Management and Future Technologies | Volume 2, Issue 1 | № 005

Management and Future Technologies journal.umft.uz March 2025 Volume 2, Issue 1 N-gramm aniqligi: BLEU mos yozuvlar tarjimalari bilan solishtirganda savollar javoblarini, matnlar tarjimasida N-grammlarning (N tokenning qo‘shni ketma-ketligi) aniqligini o‘lchaydi. U har xil uzunlikdagi N-grammlarni ko‘rib chiqadi. U odatda unigram (bitta so‘z) lardan fourgram (to‘rt so‘zli ketma-ketliklari) gacha bo‘lgan o‘xshashliklarni baholaydi. Yuqori aniqlik ballari savollarga javoblarni yoki tarjimasidagi ko‘proq N-grammlar mos yozuvlar tarjimalaridagiga mos kelishini ko‘rsatadi [8]. BLEU ballari 0 dan 1 gacha o‘zgarib turadi. Yuqori ball tizim tomonidan berilgan javob yoki tarjima sifati yaxshilanganligini ko‘rsatadi. BLEU 1 balli mukammal javob sifatini ifodalaydi. Bunda tizim javobi N-gramm aniqligi bo‘yicha maqsadli javobga to‘liq mos keladi. BLEU da bir nechta cheklovlar mavjud. BLEU faqat N-gramm aniqligiga tayanganligi sababli ravonlik, grammatiklik va semantik aniqlik kabi sifatining barcha jihatlarini qamrab ololmasligi mumkin. Shuningdek, u baholashning to‘g‘riligiga ta’sir qilishi mumkin bo‘lgan jumla uzunligi va so‘zning nomuvofiqligi kabi omillarga sezgir. U ko‘pincha savollarga javoblarni generatsiya qilgan matnni yoki tarjima sifatini yanada to‘liqroq baholash uchun boshqa baholash ko‘rsatkichlari va usullari bilan birgalikda qo‘llaniladi[3]. N 1 BLUE BP * exp(n1 log ( pn )) N (1) bu yerda pn – N-grammlar o‘zgartirilgan aniqligidir. U quyida keltirilgan (3) formula asosida hisoblanadi. N – maksimal N-grammlar uzunligi (odatda N=4), BP (Brevity Penalty) qisqartirish jarimasi hisobladi. Ayrim hollarda tarjima natijasi maqsadli chiqishdan uzun bo‘lishi mumkin. U quyidagi (2) formula asosida hisoblanadi: �� � � 1, 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 � � 𝑎𝑎 � exp �1 � � , 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑎𝑎 � � (2) � bu yerda c nomzod chiqish uzunligi, r madsadli chiqish uzunligi hisoblanadi. pn Cn Cm (3) bu yerda Cn – nomzodaning maqsadli javobida yoki tarjimada uchraydigan N-grammlar soni va Cm – maqsali javobda yoki tarjimada yaratilgan N-grammlar soni. ROUGE (Recall-oriented understudy for Gisting Evaluation): ROUGE birinchi navbatda mashina tomonidan yaratilgan javoblarni baholash uchun ishlatiladi, lekin u so‘z yoki N-gramm darajasida nomzod va mos yozuvlar tarjimalari o‘rtasidagi o‘xshashlikni solishtirish orqali mashina tarjimasini baholash uchun ham moslashtirilishi mumkin. ROUGE shuningdek, mashina tarjima tizimida hosil qilingan nomzod matn va maqsadli tarjima o‘rtasidagi o‘xshashlik belgilarini hisoblashga asoslangan. ROUGE ning asl taqdimotida u aniqroq yo‘naltirilgan BLEU bilan solishtirganda eslab qolish (Recall) tomoniga ko‘proq e’tibor qaratildi. Hozirgi kunda biz buni odatda bir-biriga o‘xshashlik uchun F1-balli (F1-score) ni hisoblash asosida ko‘ramiz. ROUGE turli mezonlar, jumladan, N-gramm 21

Volume 2, Issue 1 22 March 2025 Management and Future Technologies journal.umft.uz o‘xshashligi, so‘zlarning o‘zaro mos kelishi va eng uzun umumiy ketma-ketlik asosida tizim tomonidan yaratilgan xulosalar va mos yozuvlar xulosalari o‘rtasidagi o‘xshashlikni o‘lchaydi[7]. N-gramm o‘xshashligi: ROUGE-N N-gramm larning (N so‘zning qo‘shni ketma-ketligi) tizim tomonidan yaratilgan xulosa va mos matnlar o‘rtasidagi o‘xshashligini o‘lchaydi. Odatda 1 dan 4 gacha bo‘lgan N ning turli qiymatlari uchun aniqlik (Precision), eslab qolish (Recall) va F1 balli (F1score) ni hisoblaydi. ROUGE-N tizim tomonidan yaratilgan nomzod tarjima maqsadli tarjimada mavjud bo‘lgan asosiy tarkib va iboralarni qanchalik yaxshi qamrab olishini baholaydi. So‘zlarning o‘xshashligi: ROUGE-W tizim tomonidan yaratilgan tizim javobi va tarjima o‘rtasidagi so‘zlarning bir-biriga mos kelishini o‘lchaydi. U matnlar orasidagi semantik o‘xshashlikni aniqlash uchun barcha bir-biriga o‘xshash so‘zlarni, ularning tartibidan qat’iy nazar, hisobga oladi. ROUGE-W N-grammlarga qaratilgan ROUGE-N bilan solishtirganda matnlar o‘rtasidagi o‘xshashlikning yanada yaxlit ko‘rinishini beradi. Eng uzun umumiy ketma-ketlik (LCS): ROUGE-L tizim tomonidan yaratilgan matn va maqsadli tarjimada mavjud bo‘lgan so‘zlarning eng uzun ketma-ketligini aniqlaydi. Bu esa so‘z tartibi va jumla tuzilishidagi o‘zgarishlarga imkon beradi. ROUGE-L ayniqsa tarjimning ravonligi va uyg‘unligini baholash uchun foydalidir. Chunki, u so‘zlarning aniq mosligini emas, balki tarkibiy o‘xshashlikni hisobga oladi. F o‘lchovi: Har bir ROUGE ko‘rsatkichi (ROUGE-N, ROUGE-W, ROUGE-L) uchun F-o‘lchovi aniqlik va eslab qolishning garmonik o‘rtacha qiymati sifatida hisoblanadi (4-ifoda). F-o‘lchovi aniqlikni (tizim tomonidan yaratilgan matn qancha qismi haqiqiy javob bilan mos kelishini) va eslab qolishni (tizim tomonidan yaratilgan matnning qancha qismi qaralgani) muvozanatlashtiradigan yagona ball beradi. Umuman olganda, ROUGE ko‘rsatkichlari tizim tomonidan yaratilgan va mos yozuvlar matni o‘rtasidagi o‘xshashlikni miqdoriy baholash orqali avtomatik umumlashtirish tizimlari va boshqa tabiiy tillarni qayta ishlash vazifalari samaradorligini baholash uchun qimmatli vositani taqdim etadi. cn cw * precision cm ca f 1 score cn cw recall cm ca (4) bu yerda Cw – tizimda tomonidan berilgan javobda uchraydigan so‘zlar soni, Ca – javobdagi barcha so‘zlar soni, Cn – tizim tomonidan berilgan javobda uchraydigan N-grammlar soni va Cm tizim javobidagi N-grammlar soni. 3. Natija Xorijda amalga oshirilgan ko‘plab tadiqot ishlarida T5 modelidan ko‘ra Flan-T5 modeli yuqori natijalarni qayt etganligini takidlangan shuning uchun o‘z masalamizda T5-small modeli va Flan T5small modellari ustida o‘qitishlar soni (epochs) 3, 6, 8 qiymatlarida sinov olib bordik. O‘qitish natijlariga ko‘ra yo‘qotilish (loss) qiymatlar quyidagilarni qayt etdi(4-jadval).

