energeticky efekt\u00edvne a kompatibiln\u00e9 s misiou roja. K\u013e\u00fa\u010dom je prepojenie vn\u00edmania (perception), predikcie (prediction) a pl\u00e1novania (planning) do jednej slu\u010dky s kr\u00e1tkou latenciou.<\/p>\n<h2>Formul\u00e1cia probl\u00e9mu a po\u017eiadavky<\/h2>\n<ul>\n<li><strong>Stavov\u00e9 premenn\u00e9 UAV:<\/strong> $\\mathbf{x}=[\\mathbf{p},\\mathbf{v},\\mathbf{a},\\psi]$ (poloha, r\u00fdchlos\u0165, zr\u00fdchlenie, orient\u00e1cia), s dynamikou obmedzenou maxim\u00e1lnym \u0165ahom, n\u00e1klonom a jerk limitmi.<\/li>\n<li><strong>Reprezent\u00e1cia prek\u00e1\u017eok:<\/strong> mno\u017eina $\\mathcal{O}=\\{o_i\\}$ s \u010dasovo z\u00e1visl\u00fdmi stavmi a neistotou $\\Sigma_i(t)$.<\/li>\n<li><strong>Cie\u013eov\u00e1 funkcia:<\/strong> minimaliz\u00e1cia funkcion\u00e1lu n\u00e1kladov $J=\\int (\\alpha E + \\beta T + \\gamma C + \\delta R)\\,dt$ (energia, \u010das, komfort\/hladkos\u0165, riziko kol\u00edzie), pri dodr\u017ean\u00ed bezpe\u010dnostn\u00fdch a dynamick\u00fdch obmedzen\u00ed.<\/li>\n<li><strong>Bezpe\u010dnostn\u00e9 krit\u00e9ri\u00e1:<\/strong> pravdepodobnos\u0165 kol\u00edzie $P_{col}\\leq \\epsilon$, minim\u00e1lne separa\u010dn\u00e9 vzdialenosti a <em>no-fly<\/em> z\u00f3ny; kompatibilita s UTM\/UTM-like pravidlami.<\/li>\n<\/ul>\n<h2>Modelovanie dynamick\u00fdch prek\u00e1\u017eok<\/h2>\n<ul>\n<li><strong>Fyzik\u00e1lne a kinematick\u00e9 modely:<\/strong> CV\/CVA (constant velocity\/acceleration), bicyklov\u00fd model pre pozemn\u00e9 vozidl\u00e1, holonomick\u00fd bod pre mal\u00e9 UAV.<\/li>\n<li><strong>Stochastick\u00e9 roz\u0161\u00edrenia:<\/strong> procesn\u00fd \u0161um a merac\u00ed \u0161um; Gaussovsk\u00e9 aproxim\u00e1cie pre analytick\u00fa inferenciu.<\/li>\n<li><strong>Interak\u010dne podmienen\u00e9 modely:<\/strong> agenti menia trajekt\u00f3rie v reakcii na UAV; zah\u0155\u0148a\u0165 soci\u00e1lne sily, <em>game-theoretic<\/em> utility, resp. pravidl\u00e1 prednosti.<\/li>\n<li><strong>Neparametrick\u00e9 pr\u00edstupy:<\/strong> Gaussian Processes pre hladk\u00e9 dr\u00e1hy s kvantifik\u00e1ciou neistoty; zmesov\u00e9 modely pre viacm\u00f3dov\u00e9 spr\u00e1vanie (napr. \u201ezastav\u00ed\/nezastav\u00ed\u201c).<\/li>\n<\/ul>\n<h2>Predik\u010dn\u00e9 met\u00f3dy: od Bayesovsk\u00fdch filtrov po hlbok\u00e9 u\u010denie<\/h2>\n<ol>\n<li><strong>Bayesovsk\u00e9 filtre:<\/strong> Kalman\/UKF pre line\u00e1rne\/kv\u00e1zi-line\u00e1rne dynamiky; Particle Filter pri nelinearit\u00e1ch a multimodalite. Dobr\u00e1 vysvetlite\u013enos\u0165 a mal\u00e9 v\u00fdpo\u010dtov\u00e9 n\u00e1roky.<\/li>\n<li><strong>Viaccie\u013eov\u00e9 sledovanie:<\/strong> PHD\/CPHD filtre, JPDA a MHT pre asoci\u00e1ciu meran\u00ed pri vy\u0161\u0161ej hustote objektov a klamn\u00fdch detekci\u00e1ch.