{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:34:40Z","timestamp":1760060080816,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,3]],"date-time":"2025-08-03T00:00:00Z","timestamp":1754179200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>Ensuring the safe operation of Unmanned Aerial Vehicles (UAVs) is crucial for both mission-critical and safety-critical tasks. In scenarios where UAVs must track airborne targets, they need to follow the target\u2019s path while maintaining a safe distance, even in the presence of unmodeled dynamics and environmental disturbances. This paper presents a novel collision avoidance strategy for dynamic quadrotor UAVs during target-tracking missions. We propose a safety controller that combines a learning-based Control Barrier Function (CBF) with standard sliding mode feedback. Our approach employs a neural network that learns the true CBF constraint, accounting for wind disturbances, while the sliding mode controller addresses unmodeled dynamics. This unified control law ensures safe leader-following behavior and precise trajectory tracking. By leveraging a learned CBF, the controller offers improved adaptability to complex and unpredictable environments, enhancing both the safety and robustness of the system. The effectiveness of our proposed method is demonstrated through the AirSim platform using the PX4 flight controller.<\/jats:p>","DOI":"10.3390\/robotics14080108","type":"journal-article","created":{"date-parts":[[2025,8,4]],"date-time":"2025-08-04T09:41:17Z","timestamp":1754300477000},"page":"108","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Safe Autonomous UAV Target-Tracking Under External Disturbance, Through Learned Control Barrier Functions"],"prefix":"10.3390","volume":"14","author":[{"given":"Promit","family":"Panja","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, Virginia Tech, Blacksbrug, VA 24061, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4426-6364","authenticated-orcid":false,"given":"Madan Mohan","family":"Rayguru","sequence":"additional","affiliation":[{"name":"Louisville Automation and Robotics Research Institute (LARRI), University of Louisville, Louisville, KY 40208, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0245-2903","authenticated-orcid":false,"given":"Sabur","family":"Baidya","sequence":"additional","affiliation":[{"name":"Louisville Automation and Robotics Research Institute (LARRI), University of Louisville, Louisville, KY 40208, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3861","DOI":"10.1109\/TAC.2016.2638961","article-title":"Control barrier function based quadratic programs for safety critical systems","volume":"62","author":"Ames","year":"2016","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ames, A.D., Coogan, S., Egerstedt, M., Notomista, G., Sreenath, K., and Tabuada, P. (2019, January 25\u201328). Control barrier functions: Theory and applications. Proceedings of the 2019 18th European Control Conference (ECC), Naples, Italy.","DOI":"10.23919\/ECC.2019.8796030"},{"key":"ref_3","unstructured":"Panja, P. (2024). Survey Paper on Control Barrier Functions. arXiv."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Xu, B., and Sreenath, K. (2018, January 21\u201325). Safe teleoperation of dynamic uavs through control barrier functions. Proceedings of the 2018 IEEE International Conference on Robotics and Automation (ICRA), Brisbane, Australia.","DOI":"10.1109\/ICRA.2018.8463194"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Lerch, C., Dong, D., and Abraham, I. (June, January 29). Safety-critical ergodic exploration in cluttered environments via control barrier functions. Proceedings of the 2023 IEEE International Conference on Robotics and Automation (ICRA), London, UK.","DOI":"10.1109\/ICRA48891.2023.10161032"},{"key":"ref_6","unstructured":"Panja, P., Hoagg, J.B., and Baidya, S. (2023). Control Barrier Function Based UAV Safety Controller in Autonomous Airborne Tracking and Following Systems. arXiv."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1109\/100.580977","article-title":"The dynamic window approach to collision avoidance","volume":"4","author":"Fox","year":"1997","journal-title":"IEEE Robot. Autom. Mag."},{"key":"ref_8","unstructured":"Schouwenaars, T. (2006). Safe Trajectory Planning of Autonomous Vehicles. [Ph.D. Thesis, Massachusetts Institute of Technology]."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2811","DOI":"10.1007\/s11831-023-09894-0","article-title":"Intensive review of drones detection and tracking: Linear Kalman filter versus nonlinear regression, an analysis case","volume":"30","author":"Zitar","year":"2023","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1109\/TMC.2020.3003639","article-title":"Reinforcement learning-based collision avoidance and optimal trajectory planning in UAV communication networks","volume":"21","author":"Hsu","year":"2020","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Fraga-Lamas, P., Ramos, L., Mond\u00e9jar-Guerra, V., and Fern\u00e1ndez-Caram\u00e9s, T.M. (2019). A review on IoT deep learning UAV systems for autonomous obstacle detection and collision avoidance. Remote Sens., 11.","DOI":"10.3390\/rs11182144"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1080\/01691864.2022.2119888","article-title":"Platooning control of drones with real-time deep learning object detection","volume":"37","author":"Dai","year":"2023","journal-title":"Adv. Robot."