Management and Future Technologies journal.umft.uz March 2025 Volume 2, Issue 1 4-jadval. O‘qitilishlar soni (epochs) bo‘yicha xatoliklar(loss) qiymatlarning ifodalanishi Model nomi T5-small Flan T5-small Epochlar soni 1 0.643 0.578 2 0.336 0.275 3 0.192 0.152 4 0.118 0.100 5 0.080 0.064 6 0.059 0.040 7 8 0.048 0.039 0.030 0.036 Yo‘qotishlar qiymatlarini grafik orqali ifodalasak quyidagi ko‘rinishda bo‘ladi. Flan T5 modellari bilan T5 modellarining loss qiymatlarini alohida tasvirlarda ifodaladik (2-rasm). 2-rasm. Trainning jarayonida T5 modelining har bir turida loss qiymatlar Tajriba natijasida RUOGE aniqlikni baholash quyidagi natijalarni qayt etdi(5-jadval). 5-jadval. Rouge baholash usuni bo‘yicha natijalar. Model nomi va epochlar soni T5-small Flan T5-small Rouge1 0.872 0.871 Baholash usuli Rouge2 Rouge L 0.734 0.872 0.735 0.871 RougeLsum 0.872 0.871 BLEU va METEOR baholash metodlari orqali quyidagi natijalar olindi (6-jadval). 23

Volume 2, Issue 1 24 March 2025 Management and Future Technologies journal.umft.uz 6-jadval. BLEU va METEOR baholash metodlari orqali aniqlangan natijalar. Baholash metodi BLEU METEOR T5-small Flan T5-small 0.709 0.711 0.717 0.714 ROUGE baholash natijalari bo‘yicha T5-small va Flan T5-small modellarining natijalari deyarli bir xil bo‘lib, ROUGE-1 va ROUGE-L ko‘rsatkichlari bo‘yicha T5-small biroz yuqori, ROUGE-2 bo‘yicha esa Flan T5-small ozgina yaxshiroq natija qayd etgan. BLEU va METEOR baholash metodlari bo‘yicha esa Flan T5-small modeli mos ravishda 0.717 va 0.714 natijalarni ko‘rsatib, T5-small dan biroz yuqoriroq natijalarga erishgan. Umuman olganda, summarization uchun har ikkala model bir xil darajada ishlashi mumkin, lekin machine translation yoki matn generatsiyasi vazifalari uchun Flan T5-small modeli afzalroq bo‘lishi mumkin. Xulosa T5 modeli asosida o‘zbek tili uchun yartilgan savol-javob tizimi shuni ko‘rsatdiki, ananaviy T5 modeli asosida yaratilgan savol-javob tizimi ROUGE baholash ko‘rsatkichi ROUGE1 0.872, ROUGE2 0.734, ROUGE L 0.872 va BLEU baholash metodi 0.709 va METEOR baholash metodida 0.711 aniqlikni qayt etdi. Flan T5 modeli asosida yaratilgan savol-javob tizimi esa ROUGE baholash ko‘rsatkichi ROUGE1 0.871, ROUGE2 0.735, ROUGE L 0.871 va BLEU baholash metodi 0.717 va METEOR baholash metodida 0.714 aniqlikni ko‘rsatdi. Natijalar shuni ko‘rsatadiki, Flan T5 modeli yordamida o‘zbek tilida savol-javob tizimi yaratishda yetarli natijalar berishi mumkinligini aniqlandi.

Management and Future Technologies journal.umft.uz March 2025 Volume 2, Issue 1 Adabiyotlar 1. Musayev, M., Ochilov , M., Kholmatov, O. and Narzullayev , O. Vektor fazo modeli hamda jumlalar o‘xshashligi o‘lchovlariga asoslangan savol - javob tizimi ishlab chiqish. Digital transformation and artificial intelligence.3,1( Jan.2025),23–30. 2. Liu, Y, etcs. BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding. Proceedings of NAACL-HLT 2019. Minneapolis, MN, USA. June 2–7, 2019. 3. Raffel, C. Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer. Proceedings of the 37th International Conference on Machine Learning (ICML 2020). 4. Raffel, C., Shinn, E., Roberts, A., Lee, K., & Narang, S. Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer. Proceedings of the 37th International Conference on Machine Learning (ICML), Long Beach, CA, USA, June 9–15, 2019. 5. Chung, H. W., etcs. Scaling Instruction-Finetuned Language Models. Proceedings of the 40th International Conference on Machine Learning (ICML), 2023. Honolulu, HI, USA. July 23–29, 2023. 6. Roberts, A.; Chung, H. W.; Mishra, G.; Levskaya, A.; Bradbury, J. Scaling Up Models and Data with t5x and seqio Journal of Machine Learning Research. 2023. 7. Lin, C.Y. ROUGE: A Package for Automatic Evaluation of Summaries. Proceedings of the 4th International Conference on Text Summarization. Spain. July 5–7, 2004. 8. Papineni, D.; Roukos, S.; Ward, T.; Zhu, W. BLEU: A Method for Automatic Evaluation of Machine Translation. Proceedings of the 40th Annual Meeting of the Association for Computational Linguistics (ACL), Philadelphia, PA, USA, July 6–11, 2002. 25

