Autonomous operations are an essential function of urban air mobility (UAM) and other evolving aviation markets. Achieving autonomous flight within complex environments remains a bottleneck in the area of unmanned aerial vehicles (UAVs). Current progress in sensor technology has improved the payload capabilities of UAVs, allowing the incorporation of sensors, namely multispectral cameras, higher spatial resolution cameras, and light detection and ranging (LiDAR) systems. Moreover, the fusion of data from diverse sensor modalities can compensate for the limitations of individual sensors, offering a more comprehensive representation of the operating environment. Thus, a systematic analysis of path optimization methods that employ multi-sensor data fusion is critical for enhancing the autonomy and reliability of UAV systems. At present, scholars have progressively utilized deep learning (DL)-driven systems to overcome these challenges for general object detection tasks and have achieved considerable advancements. However, the application of DL methods specifically for UAV recognition and classification remains a relatively novel research field. This paper presents a novel explainable deep learning-based UAV obstacle detection framework (XDL-UAVODF) using multi-sensor data. The aim of this study is to design a UAV navigation framework for obstacle avoidance and optimal trajectory planning in dynamic and complex environments. Obstacle detection provides fundamental environmental awareness for safe navigation and serves as an essential condition for subsequent path planning and trajectory generation. The proposed approach is designed to support UAV navigation by accurately identifying obstacles rather than directly generating collision-free paths. For feature selection, a hybrid approach that integrates principal component analysis (PCA) and least absolute shrinkage and selection operator (LASSO) is leveraged to reduce dimensionality and select significant feature subsets. Moreover, the dynamic sparse graph convolutional recurrent network (DSGCGRN) is used to model spatial-temporal relationships and analyze complex patterns among multi-sensor data to improve decision-making performance. The AdaGrad optimizer is utilized in the training process to ensure faster convergence and enhance model stability. Finally, SHapley Additive exPlanations (SHAP) is employed to explain feature contributions and enhance the transparency of the deep learning model. The performance validation analysis of the XDL-UAVODF approach is conducted using the UAV Autonomous Navigation Dataset. The experimental outcomes reported the superiority of the XDL-UAVODF technique under various measures.
Citation: Sarah A. Alzakari, Shaymaa Sorour, Saleh Alghamdi, Ahmed Omer Ahmed Ismail, Nabil Almashfi, Aisha Blfgeh, Fahad F. Alruwaili, Somia A. Asklany. Mathematical modeling of an explainable deep learning-based UAV obstacle detection framework using multi-sensor data for urban air mobility systems[J]. AIMS Mathematics, 2026, 11(8): 27327-27350. doi: 10.3934/math.20261093
Autonomous operations are an essential function of urban air mobility (UAM) and other evolving aviation markets. Achieving autonomous flight within complex environments remains a bottleneck in the area of unmanned aerial vehicles (UAVs). Current progress in sensor technology has improved the payload capabilities of UAVs, allowing the incorporation of sensors, namely multispectral cameras, higher spatial resolution cameras, and light detection and ranging (LiDAR) systems. Moreover, the fusion of data from diverse sensor modalities can compensate for the limitations of individual sensors, offering a more comprehensive representation of the operating environment. Thus, a systematic analysis of path optimization methods that employ multi-sensor data fusion is critical for enhancing the autonomy and reliability of UAV systems. At present, scholars have progressively utilized deep learning (DL)-driven systems to overcome these challenges for general object detection tasks and have achieved considerable advancements. However, the application of DL methods specifically for UAV recognition and classification remains a relatively novel research field. This paper presents a novel explainable deep learning-based UAV obstacle detection framework (XDL-UAVODF) using multi-sensor data. The aim of this study is to design a UAV navigation framework for obstacle avoidance and optimal trajectory planning in dynamic and complex environments. Obstacle detection provides fundamental environmental awareness for safe navigation and serves as an essential condition for subsequent path planning and trajectory generation. The proposed approach is designed to support UAV navigation by accurately identifying obstacles rather than directly generating collision-free paths. For feature selection, a hybrid approach that integrates principal component analysis (PCA) and least absolute shrinkage and selection operator (LASSO) is leveraged to reduce dimensionality and select significant feature subsets. Moreover, the dynamic sparse graph convolutional recurrent network (DSGCGRN) is used to model spatial-temporal relationships and analyze complex patterns among multi-sensor data to improve decision-making performance. The AdaGrad optimizer is utilized in the training process to ensure faster convergence and enhance model stability. Finally, SHapley Additive exPlanations (SHAP) is employed to explain feature contributions and enhance the transparency of the deep learning model. The performance validation analysis of the XDL-UAVODF approach is conducted using the UAV Autonomous Navigation Dataset. The experimental outcomes reported the superiority of the XDL-UAVODF technique under various measures.