<\/li>\n<li><strong>Trajektorick\u00e9 prediktory HL:<\/strong> sekven\u010dn\u00e9 modely (LSTM\/GRU), <em>Social-LSTM<\/em> s poolingom susedov, grafov\u00e9 neur\u00f3nov\u00e9 siete (GNN) a transformery s <em>multi-head attention<\/em> pre dlh\u0161\u00ed horizont a viacm\u00f3dov\u00fa v\u00fdstupn\u00fa distrib\u00faciu (mixture density, CVAE).<\/li>\n<li><strong>Interak\u010dne-vedom\u00e9 predikcie:<\/strong> modely, ktor\u00e9 zoh\u013ead\u0148uj\u00fa pl\u00e1n UAV (coupled prediction-planning), aby sa predi\u0161lo nekonzistentn\u00e9mu \u201epredikuj a potom pl\u00e1nuj\u201c cyklu.<\/li>\n<\/ol>\n<h2>Mapovanie a reprezent\u00e1cie priestoru<\/h2>\n<ul>\n<li><strong>DOGMa:<\/strong> <em>Dynamic Occupancy Grid Map<\/em> s vektorov\u00fdmi r\u00fdchlos\u0165ami buniek a kovarian\u010dn\u00fdmi maticami; vhodn\u00e9 pre f\u00faziu LiDAR+RGBD+radar.<\/li>\n<li><strong>Obst\u00e1culo-centric:<\/strong> stavov\u00e9 \u0161tatistiky per objekt s trajekt\u00f3riami a pravdepodobnostn\u00fdmi tunelmi (space-time occupancy).<\/li>\n<li><strong>Bezpe\u010dn\u00e9 koridory:<\/strong> konvexn\u00e9 polytopy v priestore-\u010dase (C-\u010das), generovan\u00e9 z mapy a predikci\u00ed prek\u00e1\u017eok, vyu\u017eite\u013en\u00e9 v konvexnej optimaliz\u00e1cii.<\/li>\n<\/ul>\n<h2>Pl\u00e1novacie paradigmy a algoritmy<\/h2>\n<ol>\n<li><strong>Optimaliza\u010dn\u00e9 pl\u00e1novanie (trajopt):<\/strong> priama optimaliz\u00e1cia nad B-spline\/Bezier parametrami s penaliz\u00e1ciou rizika kol\u00edzie; <em>soft constraints<\/em> na bezpe\u010dnostn\u00e9 rezervy, <em>hard constraints<\/em> na dynamiku.<\/li>\n<li><strong>MPC s pravdepodobnostn\u00fdmi (chance) obmedzeniami:<\/strong> iterat\u00edvna receding-horizon optimaliz\u00e1cia, kde sa kol\u00edzne obmedzenia formuluj\u00fa ako $P(d(\\mathbf{x},\\mathcal{O})&lt;d_{min})\\leq \\epsilon$; aproxim\u00e1cie cez Booleho nerovnosti alebo koncentra\u010dn\u00e9 hranice.<\/li>\n<li><strong>Samplingov\u00e9 a grafov\u00e9 met\u00f3dy:<\/strong> kinodynamick\u00e9 RRT*\/BIT*\/FMT* so vzorkovan\u00edm v priestore-\u010dase; <em>lazy<\/em> evalu\u00e1cia kol\u00edzi\u00ed s r\u00fdchlou aktualiz\u00e1ciou, <em>rewiring<\/em> pri nov\u00fdch predikci\u00e1ch.<\/li>\n<li><strong>Velocity Obstacles a ORCA:<\/strong> r\u00fdchlostn\u00e9 ku\u017eele (VO), Reciprocal VO a ORCA pre multiagentov\u00fa vyh\u00fdbav\u00fa navig\u00e1ciu s garanciami bezpe\u010dnosti pri vz\u00e1jomnej kooper\u00e1cii.<\/li>\n<li><strong>Reachability a bezpe\u010dnostn\u00e9 filtre:<\/strong> Hamilton\u2013Jacobi dosiahnute\u013enos\u0165 pre najhor\u0161ie pr\u00edpady; <em>Control Barrier Functions<\/em> (CBF) pre on-line korekciu referen\u010dnej trajekt\u00f3rie do bezpe\u010dn\u00e9ho invariantn\u00e9ho mno\u017estva.