Volume 2, Issue 1 March 2025 26 Mualliflar Ravshan Shirinboyev Jizzakh branch of the National University, Jizzakh, Uzbekistan; forravshanrsh@gmail.com Ma’ruf Tojiyev Samarkand State University, Samarkand, Uzbekistan; mrtojiyev6886@gmail.com Jo’ra Kuvandikov Jizzakh branch of the National University, Jizzakh, Uzbekistan; quvondiqov86@mail.ru Correspondence: forravshanrsh@ gmail.com Copyright: © 2024 by the authors. Ushbu maqola Creative Commons Attribution (CC BY) litsenziyasi shartlari asosida tarqatiladigan ochiq foydalanish maqolasi hisoblanadi (https://creativecommons.org/ licenses/by/4.0/). Management and Future Technologies journal.umft.uz FIRE DETECTION BASED ON OPTICAL FLOW TECHNOLOGY A bstract: Ensuring fire safety and preventing emergencies has always been an important issue. Fires are one of the natural and man-made disasters that pose a great threat to human life and property. Their rapid spread and difficulty in preventing require increasing the efficiency of fire detection systems. Modern technologies, in particular, the development of artificial intelligence and optical flow algorithms, allow for early detection of fires. Alyzes the principles of operation, technical approaches and effectiveness of automatic fire detection systems based on optical flow technology. Optical flow technology can detect early fire symptoms by monitoring movement dynamics and analyzing changes. Traditional sensors often face the problem of late detection in the development stage of a fire, which causes material damage and endangers human life. The optical flow approach can overcome these problems by detecting the initial movement patterns of a fire. Discusses the basic principles of optical flow technology, motion detection methods using various algorithms, and their contribution to early fire detection. In addition, the possibilities of integrating this technology with artificial intelligence and video surveillance systems are also discussed. By combining optical flow and machine learning approaches, fire detection systems can be more reliable and faster.The article also analyzes the accuracy and performance of algorithms used for fire detection. The results of early fire detection using optical flow technology in various real-world conditions are reviewed, and recommendations are made for future development of this technology. Key words: Optical flow, lucas-kanade method, hornschunck algorithm, farneback, optical flow, motion estimation, fire detection, computer vision, image processing, real-time monitoring, deep learning in fire detection, video surveillance, feature tracking, ai-based fire recognition, early fire detection systems, smoke and flame detection.

Management and Future Technologies journal.umft.uz March 2025 Volume 2, Issue 1 Introduction 27 Fire is one of the disasters that can cause serious damage to human life, property and ecological systems. The rapid spread of fire and the difficulty of prevention increase the importance of early detection systems. Today, there are traditional fire detection methods , which mainly work through smoke detectors, temperature sensors and infrared cameras. However, these methods may not give accurate results in the early stages of a fire or may lead to false positives. Optical flow technology is seen as an innovative approach to solve this problem. This technology analyzes the movement patterns of fire and smoke by processing images in real time , helping to detect fires at an early stage. This approach is much more effective than traditional sensors , allowing for rapid response and fire prevention. Optical flow technology has several advantages in fire detection systems. It provides rapid warning by tracking the movement of fire and smoke. While fire detection systems are usually based on smoke or temperature sensors, optical flow works in the visible spectrum using cameras. It can be integrated into existing surveillance cameras , eliminating the need for new hardware. It can be combined with machine learning methods to reduce false positives and increase accuracy. It has the ability to detect where a fire is starting and predict its trajectory. During a fire, the optical flow approach adapts to environmental conditions and works effectively in both natural and artificial lighting conditions of the fire. These advantages of optical flow technology make it a promising tool in the field of fire detection. This article analyzes the theoretical basis of optical flow, its application to fire detection , and the results. Materials and Methods Lucas - Canadian method optical stream 𝑣𝑣� , 𝑣𝑣� small 𝑊𝑊size in the mirror ( of the image) small part ) permanent to be guess So the optical flow equation is for all the objects inside this window 𝑞𝑞 � ��, ��. is performed for pixels with coordinates : 𝐼𝐼� �𝑞𝑞�𝑣𝑣� � 𝐼𝐼� �𝑞𝑞�𝑣𝑣� � �𝐼𝐼� �𝑞𝑞�, �𝑞𝑞 � ��, �� � 𝑊𝑊 These equations form a system of linear equations and can be written in the following matrix form: 𝐴𝐴𝑣𝑣 � � here : 𝐴𝐴– size 𝑛𝑛� � 2 is a matrix that 𝑊𝑊 contains the image gradient components for each pixel within the window: 𝐼𝐼� �𝑞𝑞� � ⎡ 𝐼𝐼 �𝑞𝑞 � 𝐴𝐴 � ⎢ � � ⋮ ⎢ 𝐼𝐼 �𝑞𝑞 � ⎣� � 𝐼𝐼� �𝑞𝑞� � ⎤ 𝐼𝐼� �𝑞𝑞� � ⎥ ⋮ ⎥ 𝐼𝐼� �𝑞𝑞� �⎦ 𝑣𝑣 – mirror 𝑊𝑊The vector representing the optical flow for:

Volume 2, Issue 1 March 2025 Management and Future Technologies 28 journal.umft.uz 𝑣𝑣� 𝑣𝑣 � �𝑣𝑣 � � 𝑏𝑏– size 𝑛𝑛� is a vector that contains the time derivatives of the image: ��� ��� � �� �� � 𝑏𝑏 � � � � � ⋮ ��� ��� � This linear system has 𝑛𝑛� one equation and two unknowns, which means it is an overdetermined system . The Lucas-Canade method finds the solution to this equation using the least squares method : where is the transpose of 𝐴𝐴� the matrix 𝐴𝐴. 𝐴𝐴� 𝐴𝐴𝑣𝑣 � 𝐴𝐴� 𝑏𝑏 The least squares solution looks like this : Expanding this formula, we write: 𝑣𝑣 � �𝐴𝐴� 𝐴𝐴��� 𝐴𝐴� b � �� ��� �� � �� ��� ��� ��� � 𝑣𝑣� � �𝑣𝑣 � � � � � �� ��� ��� ��� � � � � �� ��� �� � �� � � � �� ��� ��� ��� � � � � � � �� ��� ��� ��� � � The optical flow can 𝑣𝑣only be evaluated if 𝐴𝐴� 𝐴𝐴the matrix is inverse and well-conditioned. This condition is satisfied if: 𝐴𝐴� the eigenvalues 𝜆𝜆� , 𝜆𝜆� of the matrix are large and of the same order. The condition for determining the angle is met , because this condition is also important for calculating optical flow. On the contrary, if the window: Is a flat region , the gradients are close to zero and the motion cannot be detected. If there is an edge in only one direction , only one component of the motion can be detected. The Lucas-Canade method is one of the important techniques in computer vision . We use the concept of optical flow and the mathematical formulas of the Lucas-Canade method . This method is effective for detecting small movements and is widely used in areas such as object tracking , face detection, and video stabilization.