| [1] |
G. S. Li, J. C. Dai, J. H. Wang, X. Y. Jing, T. Zhao, D. Q. Chen, Graph neural network and dynamic graph reconstruction based adaptive path planning method for unmanned aerial vehicles (UAVs) in three-dimensional environments, Meas. Sci. Technol., 37 (2026), 056304. https://doi.org/10.1088/1361-6501/ae39fb doi: 10.1088/1361-6501/ae39fb
|
| [2] |
S. J. Yang, J. T. Yuan, Z. P. Zhang, Z. B. Chen, H. C. Zhang, X. H. Cui, Multi-UAV collaborative mission planning method for self-organized sensor data acquisition, Comput. Mater. Con., 81 (2024), 1529–1563. https://doi.org/10.32604/cmc.2024.055402 doi: 10.32604/cmc.2024.055402
|
| [3] |
Y. X. Liu, Q. X. Zhou, W. C. Mao, X. L. Li, H. F. Wei, M. Tsukada, Multi-modal trajectory planning for emergency-oriented air-ground collaborative sensing and communication, IEEE Trans. Cogn. Commun. Netw., 11 (2025), 3094–3111. https://doi.org/10.1109/TCCN.2025.3585254 doi: 10.1109/TCCN.2025.3585254
|
| [4] |
Y. L. Zhang, Z. L. Sun, W. H. Peng, Y. Q. Lin, X. T. Li, K. T. Yan, et al., Key technologies for intelligent operation of plant protection UAVs in hilly and mountainous areas: progress, challenges, and prospects, Agronomy, 16 (2026), 193. https://doi.org/10.3390/agronomy16020193 doi: 10.3390/agronomy16020193
|
| [5] |
D. Z. Yuan, Y. X. Zhong, X. P. Zhu, Y. Chen, Y. Jin, X. Z. Du, et al., Trajectory planning for unmanned vehicles on airport apron under aircraft-vehicle-airfield collaboration, Sensors, 25 (2025), 71. https://doi.org/10.3390/s25010071 doi: 10.3390/s25010071
|
| [6] |
C. Y. Yin, C. W. Wang, Z. K. Huang, H. Jiang, J. Chen, X. R. Miao, CiUAV: Scalable device-free indoor UAV localization via multiobjective optimized network using channel state information, IEEE Int. Things J., 13 (2026), 15297–15307. https://doi.org/10.1109/JIOT.2026.3654645 doi: 10.1109/JIOT.2026.3654645
|
| [7] |
Z. Haider, C. J. Sreenan, K. N. Brown, A. O'Mahony, Indoor autonomous multi-UAVs: a review of current research, enabling technologies and open challenges, IEEE Access, 13 (2025), 212231–212265. https://doi.org/10.1109/ACCESS.2025.3642189 doi: 10.1109/ACCESS.2025.3642189
|
| [8] | V. P. Modcoicar, T. Baraskar, ML-driven analysis of NavIC-based tracking for route optimization in urban air mobility, In: Inventive communication and computational technologies, Cham: Springer, 2025,315–328. https://doi.org/10.1007/978-3-032-04312-2_26 |
| [9] | T. Lombaerts, E. Kawamura, K. Kannan, C. A. Ippolito, V. Stepanyan, G. Gorospe, et al., Cross validation of sensor inputs as part of position estimation for urban air mobility, In: AIAA SCITECH 2026 Forum, 2026, 2576. https://doi.org/10.2514/6.2026-2576 |
| [10] | G. Ariante, U. Papa, Embedded platforms for UAS landing path and obstacle detection II: Navigation support systems for urban air mobility operations, Cham: Springer, 2024. https://doi.org//10.1007/978-3-031-59754-1 |