<\/li>\n<\/ol>\n<h2>Interakcia pl\u00e1novania a predikcie: uzavret\u00e1 slu\u010dka<\/h2>\n<p>Predikcie ovplyv\u0148uj\u00fa pl\u00e1n a pl\u00e1n ovplyv\u0148uje spr\u00e1vanie ostatn\u00fdch agentov. Uzavretie slu\u010dky zah\u0155\u0148a <em>game-theoretic<\/em> alebo <em>best-response<\/em> aktualiz\u00e1cie, kde sa strieda (alebo rie\u0161i spolo\u010dne) optimaliz\u00e1cia trajekt\u00f3ri\u00ed UAV a <em>intent-aware<\/em> predikcia okolia. Prakticky sa pou\u017e\u00edva <strong>hierarchia<\/strong>: r\u00fdchly reakt\u00edvny \u201esafety layer\u201c (CBF\/ORCA) + <em>mid-level<\/em> MPC + pomal\u0161ie glob\u00e1lne pl\u00e1novanie.<\/p>\n<h2>Neistota a robustnos\u0165<\/h2>\n<ul>\n<li><strong>Rizikovo-senzit\u00edvne n\u00e1klady:<\/strong> CVaR (Conditional Value at Risk) penalizuje chvostov\u00e9 rizik\u00e1, nie iba o\u010dak\u00e1van\u00e9 hodnoty.<\/li>\n<li><strong>Tube MPC a feedback linearization:<\/strong> pl\u00e1novanie nomin\u00e1lnej trajekt\u00f3rie a riadenie odch\u00fdlky v robustnej \u201er\u00fare\u201c okolo nej, ktor\u00e1 absorbuje ru\u0161iv\u00e9 vplyvy a chyby predikcie.<\/li>\n<li><strong>Multi-m\u00f3dov\u00e9 predikcie:<\/strong> dekompoz\u00edcia na scen\u00e1re (napr. 3\u20135 modal\u00edt), <em>branch-and-bound<\/em> alebo <em>ensemble<\/em> MPC pre pokrytie alternat\u00edv spr\u00e1vania prek\u00e1\u017eok.<\/li>\n<\/ul>\n<h2>Kooperat\u00edvne pl\u00e1novanie v roji<\/h2>\n<ul>\n<li><strong>Distribuovan\u00e9 MPC:<\/strong> lok\u00e1lne optimaliz\u00e1cie s obmedzenou komunik\u00e1ciou (V2V), konsenzu\u00e1lne aktualiz\u00e1cie (ADMM) na zos\u00faladenie trajekt\u00f3ri\u00ed.<\/li>\n<li><strong>Deconfliction a priradenie cie\u013eov:<\/strong> auk\u010dn\u00e9 mechanizmy (CBBA), <em>task allocation<\/em> so sp\u00e4tnou v\u00e4zbou na kol\u00edzne riziko a energetick\u00e9 n\u00e1klady.<\/li>\n<li><strong>Form\u00e1cie a bezpe\u010dn\u00e9 koridory:<\/strong> spolo\u010dn\u00e9 pos\u00favanie konvexn\u00fdch koridorov v priestore-\u010dase, elasticita form\u00e1cie pod\u013ea hustoty prem\u00e1vky.<\/li>\n<\/ul>\n<h2>Implementa\u010dn\u00e9 aspekty: v\u00fdpo\u010det, latencia a integr\u00e1cia<\/h2>\n<ul>\n<li><strong>Re\u00e1lne \u010dasov\u00e9 rozpo\u010dty:<\/strong> perception 20\u201340 ms, predikcia 10\u201330 ms (edge modely INT8), MPC\/trajopt 20\u201360 ms; celkov\u00fd cyklus &lt; 100\u2013150 ms.<\/li>\n<li><strong>Akceler\u00e1cia:<\/strong> GPU\/NNAPI pre HL prediktory, QP\/SOCP solvery s tepl\u00fdm \u0161tartom; kni\u017enice s podporou <em>sparse<\/em> optimaliz\u00e1cie.