Management and Future Technologies journal.umft.uz March 2025 Volume 2, Issue 1 29 Figure 1. Lucas-Canade optical flow. Lucas-Canade is a popular approach to optical flow calculation , which improves optical flow calculation by applying a global smoothness constraint. This method, unlike the Lucas-Kanade method, attempts to find optical flow over the entire image and ensures logical smoothness of the optical flow vectors. The Horn-Schunck method relies on two main assumptions in calculating optical flow. Optical Flow Equation (Brightness Constancy Assumption): The light intensity in an image is virtually constant over time. 𝐼𝐼�𝑥𝑥, 𝑦𝑦, �� � 𝐼𝐼�𝑥𝑥 � �𝑥𝑥, 𝑦𝑦 � �𝑦𝑦, � � ��� Expanding this equation into a first-order Taylor series yields the optical flow equation: 𝐼𝐼� 𝑣𝑣� � 𝐼𝐼� 𝑣𝑣� � 𝐼𝐼� � 0 here : 𝐼𝐼� , 𝐼𝐼� – image 𝑥𝑥and 𝑦𝑦gradients in the direction. 𝐼𝐼� – gradient over time . 𝑣𝑣� , 𝑣𝑣� – components of the optical flow in 𝑥𝑥the and 𝑦𝑦directions. Smoothness Constraint : The Horn-Schunck method assumes that the optical flow is smooth over the entire image area. It assumes that the optical flow vectors for neighboring pixels should be similar . This is achieved by the following smoothing function: � � 𝜕𝜕𝜕𝜕� 𝜕𝜕𝜕𝜕� 𝜕𝜕𝜕𝜕� � 𝜕𝜕𝜕𝜕� � 𝐸𝐸� � � �� � �� � � 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 � �� � �� 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 The weight of this s y l l i s t i n g constraint is introduced as 𝛼𝛼( smoothness coefficient ) . Thus, the overall optimization function becomes : � � 𝜕𝜕𝜕𝜕� 𝜕𝜕𝜕𝜕� 𝜕𝜕𝜕𝜕� � 𝜕𝜕𝜕𝜕� � � �� � �� 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝐸𝐸� � � ��𝐼𝐼� 𝑣𝑣� � 𝐼𝐼� 𝑣𝑣� � 𝐼𝐼� � � 𝛼𝛼 �� � �� � �� 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 � � This energy function, the best optical flow vectors can be found. Uses the Euler-Lagrange equations

Volume 2, Issue 1 30 March 2025 Management and Future Technologies journal.umft.uz to minimize the above optimization function. finds the optical flow vectors by solving. Using the variational calculus method, the following equations are obtained: 𝐼𝐼� �𝐼𝐼� 𝑣𝑣� � 𝐼𝐼� 𝑣𝑣� � 𝐼𝐼� � � 𝛼𝛼 � ∇� 𝑣𝑣� � 0 𝐼𝐼� �𝐼𝐼� 𝑣𝑣� � 𝐼𝐼� 𝑣𝑣� � 𝐼𝐼� � � 𝛼𝛼 � ∇� 𝑣𝑣� � 0 where and are ∇� 𝑣𝑣� the ∇� 𝑣𝑣� Laplacian operators of the optical flow vectors, which provide smoothness across the image. The Horn-Schunck method finds the optical flow by iteratively solving this system of equations. The optical flow for each pixel is updated using the following formulas: 𝐼𝐼� �𝐼𝐼� 𝑣𝑣̅� ��� � 𝐼𝐼� 𝑣𝑣̅� ��� 𝐼𝐼� � ��� ��� 𝑣𝑣� � 𝑣𝑣̅� � 𝛼𝛼 � � 𝐼𝐼�� � 𝐼𝐼�� here : 𝐼𝐼� �𝐼𝐼� 𝑣𝑣̅� ��� � 𝐼𝐼� 𝑣𝑣̅� ��� 𝐼𝐼� � ��� ��� 𝑣𝑣� � 𝑣𝑣̅� � 𝛼𝛼 � � 𝐼𝐼�� � 𝐼𝐼�� 𝑣𝑣̅� and 𝑣𝑣̅� – average values of the optical flux of neighboring pixels. 𝑘𝑘– iteration number. Figure 2. Horn-Schunk optical flow This iteration is performed multiple times over the image , and at each step the optical flow vectors are significantly updated. It computes global optical flow , i.e., it provides smooth results over