| [11] | V. Donato, G. Giangreco, F. Mattei, C. Conte, G. Rufino, D. Accardo, et al., Error analysis of extensive drone flight data for satellite navigation in urban environment, In: AIAA SCITECH 2026 Forum, 2026, 1071. https://doi.org/10.2514/6.2026-1071 |
| [12] | C. CHERIF, M. MAIZA, A. TALEB-AHMED, A study on autonomous navigation and obstacle avoidance systems for UAVs using deep learning techniques, 2025, submitted for publication. https://doi.org/10.21203/rs.3.rs-7303597/v1 |
| [13] |
G. Liu, Y. Tang, Z. P. Tan, M. W. Fang, A multi-stage optimization strategy for multi-UAV path planning in complex urban 3D environments with obstacle avoidance, Complex Intell. Syst., 12 (2026), 17. https://doi.org/10.1007/s40747-025-02159-2 doi: 10.1007/s40747-025-02159-2
|
| [14] |
C. Q. Weng, C. Chen, J. J. Tan, T. L. Pan, R. X. Zhong, Real-time traffic simulation and management for large-scale urban air mobility: integrating route guidance and collision avoidance, Transport. Res. Part C Emerging Technol., 183 (2026.), 105477. https://doi.org/10.1016/j.trc.2025.105477 doi: 10.1016/j.trc.2025.105477
|
| [15] |
J. Kim, H. Yoon, S. Yoon, Y. Kwon, K. Lee, A deep learning-based trajectory and collision prediction framework for safe urban air mobility, Drones, 9 (2025), 460. https://doi.org/10.3390/drones9070460 doi: 10.3390/drones9070460
|
| [16] |
Q. Y. Liu, W. Dai, Z. C. Yan, C. J. Tessone, An intelligent path planning system for urban airspace monitoring: from infrastructure assessment to strategic optimization, Smart Cities, 8 (2025), 100. https://doi.org/10.3390/smartcities8030100 doi: 10.3390/smartcities8030100
|
| [17] |
G. Veiga-Piñeiro, E. Aldao-Pensado, E. Martín-Ortega, Hybrid CFD-deep learning approach for urban wind flow predictions and risk-aware UAV path planning, Drones, 9 (2025), 791. https://doi.org/10.3390/drones9110791 doi: 10.3390/drones9110791
|
| [18] | S. Deniz, Z. B. Wang, Autonomous conflict resolution in urban air mobility: a deep multi-agent reinforcement learning approach, In: AIAA AVIATION FORUM AND ASCEND 2024, 2024, 4005. https://doi.org/10.2514/6.2024-4005 |
| [19] |
O. K. Isik, I. Petrunin, A. Tsourdos, Machine learning-based environment-aware GNSS integrity monitoring for urban air mobility, Drones, 8 (2024), 690. https://doi.org/10.3390/drones8110690 doi: 10.3390/drones8110690
|
| [20] |
J. Li, D. Shen, F. P. Yu, D. Qi, A method for air route network planning of urban air mobility, Aerospace, 11 (2024), 584. https://doi.org/10.3390/aerospace11070584 doi: 10.3390/aerospace11070584
|
| [21] | A. K. Biswas, M. S. A. Bhuiyan, M. N. H. Mir, A. Rahman, M. F. Mridha, M. R. Islam, A dual output temporal convolutional network with attention architecture for stock price prediction and risk assessment, IEEE Access, 13 (2025), 53621–53639. |
| [22] |
C. B. Qin, X. T. Ran, D. H. Zhang, Unsupervised image stitching based on generative adversarial networks and feature frequency awareness algorithm, Appl. Soft Comput., 183 (2025), 113466. https://doi.org/10.1016/j.asoc.2025.113466 doi: 10.1016/j.asoc.2025.113466