<\/li>\n<li><strong>Degradovan\u00e9 re\u017eimy:<\/strong> fallback na CV\/CVA extrapol\u00e1ciu a reakt\u00edvne vyh\u00fdbanie (ORCA\/CBF) pri strate HL prediktora \u010di d\u00e1t zo senzorov.<\/li>\n<li><strong>Integr\u00e1cia so senzormi:<\/strong> f\u00fazia LiDAR\/RGBD\/radar\/ADS-B; radar zvy\u0161uje robustnos\u0165 v da\u017edi\/hmle, ADS-B pre kooperat\u00edvne lietadl\u00e1.<\/li>\n<\/ul>\n<h2>Valid\u00e1cia, metriky a testovanie<\/h2>\n<ul>\n<li><strong>Bezpe\u010dnos\u0165:<\/strong> priemern\u00e1 a 99. percentilov\u00e1 minim\u00e1lna vzdialenos\u0165, po\u010det <em>near-miss<\/em> udalost\u00ed, <em>time-to-collision<\/em> po\u010das misie.<\/li>\n<li><strong>Efektivita:<\/strong> \u010das do cie\u013ea, preleten\u00e1 vzdialenos\u0165, energia, plynulos\u0165 (jerk, snap) a po\u010det re-pl\u00e1novan\u00ed.<\/li>\n<li><strong>Predikcia:<\/strong> ADE\/FDE (Average\/Final Displacement Error), Brier score pre pravdepodobnostn\u00e9 predikcie, <em>calibration error<\/em> (ECE).<\/li>\n<li><strong>Robustnos\u0165:<\/strong> v\u00fdkonnos\u0165 pri strat\u00e1ch detekci\u00ed, falo\u0161n\u00fdch pozit\u00edvach, zmen\u00e1ch hustoty dopravy a po\u010das\u00ed.<\/li>\n<\/ul>\n<h2>\u0160pecifik\u00e1 mestsk\u00e9ho n\u00edzkeho priestoru (U-Space\/UTM)<\/h2>\n<p>V mest\u00e1ch vznikaj\u00fa \u00fazke \u201eka\u0148ony\u201c s occlusion a viaccestnos\u0165ou; predikcie musia zvl\u00e1da\u0165 n\u00e1hle objavenia prek\u00e1\u017eok. Pri kooper\u00e1cii s UTM v\u00fdhodou je <em>networked intent sharing<\/em> \u2013 v\u00fdmena pl\u00e1novan\u00fdch segmentov trajekt\u00f3ri\u00ed a rozpo\u010dtov \u010dasu, \u010do zni\u017euje neur\u010ditos\u0165 v predikci\u00e1ch.<\/p>\n<h2>Bezpe\u010dnostn\u00e9 vrstvy a form\u00e1lne garancie<\/h2>\n<ul>\n<li><strong>CBF\/QP Safety filter:<\/strong> na vstupe riadenia rie\u0161i mal\u00fd QP, ktor\u00fd minim\u00e1lne men\u00ed referenciu a udr\u017eiava bezpe\u010dnostn\u00e9 invariance s oh\u013eadom na predik\u010dn\u00e9 rozptyly.<\/li>\n<li><strong>Reachability analysis:<\/strong> offline polytopov\u00e9\/ellipsoidn\u00e9 aproxim\u00e1cie pre \u201ecertified\u201c vyh\u00fdbanie najhor\u0161\u00edm pr\u00edpadom (napr. neo\u010dak\u00e1van\u00e9 zr\u00fdchlenie prek\u00e1\u017eky).<\/li>\n<li><strong>Fail-safe z\u00e1sady:<\/strong> definovan\u00e9 <em>emergency corridors<\/em>, zn\u00ed\u017een\u00fd re\u017eim (minim\u00e1lny jerk, zv\u00fd\u0161en\u00e1 separ\u00e1cia), bezpe\u010dn\u00e9 zastavenie a klesanie.