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Redmon, J., Divvala, S., Girshick, R., and Farhadi, A. (2016, January 27\u201330). You only look once: Unified, real-time object detection. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.91"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Tayal, M., and Kolathaya, S. (2023). Control Barrier Functions in Dynamic UAVs for Kinematic Obstacle Avoidance: A Collision Cone Approach. arXiv.","DOI":"10.23919\/ACC60939.2024.10644548"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1109\/LCSYS.2020.3000748","article-title":"Guaranteed obstacle avoidance for multi-robot operations with limited actuation: A control barrier function approach","volume":"5","author":"Chen","year":"2020","journal-title":"IEEE Control Syst. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Zhang, H., Zhang, X., Li, T., Zhang, S., and Zhang, X. (2022, January 9\u201311). Barrier Function Enhanced Geometric Controller for Safe Control of a Quadrotor UAV. Proceedings of the 2022 International Conference on Advanced Robotics and Mechatronics (ICARM), Guilin, China.","DOI":"10.1109\/ICARM54641.2022.9959280"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"6975","DOI":"10.1109\/TSMC.2023.3292810","article-title":"Multi-UAV safe collaborative transportation based on adaptive control barrier function","volume":"53","author":"Wang","year":"2023","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Wang, L., Theodorou, E.A., and Egerstedt, M. (2018, January 21\u201325). Safe learning of quadrotor dynamics using barrier certificates. Proceedings of the 2018 IEEE International Conference on Robotics and Automation (ICRA), Brisbane, Australia.","DOI":"10.1109\/ICRA.2018.8460471"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Machida, M., and Ichien, M. (June, January 30). Consensus-based control barrier function for swarm. Proceedings of the 2021 IEEE International Conference on Robotics and Automation (ICRA), Xi\u2019an, China.","DOI":"10.1109\/ICRA48506.2021.9561971"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Qing, W., Chen, H., Wang, X., and Yin, Y. (2021, January 27\u201331). Collision-free trajectory generation for UAV swarm formation rendezvous. Proceedings of the 2021 IEEE International Conference on Robotics and Biomimetics (ROBIO), Sanya, China.","DOI":"10.1109\/ROBIO54168.2021.9739428"},{"key":"ref_21","unstructured":"Gunnarsson, H., and \u00c5sbrink, A. (2022). Intelligent Drone Swarms: Motion Planning and Safe Collision Avoidance Control of Autonomous Drone Swarms, Chalmers University of Technology."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2069631","DOI":"10.1155\/2020\/2069631","article-title":"Distance-based formation control for quadrotors with collision avoidance via Lyapunov barrier functions","volume":"2020","author":"Ghommam","year":"2020","journal-title":"Int. J. Aerosp. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2056","DOI":"10.1109\/LRA.2024.3349917","article-title":"Safe Control for Navigation in Cluttered Space using Multiple Lyapunov-Based Control Barrier Functions","volume":"9","author":"Jang","year":"2024","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Dan, H., Hatanaka, T., Yamauchi, J., Shimizu, T., and Fujita, M. (2021). Persistent object search and surveillance control with safety certificates for drone networks based on control barrier functions. Front. Robot. AI, 8.","DOI":"10.3389\/frobt.2021.740460"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Cohen, M.H., and Belta, C. (2022, January 8\u201310). High order robust adaptive control barrier functions and exponentially stabilizing adaptive control lyapunov functions. Proceedings of the 2022 American Control Conference (ACC), Atlanta, GA, USA.","DOI":"10.23919\/ACC53348.2022.9867633"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1109\/LCSYS.2020.3005923","article-title":"Robust adaptive control barrier functions: An adaptive and data-driven approach to safety","volume":"5","author":"Lopez","year":"2020","journal-title":"IEEE Control Syst. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Taylor, A.J., and Ames, A.D. (2020, January 1\u20133). Adaptive safety with control barrier functions. Proceedings of the 2020 American Control Conference (ACC), Denver, CO, USA.","DOI":"10.23919\/ACC45564.2020.9147463"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2267","DOI":"10.1109\/TAC.2021.3074895","article-title":"Adaptive control barrier functions","volume":"67","author":"Xiao","year":"2021","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Liu, S., Xiao, W., and Belta, C.A. (2023, January 13\u201315). Auxiliary-Variable Adaptive Control Barrier Functions for Safety Critical Systems. Proceedings of the 2023 62th IEEE Conference on Decision and Control (CDC), Singapore.","DOI":"10.1109\/CDC49753.2023.10383595"},{"key":"ref_30","unstructured":"Xiao, W., Belta, C., and Cassandras, C. (2020). Adaptive Control Barrier Functions for Safety-Critical Systems. arXiv."