Management and Future Technologies journal.umft.uz March 2025 Volume 2, Issue 1 the entire image. It is robust to noise , as smoothness constraints reduce subtle image errors. It produces accurate and consistent results , especially for small motions. It can be problematic for detecting large motions , as the smoothness constraint links all pixels together. It is computationally intensive , and computationally expensive because of the iterative method used. It can produce very smooth results , which sometimes makes it difficult to detect precise motions. The Horn-Schunck method attempts to compute optical flow over the entire image and improves the results by applying a smoothness constraint . It allows for smoother and more accurate detection of motions across the image . This method is widely used in the fields of video stabilization, object tracking , and motion analysis . was introduced by Gunnar Farneback in 2003 , and it is used to calculate the dense optical flow of images. for mathematical models and polynomials uses approximation techniques. The Farneback method estimates motion continuously and densely by modeling the image with local quadratic polynomials . This approach, unlike the Lucas-Kanade and Horn-Schunck methods , does not only use gradient information, but also analyzes image structures. allows for the calculation of optical flow vectors for each pixel in a dense form (dense optical flow) . This is a direct result of the Lucas-Kanade method. This allows for a separate optical flow value to be obtained for each pixel. proposes to represent the intensity function in each part of the image by a quadratic polynomial . This means that the image intensity in each small region is approximated as follows : here : 𝑓𝑓�𝑥𝑥� � 𝑥𝑥 � 𝐴𝐴𝑥𝑥 � 𝑏𝑏 � 𝑥𝑥 � 𝑐𝑐 𝑥𝑥– pixel coordinates �𝑥𝑥, ��, 𝐴𝐴– symmetric matrix (contains second-order derivatives of the image), 𝑏𝑏– gradient vector, 𝑐𝑐– scalar value. Using this model, information about the location and orientation of the image can be obtained. If the image is moving , then a new image (frame) can be obtained from the old image using optical flow vectors: Here: 𝑓𝑓� �𝑥𝑥� � 𝑓𝑓� �𝑥𝑥 � 𝑑𝑑� 𝑓𝑓� �𝑥𝑥� and 𝑓𝑓� �𝑥𝑥�– intensity functions in the initial and subsequent frames of the image. 𝑑𝑑– optical flow vector (direction of motion). the vectors for each pixel 𝑑𝑑. The Farneback method calculates optical flow through the following steps: 1. A small region around each pixel is represented by a quadratic polynomial. Image Resizing with Gaussian Pyramid (Scale Space) The image is zoomed in several times to detect large movements . The optical flow at each dimension level is calculated separately. Step-by-step calculation of optical flow Starting from small images and moving to large images, updating the motion vectors at each stage. 31

Volume 2, Issue 1 32 March 2025 Management and Future Technologies journal.umft.uz Smoothing motion vectors and stabilizing the detected motion vectors using filters . Figure 3. Farneback optic flow Results. To evaluate the effectiveness of optical flow algorithms for early fire detection, various experimental tests were conducted. These tests were carried out under different conditions, including real-time monitoring, varying lighting levels, and different fire intensity stages. The following results compare the performance of each algorithm in terms of fire detection accuracy, false positive rates, and computation speed. Table 1. Comparative experimental results. Algorithm Accuracy (%) False positive (%) Lucas-Canade Horn-Schunck Farneback 85.3 88.7 92.1 10.5 8.2 6.8 Calculation time (ms) 50 70 35 The Lucas-Kanade algorithm is designed to detect small movements related to fire symptoms. It accurately identifies early fire indicators such as light smoke and sparks. However, its accuracy decreases when detecting large fires and rapidly moving smoke flows. The probability of false alarms is relatively high (10.5%), which can lead to excessive alerts. The computation speed is 50 ms, making it suitable for real-time monitoring. The Horn-Schunck algorithm provided good results for monitoring fire spread. It allows for

Management and Future Technologies journal.umft.uz March 2025 Volume 2, Issue 1 smooth global motion representation, making it well-suited for tracking fire and smoke directions in video frames. However, the computation process is relatively heavy, requiring 70 ms for processing. While its accuracy in tracking large movements is higher than the Lucas-Kanade method, it is not efficient enough for real-time monitoring. The false positive rate is 8.2%, which is lower compared to other algorithms. The Farneback algorithm demonstrated the highest accuracy across all test conditions – 92.1%. It quickly detects smoke and fire movements at the early stages. This method calculates dense optical flow, meaning it analyzes movement for each pixel, leading to improved accuracy. The computation speed is the fastest (35 ms), making it highly suitable for real-time monitoring. The false alarm rate is low (6.8%), which increases system reliability. However, one drawback is that in some cases, it may mistakenly classify non-fire movements as fire. Early detection of initial fire indicators (e.g., smoke and fire movement). Faster and more accurate than heat and smoke detectors. High-speed and precise analysis due to the Farneback algorithm. Improved accuracy when combined with machine learning and deep learning techniques. Can be integrated into existing surveillance cameras, reducing the need for additional hardware. Requires high computational power, such as a powerful GPU and optimized software for real-time monitoring. Environmental movements (e.g., wind, moving objects) can sometimes cause false fire alarms. For more reliable results, optical flow technology should be combined with infrared or thermal cameras. When combined with deep learning models such as CNN or RNN, fire detection can become even more precise. Using infrared and thermal cameras along with conventional cameras can enhance detection accuracy.Optical flow algorithms can be integrated into drones to monitor large areas, enabling early fire detection. Current results are based on laboratory conditions, but field tests in forests and industrial areas will help assess real-world effectiveness.Optimizing optical flow algorithms can improve computation speed and adapt them for low-power devices. Conclusion Optical flow technology is a new way of fire detection and prevention early on. Compared to standard fire detection methods, optical flow technology is better and more accurate since it can scan video frames in real-time to detect movements in flames and smoke. Farneback algorithm proved to be the most effective one with 92.1% accuracy and a best processing time of 35 ms for fire detection. Horn-Schunck algorithm easily detected global motion but was a resource-intensive computer algorithm. Lucas-Kanade algorithm could detect minor movements but suffered from low accuracy in detecting large fire with a false positive rate of 10.5%. Merging fire safety systems with optical flow technology has the potential to improve response and detection time for fires significantly, saving human life and property in the long run. The greatest advantages of this technology are. Instant response and detection the moment a fire is started. Picks up fire signs earlier than traditional heat and smoke detectors. Can be integrated into existing surveillance systems without additional hardware costs. Fire detection systems can be made more efficient and reliable if they are combined with machine learning and deep learning techniques. Optical flow algorithms can be employed in drones as well as surveillance cameras for monitoring large areas such as forests and industrial zones. 33

Volume 2, Issue 1 34 March 2025 Management and Future Technologies journal.umft.uz Several areas for improvement in optical flow-based fire detection systems are suggested on the basis of the outcomes of the research. Combining optical flow algorithms with infrared sensors has the potential to improve accuracy by detecting fire-caused movements outside the visual spectrum. Incorporation of optical flow technology into drone systems can greatly enhance fire detection in vast environments such as forests and industrial complexes. Utilization of deep learning networks such as Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) will also assist in simplifying fire and smoke movement. In an effort to enhance real-time monitoring, optical flow algorithms need to be optimized for running on GPUs as well as FPGA accelerators to speed up processing time and reduce computing overhead. While this research has been conducted in laboratory conditions, more work needs to be conducted in field tests within industrial and natural settings to examine the real-world efficiency of optical flow fire detection. Optical flow technology holds vast potential for transforming fire detection and prevention systems. Through faster and more accurate detection than traditional means, it can have a significant effect on fire safety. Also, the integration of this technology with artificial intelligence, infrared sensors, and drone monitoring can lead to even more powerful and reliable fire detection systems. Advances and utilizations of this technology in the future will be of great importance in improving fire safety measures and protecting human life.

Management and Future Technologies journal.umft.uz March 2025 Volume 2, Issue 1 References 1. Lucas, B. D., & Kanade, T. (1981). An Iterative Image Registration Technique with an Application to Stereo Vision. Proceedings of Imaging Understanding Workshop, 121–130. 2. Horn, B. K. P., & Schunck, B. G. (1981). Determining Optical Flow. Artificial Intelligence, 17(1-3), 185-203. 3. Farnebäck, G. (2003). Two-Frame Motion Estimation Based on Polynomial Expansion. Scandinavian Conference on Image Analysis (SCIA), 363-370. 4. Fleet, D. J., & Weiss, Y. (2006). Optical Flow Estimation. Handbook of Mathematical Models in Computer Vision, 239-258. 5. Gonzalez, R. C., & Woods, R. E. (2018). Digital Image Processing (4th ed.). Pearson. 6. Beauchemin, S. S., & Barron, J. L. (1995). The Computation of Optical Flow. ACM Computing Surveys, 27(3), 433-467. 7. Chino, T., et al. (2020). Deep Learning-Based Fire Detection Using Optical Flow Analysis. IEEE Transactions on Image Processing, 29, 610-622. 8. Yuan, C. (2019). A Review of Fire Detection Using Computer Vision Techniques. Journal of Fire Sciences, 37(2), 85-102. 9. Baeldung Computer Science (2024). Lucas-Kanade Optical Flow Method. Retrieved from: https:// www.baeldung.com/cs/optical-flow-lucas-kanade-method 10. OpenCV Documentation (2024). Optical Flow Techniques. Retrieved from: https://docs.opencv. org 11. Shirinboyev, R., Rakhimov, N., Khasanov, D., & Xafizadinov, U. (2024). EVALUATING THE PERFORMANCE OF CONVOLUTIONAL NEURAL NETWORKS AND HYBRID CNN-SVM MODELS FOR SYMBOL RECOGNITION IN COMPLEX DATASETS. DTAI–2024, 1(DTAI), 295-299. 12. Rustamovich, A. A., Ruzikulovich, T. M. R., & O‘G‘Li, S. R. S. (2023). Yong‘inni videotasvirda rangli filtrlash bilan intensivlik o‘zgarishi asosida aniqlash. Илм-фан ва инновацион ривожланиш/Наука и инновационное развитие, 6(2), 13-21. 13. Рахимов, Н., Ширинбаев, Р., & Саидова, З. (2023). Ma’lumotlarni intellektual tahlillash uchun oldindan tasniflash va yakuniy konvolyutsion neyron tarmog ‘i. Информатика и инженерные технологии, 1(2), 55-61. 14. Dilmurod, H., & Shirinboyеv, R. (2024). THЕ MАIN THЕORY OF LINЕАR RЕGRЕSSION MODЕLS IN DАTА MINING. Sun’iy Intellekt Nazariyasi va Amaliyoti: Tajribalar, Muammolar va Istiqbollari, 143-147. 15. Xolboyevich, A. S. (2022). Pythonda chiziqli regressiya. International Journal of Contemporary Scientific and Technical Research, 233-238. 16. Akhatov, A., Shirinboyev, R., & Bobolov, J. (2023). Correction of integrity violations in the video image area using the retinex algorithm. International Journal of Contemporary Scientific and Technical Research, (Special Issue), 162-172. 17. Ruzikulovich, T. M. R. (2022). Neyron tarmoq algoritmlari yordamida murakkab fondagi belgilarni aniqlash algoritmlari. International Journal of Contemporary Scientific and Technical Research, 238241. 18. Rustamovich, A. A., & Ruzikulovich, T. M. R. (2022). Konvolyutsion neyron tarmog ‘i asosida video tasvirdan yong ‘inni erta aniqlash. International Journal of Contemporary Scientific and Technical Research, 128-132. 35

Volume 2, Issue 1 36 March 2025 Management and Future Technologies journal.umft.uz 19. Таджиев, М., Ширинбоев, Р., & Сулаймонова, М. (2022). Open cv kutubxonasida tasvirlarga rang modellari bilan ishlov berish. Современные инновационные исследования актуальные проблемы и развитие тенденции: решения и перспективы, 1(1), 212-215. 20. Shirinboyev, R., & Bobolov, J. (2023). Image segmentation by otsu method. International Journal of Contemporary Scientific and Technical Research, (Special Issue), 64-72.

Management and Future Technologies Mualliflar Ilyos Xujayarov Axborot texnologiyalari kafedrasi, Toshkent axborot texnologiyalari universiteti Samarqand filiali, Samarqand, O‘zbekiston; ilyoskhujayorov@gmail.com Quvonchbek Norqo‘ziyev Kompyuter ilmlari va dasturlashtirish kafedrasi, O‘zbekiston Milliy universiteti Jizzax filiali, Jizzax, O‘zbekiston; quvonchbek9535@gmail.com Mas’ul: quvonchbek9535@gmail.com journal.umft.uz Ushbu maqola Creative Commons Attribution (CC BY) litsenziyasi shartlari asosida tarqatiladigan ochiq foydalanish maqolasi hisoblanadi (https://creativecommons.org/ licenses/by/4.0/). Volume 2, Issue 1 THE CONSTRUCTSIM MUHITIDA ROS YORDAMIDA AVTONOM MOBIL ROBOTLARNING LOKALLASHTIRISH VA KARTOGRAFIYALASH ASOSIDA NAVIGATSIYA ALGORITMLARI TAHLILI A Copyright: © 2024 by the authors. March 2025 nnotatsiya: Ushbu tadqiqotda TheConstructSim muhitidan foydalanib, avtonom mobil robotlarning lokallashtirish, kartografiyalash va navigatsiya algoritmlarini tadqiq qilish jarayoni bayon etiladi. SLAM (Simultaneous Localization and Mapping), yo‘l rejalashtirish algoritmlari (Dijkstra, A*, RRT, va DWA) va sensor birlashtirish texnikalarining amaliy sinovlari TurtleBot 3 va Jackal UGV robot modellari yordamida simulyatsiya qilindi. Ish jarayonida ROS (Robot Operating System), Gazebo, RViz va robot_localization kabi vositalardan foydalanildi. Tadqiqot natijalariga ko‘ra, turli lokallashtirish va navigatsiya algoritmlarining samaradorligi solishtiriladi hamda optimal yondashuvlar aniqlanadi. Natijalarga ko‘ra, turli lokallashtirish va navigatsiya metodlari o‘rtasida samaradorlik, hisoblash resurslari va real vaqt rejimidagi bajarilish tezligi kabi jihatlar bo‘yicha taqqoslashlar o‘tkazildi. Ushbu yondashuvlar va tahlillar kelgusidagi robototexnika tizimlarini yanada takomillashtirish hamda haqiqiy sharoitga moslashtirishda muhim asos bo‘lib xizmat qiladi. Kalit so‘zlar: SLAM, path planning, ROS, Gazebo, TheConstructSim, Gmapping, Dijkstra, A*, RRT va DWA. 37

Volume 2, Issue 1 38 March 2025 Management and Future Technologies journal.umft.uz Kirish Avtonom mobil robotlar zamonaviy texnologiyalarning ajralmas qismiga aylanib, sanoat, logistika, qishloq xo‘jaligi, xavfsizlik va transport sohalarida keng qo‘llanilmoqda. Ushbu robotlarning samarali ishlashi uchun ularning atrof-muhitni tushunishi, aniqlik bilan lokallashtirilishi va optimal harakatlanish trayektoriyasini belgilashi muhim ahamiyatga ega. Lokallashtirish va navigatsiya avtonom tizimlarning asosiy komponentlari bo‘lib, bu jarayonlarning aniqligi robotlarning to‘g‘ri va xavfsiz harakatlanishiga bevosita ta’sir ko‘rsatadi. Ushbu yo‘nalishda turli algoritmlar va texnologiyalar ishlab chiqilgan bo‘lsa-da, ularning haqiqiy sharoitda va simulyatsiya muhiti orqali sinovdan o‘tkazilishi ilmiy izlanishlar uchun muhim ahamiyat kasb etadi [1]. Lokallashtirish va kartografiyalash texnologiyalari robotning o‘z muhitida joylashuvini aniqlash va atrof-muhit xaritasini yaratishga asoslanadi. Ushbu jarayonlarda SLAM (Simultaneous localization and mapping) algoritmlari yetakchi rol o‘ynaydi. SLAM texnologiyasi turli sensorlar, jumladan, LIDAR, RGB-D kameralar, IMU va GPS yordamida amalga oshiriladi. An’anaviy SLAM yondashuvlari orasida Gmapping, Hector SLAM, RTAB-Map va Cartographer kabi algoritmlar keng qo‘llaniladi. Ushbu algoritmlar odometrik ma’lumotlar va vizual sensorlardan olingan ma’lumotlarni qayta ishlash orqali robotning harakatlanish traektoriyasini aniq belgilaydi va xaritalarni yaratadi. Biroq, har bir usulning o‘ziga xos cheklovlari mavjud bo‘lib, real sharoitda ularning samaradorligi turlicha bo‘lishi mumkin. [2] Avtonom navigatsiya esa harakatlanish rejasini tuzish va to‘siqlardan qochish mexanizmlarini o‘z ichiga oladi. Navigatsiya algoritmlaridan Dijkstra, va DWA* A va RRT (Rapidly-exploring random tree)* kabi klassik yondashuvlar keng foydalaniladi. Dijkstra algoritmi eng qisqa yo‘lni topishda ishonchli natijalar bersa, A* algoritmi optimal va samarali yo‘l rejalashtirish imkoniyatini yaratadi. RRT esa tasodifiy daraxt asosida yo‘l rejalashtirishga mo‘ljallangan bo‘lib, real vaqt rejimida murakkab muhitlarda robot harakatini rejalashtirishda qo‘llaniladi. Ushbu algoritmlarning ishlashi simulyatsiya muhiti orqali sinovdan o‘tkazilib, ularning aniqligi va samaradorligi baholanadi. Tadqiqotlarda real muhitni imitatsiya qilish muhim ahamiyat kasb etadi. Simulyatsiya muhitlari ilmiy tadqiqotlar va amaliy testlar o‘tkazish uchun qulay platformalar hisoblanadi. TheConstructSim platformasi bu borada ROS (Robot operating system) bilan ishlash uchun mo‘ljallangan bo‘lib, unda turli mobil robotlar bilan ishlash va ularning harakatlanishini sinash imkoniyati mavjud. Ushbu muhit Gazebo, RViz kabi vositalarni qo‘llab-quvvatlaydi va real sharoitlarga yaqin modellar yaratish imkonini beradi. TheConstructSim yordamida avtonom mobil robotlarning turli navigatsiya va lokallashtirish algoritmlarini sinash orqali ularning real tizimlardagi samaradorligini baholash mumkin [1]. Ushbu tadqiqot doirasida TheConstructSim muhitida TurtleBot 3 va Jackal UGV mobil robotlaridan foydalanildi. Ushbu robotlar odatda ilmiy tadqiqotlarda, akademik muhitda va sanoat sharoitlarida test sinovlari uchun keng qo‘llaniladi. Tadqiqot jarayonida SLAM algoritmlari asosida xaritalash, turli lokallashtirish usullari, GPS va IMU ma’lumotlarining integratsiyasi hamda navigatsiya algoritmlarining samaradorligi sinovdan o‘tkazildi. Har bir algoritmning aniqligi, ishlash tezligi va real vaqt rejimidagi samaradorligi tahlil qilindi [3].