<\/li>\n<\/ul>\n<h2>Pr\u00edpadov\u00e1 \u0161t\u00fadia A: Priemyseln\u00fd are\u00e1l s robotick\u00fdmi voz\u00edkmi<\/h2>\n<p>UAV s LiDAR+RGBD f\u00faziou a GNN-transformer prediktorom (horizont 3 s, 5 modal\u00edt). MPC s <em>chance constraints<\/em> a CBF filtrom; cyklus 80 ms. Po\u010das 50 misi\u00ed nebol zaznamenan\u00fd <em>near-miss<\/em> &lt; 1,0 m pri priemernej hustote 12 dynamick\u00fdch objektov. Energetick\u00e9 n\u00e1klady klesli o 9 % v\u010faka hlad\u0161iemu profilovaniu r\u00fdchlosti.<\/p>\n<h2>Pr\u00edpadov\u00e1 \u0161t\u00fadia B: Roj 12 UAV v meste<\/h2>\n<p>Distribuovan\u00e9 MPC s ADMM konsenzom, v\u00fdmena trajekt\u00f3ri\u00ed v 5 Hz (komprimovan\u00e9 spline koeficienty). Prediktor pon\u00fakal 3 modalitn\u00e9 scen\u00e1re pre vozidl\u00e1 a chodcov. Syst\u00e9m dosiahol 99,7 % disponibilitu trajekt\u00f3ri\u00ed bez z\u00e1sahu oper\u00e1tora, s priemernou minim\u00e1lnou separ\u00e1ciou medzi UAV 3,6 m a \u017eiadnym poru\u0161en\u00edm no-fly koridorov.<\/p>\n<h2>In\u017einiersky \u201ecookbook\u201c: implementa\u010dn\u00e9 kroky<\/h2>\n<ol>\n<li><strong>V\u00fdber reprezent\u00e1cie:<\/strong> DOGMa + objektovo-centrick\u00e9 stavy s kovarianciou.<\/li>\n<li><strong>Prediktor:<\/strong> jednoduch\u00fd UKF + heuristika pre modalitu \u2192 n\u00e1sledne GNN\/Transformer s kvantiz\u00e1ciou INT8.<\/li>\n<li><strong>Pl\u00e1novanie:<\/strong> MPC s bezpe\u010dn\u00fdmi koridormi; QP\/SOCP solver s tepl\u00fdm \u0161tartom; CBF filter ako posledn\u00e1 l\u00ednia.<\/li>\n<li><strong>Kalibr\u00e1cia rizika:<\/strong> nastavi\u0165 $\\epsilon$ pod\u013ea triedy misie (napr. 10<sup>\u22123<\/sup> pre prelet nad \u013eu\u010fmi vs. 10<sup>\u22122<\/sup> v uzavretom are\u00e1li).<\/li>\n<li><strong>Telemetria a z\u00e1znam:<\/strong> logova\u0165 predik\u010dn\u00e9 rozdelenia, latencie a z\u00e1sahy CBF na sp\u00e4tn\u00fa anal\u00fdzu a zlep\u0161ovanie modelov.<\/li>\n<\/ol>\n<h2>Obmedzenia, \u00faskalia a bud\u00face trendy<\/h2>\n<ul>\n<li><strong>Dom\u00e9nov\u00fd posun:<\/strong> HL modely degraduj\u00fa mimo tr\u00e9ningovej distrib\u00facie; nutn\u00fd <em>continual learning<\/em> a monitorovanie kalibr\u00e1cie.<\/li>\n<li><strong>Komunika\u010dn\u00e9 limity:<\/strong> v roji limituj\u00fa frekvenciu v\u00fdmeny trajekt\u00f3ri\u00ed; rie\u0161en\u00edm je predik\u010dn\u00e9 zdie\u013eanie <em>intentu<\/em> a kompaktn\u00fdch parametriz\u00e1ci\u00ed.<\/li>\n<li><strong>Form\u00e1lne verifikovan\u00e9 HL:<\/strong> rast\u00fa snahy sp\u00e1ja\u0165 neur\u00f3nov\u00e9 prediktory s verifikovate\u013en\u00fdmi bezpe\u010dnostn\u00fdmi ob\u00e1lkami (hybridn\u00e9 certifik\u00e1ty).<\/li>\n<li><strong>3D hust\u00e9 prostredia:<\/strong> v\u00fd\u0165ahy vzduchu, vietor a mikrokl\u00edma \u2013 nutn\u00e9 zahrn\u00fa\u0165 do predikcie dynamiky UAV a robustnosti pl\u00e1nov.<\/li>\n<\/ul>\n<h2>Check-list pre nasadenie<\/h2>\n<ul>\n<li>Senzorick\u00e1 f\u00fazia kalibrovan\u00e1 (\u010das, extrinsiky), DOGMa be\u017e\u00ed \u2265 10 Hz.<\/li>\n<li>Prediktor poskytuje multimod\u00e1lne v\u00fdstupy s neistotou a metrikou kalibr\u00e1cie (ECE &lt; 5 %).<\/li>\n<li>MPC\/solver s garantovan\u00fdm maxim\u00e1lnym \u010dasom rie\u0161enia; tepl\u00fd \u0161tart a fallback na reakt\u00edvny modul.<\/li>\n<li>CBF\/ORCA zapnut\u00e9 ako bezpe\u010dnostn\u00e1 poistka; logovanie z\u00e1sahov.<\/li>\n<li>UTM\/geo-fencing integr\u00e1cia a pravidl\u00e1 prednosti nastaven\u00e9.<\/li>\n<\/ul>\n<p>Pl\u00e1novanie trajekt\u00f3ri\u00ed s predikciou dynamick\u00fdch prek\u00e1\u017eok prep\u00e1ja vn\u00edmanie, pravdepodobnostn\u00fa predikciu a optimaliza\u010dn\u00e9 riadenie do jednotn\u00e9ho, \u010dasovo pr\u00edsneho re\u0165azca. Spo\u013eahliv\u00e9 nasadenie vy\u017eaduje multimod\u00e1lne, neistotu re\u0161pektuj\u00face prediktory, robustn\u00e9 MPC s bezpe\u010dnostn\u00fdmi filtrami a \u0161k\u00e1lovate\u013en\u00e9 kooperat\u00edvne mechanizmy v roji. V\u00fdsledkom je vy\u0161\u0161ia bezpe\u010dnos\u0165, plynulos\u0165 letu a efekt\u00edvnos\u0165 misi\u00ed v re\u00e1lnych, meniacich sa prostrediach.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pl\u00e1novanie trajekt\u00f3ri\u00ed s predikciou pohybu prek\u00e1\u017eok. Real-time repl\u00e1novanie a MPC pre bezpe\u010dn\u00e9 m\u00ed\u0148anie v meniacich sa sc\u00e9nach.<\/p>\n","protected":false},"author":44,"featured_media":88687,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2629],"tags":[1913,2491,2492,2493,2494,2495,2262,2496],"class_list":["post-48687","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-drony","tag-garancie","tag-kolizne-kuzele","tag-mpc","tag-multi-agent","tag-planovanie-s-dynamikou-prekazok","tag-predikcie","tag-real-time","tag-replanovanie"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Reakt\u00edvne pl\u00e1novanie trajekt\u00f3ri\u00ed: Implement\u00e1cia predikcie dynamick\u00fdch prek\u00e1\u017eok v re\u00e1lnom \u010dase - Podnik\u00e1m, lietam a relaxujem<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.vrtulniky.sk\/news\/reaktivne-planovanie-trajektorii-implementacia-predikcie-dynamickych-prekazok-v-realnom-case\/\" \/>\n<meta property=\"og:locale\" content=\"sk_SK\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Reakt\u00edvne pl\u00e1novanie trajekt\u00f3ri\u00ed: Implement\u00e1cia predikcie dynamick\u00fdch prek\u00e1\u017eok v re\u00e1lnom \u010dase - Podnik\u00e1m, lietam a relaxujem\" \/>\n<meta property=\"og:description\" content=\"Pl\u00e1novanie trajekt\u00f3ri\u00ed s predikciou pohybu prek\u00e1\u017eok. 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