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Tayal, M., Zhang, H., Jagtap, P., Clark, A., and Kolathaya, S. (2024). Learning a Formally Verified Control Barrier Function in Stochastic Environment. arXiv.","DOI":"10.1109\/CDC56724.2024.10886052"},{"key":"ref_32","unstructured":"Taylor, A., Singletary, A., Yue, Y., and Ames, A. (2020, January 10\u201311). Learning for safety-critical control with control barrier functions. Proceedings of the Learning for Dynamics and Control. PMLR, Virtual."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"106706","DOI":"10.1016\/j.compchemeng.2019.106706","article-title":"Control Lyapunov-barrier function-based predictive control of nonlinear processes using machine learning modeling","volume":"134","author":"Wu","year":"2020","journal-title":"Comput. Chem. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Choi, J., Castaneda, F., Tomlin, C.J., and Sreenath, K. (2020). Reinforcement learning for safety-critical control under model uncertainty, using control lyapunov functions and control barrier functions. arXiv.","DOI":"10.15607\/RSS.2020.XVI.088"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Cheng, R., Khojasteh, M.J., Ames, A.D., and Burdick, J.W. (2020, January 14\u201318). Safe multi-agent interaction through robust control barrier functions with learned uncertainties. Proceedings of the 2020 59th IEEE Conference on Decision and Control (CDC), Jeju Island, Republic of Korea.","DOI":"10.1109\/CDC42340.2020.9304395"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"So, O., Serlin, Z., Mann, M., Gonzales, J., Rutledge, K., Roy, N., and Fan, C. (2024, January 13\u201317). How to train your neural control barrier function: Learning safety filters for complex input-constrained systems. Proceedings of the 2024 IEEE International Conference on Robotics and Automation (ICRA), Yokohama, Japan.","DOI":"10.1109\/ICRA57147.2024.10610418"},{"key":"ref_37","unstructured":"(2023, September 14). Microsoft AirSim. Available online: https:\/\/microsoft.github.io\/AirSim\/."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Shah, S., Dey, D., Lovett, C., and Kapoor, A. (2017). AirSim: High-Fidelity Visual and Physical Simulation for Autonomous Vehicles. arXiv.","DOI":"10.1007\/978-3-319-67361-5_40"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3509","DOI":"10.1109\/LRA.2020.2976321","article-title":"Federated imitation learning: A novel framework for cloud robotic systems with heterogeneous sensor data","volume":"5","author":"Liu","year":"2020","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Liu, B., Wang, L., Chen, X., Huang, L., Han, D., and Xu, C.Z. (June, January 30). Peer-assisted robotic learning: A data-driven collaborative learning approach for cloud robotic systems. Proceedings of the 2021 IEEE international conference on robotics and automation (ICRA), Xi\u2019an, China.","DOI":"10.1109\/ICRA48506.2021.9562018"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Ghods, R., Durkin, W.J., and Schneider, J. (June, January 30). Multi-agent active search using realistic depth-aware noise model. Proceedings of the 2021 IEEE International Conference on Robotics and Automation (ICRA), Xi\u2019an, China.","DOI":"10.1109\/ICRA48506.2021.9561598"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Baldini, F., Anandkumar, A., and Murray, R.M. (2020, January 1\u20133). Learning pose estimation for UAV autonomous navigation and landing using visual-inertial sensor data. Proceedings of the 2020 American Control Conference (ACC), Denver, CO, USA.","DOI":"10.23919\/ACC45564.2020.9147400"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Saunders, J., Saeedi, S., and Lil, W. (June, January 29). Parallel reinforcement learning simulation for visual quadrotor navigation. Proceedings of the 2023 IEEE International Conference on Robotics and Automation (ICRA), London, UK.","DOI":"10.1109\/ICRA48891.2023.10160675"},{"key":"ref_44","unstructured":"(2023, September 14). PX4 Autopilot. Available online: https:\/\/px4.io\/software\/software-overview\/."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Meier, L., Honegger, D., and Pollefeys, M. (2015, January 26\u201330). PX4: A node-based multithreaded open source robotics framework for deeply embedded platforms. Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA.","DOI":"10.1109\/ICRA.2015.7140074"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1109\/MRA.2010.937855","article-title":"The grasp multiple micro-uav testbed","volume":"17","author":"Michael","year":"2010","journal-title":"IEEE Robot. Autom. Mag."}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/14\/8\/108\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:22:16Z","timestamp":1760034136000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/14\/8\/108"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,3]]},"references-count":46,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["robotics14080108"],"URL":"https:\/\/doi.org\/10.3390\/robotics14080108","relation":{},"ISSN":["2218-6581"],"issn-type":[{"type":"electronic","value":"2218-6581"}],"subject":[],"published":{"date-parts":[[2025,8,3]]}}}