Management and Future Technologies journal.umft.uz March 2025 Volume 2, Issue 1 Ushbu tadqiqotda lokallashtirish, kartografiyalash va navigatsiya jarayonlarini o‘rganish, ularning amaliy tadbiqini simulyatsiya qilish hamda turli algoritmlarning qiyosiy tahlilini o‘tkazish maqsad qilingan. Tadqiqot natijalari kelajakda avtonom transport vositalari, sanoat robotlari va aqlli logistika tizimlari uchun samarali boshqaruv mexanizmlarini ishlab chiqishda muhim ahamiyatga ega bo‘lishi kutilmoqda. TheConstructSim muhitida sinov o‘tkazish robototexnika sohasida yangi yondashuvlarni kashf qilish imkonini beradi va real tizimlarga o‘tishdan oldin eng samarali echimlarni tanlashga yordam beradi [7]. Nazariy asoslari SLAM (Simultaneous localization and mapping) – bu avtonom robotlarning o‘z muhitida harakatlanishi davomida lokallashtirish va kartografiyalashni bir vaqtda amalga oshirish jarayonidir. SLAM algoritmlari robotning atrof-muhitni tasvirlash, xarita yaratish va shu xaritada o‘zining joylashuvini aniqlashiga imkon beradi. Bu jarayon odatda LIDAR, RGB-D kamera, IMU va odometriya kabi sensorlar yordamida amalga oshiriladi. SLAM robototexnika va sun’iy intellekt sohalarida keng qo‘llanilib, avtonom avtomobillar, ombor robotlari, qishloq xo‘jaligi texnikasi va hatto uchuvchi dronlar uchun ham qo‘llaniladi.[4] SLAM algoritmlarining samaradorligi uning aniqligi, ishlash tezligi va muhitdagi to‘siqlarga moslashish qobiliyatiga bog‘liq. Hozirgi vaqtda Gmapping va Hector SLAM eng ommalashgan SLAM algoritmlaridan bo‘lib, ular 2D xaritalash va navigatsiya tizimlarida keng qo‘llaniladi. Gmapping – bu 2D SLAM algoritmi bo‘lib, avtonom robotlarning muhitni xaritalash va o‘z pozitsiyasini aniqlash jarayonida eng ko‘p ishlatiladigan usullardan biridir. Ushbu algoritm Monte Carlo Localization (MCL) va Rao-Blackwellized Particle Filter (RBPF) texnologiyalariga asoslangan. Gmapping asosan LIDAR va odometriya sensorlaridan foydalanib, grid-based (to‘rli) xarita yaratadi.[5] Gmapping SLAM tizimi robotning o‘z muhitida harakatlanishi davomida sensorlardan olingan ma’lumotlarni qayta ishlaydi va real vaqt rejimida xarita hosil qiladi. Ushbu algoritm odometriya ma’lumotlari va LIDAR skanerlaridan foydalanib, robot harakatini kuzatib boradi va xaritani aniqlik bilan yaratishga yordam beradi.[6] Hector SLAM – bu 2D SLAM algoritmi bo‘lib, uning eng katta ustunligi odometriyaga bog‘liq bo‘lmagan ishlash mexanizmi. Gmapping SLAM odometriya sensorlariga tayanadi, Hector SLAM esa faqat LIDAR sensorlaridan foydalangan holda xaritalashni amalga oshiradi. Ushbu algoritm scanmatching (skanerlash bo‘yicha moslashtirish) texnikasi yordamida robotning joylashuvini real vaqt rejimida hisoblaydi va odometriya xatolaridan xalos bo‘ladi.[1] Hector SLAM tez harakatlanuvchi yoki odometriyasi mavjud bo‘lmagan robotlar uchun mo‘ljallangan. U LIDAR sensorlari yordamida atrof-muhitning xaritasini yaratadi va harakatlanish davomida robotning joylashuvini yuqori aniqlik bilan kuzatib boradi. Bu algoritm ayniqsa tez harakatlanuvchi dronlar, qidiruv-qutqaruv robotlari va real vaqt xaritalash tizimlari uchun juda mos keladi.[5] 39

Volume 2, Issue 1 40 March 2025 Management and Future Technologies journal.umft.uz Odometriya – bu harakatlanuvchi robot yoki transport vositasining joylashuvi va yo‘l bosib o‘tish masofasini hisoblash uchun ishlatiladigan texnika. Ushbu usul odatda g‘ildirak sensorlari (enkoderlar), IMU (inerisial o‘lchov birligi) va boshqa harakat o‘lchov tizimlari yordamida amalga oshiriladi. 1-jadval. Gmapping va Hector SLAM eng ommalashgan SLAM algoritmlari. Xususiyatlar Afzalliklari Kamchiliklari Qo‘llanilish sohalari Gmapping - Oddiy va samarali 2D SLAM - ROS bilan to‘liq mos - Tezkor xaritalash imkoniyati - O‘rta va kichik muhitlar uchun mos Hector SLAM - Odometriyasiz ishlaydi - Yuqori aniqlikdagi xaritalash - Tezkor real vaqt ishlashi - Dronlar va tez harakatlanuvchi robotlar uchun mos - Odometriya xatolariga sezgir - IMU va LIDAR talab qiladi - Katta va murakkab muhitlarda aniq - Dinamik muhitlarda aniqligi ishlamasligi mumkin pasayishi mumkin - GPS bilan cheklangan ishlash - GPS bilan ishlash qiyin - Ichki muhit robotlari (ombor, ofis, uy - Dronlar va uchuvchi robotlar robotlari) - Qutqaruv robotlari va xavfsizlik - Sanoat logistika tizimlari tizimlari - ROS muhitida SLAM tadqiqotlari - Ichki muhitda aniq xaritalash talablari Navigatsiya – bu avtonom robot yoki transport vositasining muayyan maqsadga eng samarali va xavfsiz yo‘l bilan yetib borishini ta’minlash jarayoni. Navigatsiya algoritmlari robotning marshrutini rejalashtirish va to‘siqlardan qochish uchun ishlatiladi. Ushbu algoritmlar asosan graf nazariyasi va qidiruv strategiyalari asosida quriladi. Eng ko‘p qo‘llaniladigan algoritmlar orasida Dijkstra va A* (AStar) usullari mavjud. Avtonom robotlar va transport vositalari uchun sensor integratsiyasi muhim rol o‘ynaydi. IMU (Inertial Measurement Unit), GPS (Global Positioning System) va LIDAR (Light Detection and Ranging) sensorlari birgalikda ishlatilganda, robotning joylashuvi aniqroq aniqlanadi, harakat traektoriyasi kuzatiladi va atrof-muhitning batafsil xaritasi yaratiladi. Ushbu integratsiya lokallashtirish, kartografiyalash va navigatsiya tizimlarida samarali qo‘llaniladi. Amaliy ishlar va eksperimentlar Avtonom mobil robotlarning lokallashtirish va navigatsiya algoritmlari real dunyo sharoitida aniq harakatlanish, yo‘l rejalashtirish va to‘siqlardan qochish imkoniyatini beradi. Ushbu tadqiqotda TheConstructSim muhitida ROS yordamida TurtleBot 3 va Jackal UGV robotlarida navigatsiya va SLAM algoritmlarining samaradorligi sinovdan o‘tkaziladi. Eksperimentlar davomida Dijkstra, A, RRT va DWA* algoritmlarining ishlash natijalari baholanadi, lokallashtirish va xaritalash uchun Gmapping va Hector SLAM tahlil qilinadi.