|
| [23] | M. Ngcukayitobi, Artificial intelligence-driven design and deployment of autonomous eVTOL drones for urban air mobility: a comprehensive review of challenges, technologies, and integration strategies, CEAS Aeronaut. J., 2026. https://doi.org/10.1007/s13272-026-00985-9 |
| [24] |
S. Song, Y. Jiang, X. Song, V. Stojanovic, Composite neural learning-based adaptive actuator failure compensation control for full-state constrained autonomous surface vehicle, Neural Comput. Appl., 37 (2025), 6369–6381. https://doi.org/10.1007/s00521-024-10651-y doi: 10.1007/s00521-024-10651-y
|
| [25] |
C. B. Qin, X. T. Ran, Efficient unsupervised image stitching using attention mechanism with deep homography estimation, Comput. Mater. Contin., 79 (2024), 1319–1334. https://doi.org/10.32604/cmc.2024.048850 doi: 10.32604/cmc.2024.048850
|
| [26] |
P. K. Dongre, V. Patel, U. Bhoi, N. N. Maltare, An outlier detection framework for air quality index prediction using linear and ensemble models, Decis. Anal. J., 14 (2025), 100546. https://doi.org/10.1016/j.dajour.2025.100546 doi: 10.1016/j.dajour.2025.100546
|
| [27] |
P. K. Sahu, T. Fatma, Optimized breast cancer classification using PCA-LASSO feature selection and ensemble learning strategies with Optuna optimization, IEEE Access, 13 (2025.), 35645–35661. https://doi.org/10.1109/ACCESS.2025.3539746 doi: 10.1109/ACCESS.2025.3539746
|
| [28] |
J. H. Chang, J. L. Yin, Y. R. Hao, C. X. Gao, STFDSGCN: Spatio-temporal fusion graph neural network based on dynamic sparse graph convolution GRU for traffic flow forecast, Sensors, 25 (2025), 3446. https://doi.org/10.3390/s25113446 doi: 10.3390/s25113446
|
| [29] |
A. Q. Albayati, S. A. J. Altaie, W. N. I. Al-Obaydy, F. F. Alkhalid, Performance analysis of optimization algorithms for convolutional neural network-based handwritten digit recognition, IAES Int. J. Artif. Intell, 13 (2024), 563–571. http://doi.org/10.11591/ijai.v13.i1.pp563-571 doi: 10.11591/ijai.v13.i1.pp563-571
|
| [30] |
J. Graham, V. S. Sheng, SHAP informed neural network, Mathematics, 13 (2025), 849. https://doi.org/10.3390/math13050849 doi: 10.3390/math13050849
|
| [31] | UAV Autonomous Navigation Dataset. Available from: https://www.kaggle.com/datasets/ziya07/uav-autonomous-navigation-dataset/data |
| [32] |
A. V. R. Katkuri, H. Madan, N. Khatri, A. S. H. Abdul-Qawy, K. S. Patnaik, Autonomous UAV navigation using deep learning-based computer vision frameworks: a systematic literature review, Array, 23 (2024.), 100361. https://doi.org/10.1016/j.array.2024.100361 doi: 10.1016/j.array.2024.100361
|
Figures(14) / Tables(8)
Sarah A. Alzakari, Shaymaa Sorour, Saleh Alghamdi, Ahmed Omer Ahmed Ismail, Nabil Almashfi, Aisha Blfgeh, Fahad F. Alruwaili, Somia A. Asklany. Mathematical modeling of an explainable deep learning-based UAV obstacle detection framework using multi-sensor data for urban air mobility systems[J]. AIMS Mathematics, 2026, 11(8): 27327-27350. doi: 10.3934/math.20261093
DownLoad: