Abstract
This paper proposes a robot autonomous exploration algorithm based on multi-resolution fields to solve the problems of low efficiency, high path repetition, and limited environmental adaptability in complex environments. First, OctoMap’s layered architecture is used to create a multi-resolution voxel map. A coarse-fine dual stage is then used to detect frontiers and balance point numbers. Second, polar coordinate sampling is utilized to avoid the sampling points being too concentrated in the center of the circle, and the scoring function is constructed by combining the distance decay function to prevent the robot from repeating the search. Finally, Monte Carlo integration’s gain calculation method is introduced to eliminate step errors caused by discretization and improve gain calculation accuracy. Simulation experiments are carried out in different environments, and the data prove that the method in this paper is better than the comparison algorithm in terms of moving distance, running time and exploration efficiency. The results show that the algorithm proposed in this paper effectively improves the robot’s autonomous exploration performance in unknown complex environments and provides a new solution for practical applications.
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The accessibility of the raw data and code utilized in this study is restricted. Should further experimental data be required related to the results, interested parties should contact the corresponding author.
References
Gao, Y. & Chien, S. Review on space robotics: Toward top-level science through space exploration. Sci. Robot. 2, eaan5074 (2017).
Delmerico, J. et al. The current state and future outlook of rescue robotics. J. Field Robot. 36, 1171–1191 (2019).
Nahavandi, S. et al. A comprehensive review on autonomous navigation. ACM Comput. Surv. 57, 1–67 (2025).
Zhang, S., Zhang, X., Li, T., Yuan, J. & Fang, Y. Fast active aerial exploration for traversable path finding of ground robots in unknown environments. IEEE Trans. Instrum. Meas. 71, 1–13 (2022).
Jones, M., Djahel, S. & Welsh, K. Path-planning for unmanned aerial vehicles with environment complexity considerations: A survey. ACM Comput. Surv. 55, 1–39 (2023).
Liu, L. et al. Path planning techniques for mobile robots: Review and prospect. Expert Syst. Appl. 227, 120254 (2023).
Garaffa, L. C., Basso, M., Konzen, A. A. & de Freitas, E. P. Reinforcement learning for mobile robotics exploration: A survey. IEEE Trans. Neural Netw. Learn. Syst. 34, 3796–3810 (2021).
Batinovic, A., Petrovic, T., Ivanovic, A., Petric, F. & Bogdan, S. A multi-resolution frontier-based planner for autonomous 3d exploration. IEEE Robot. Autom. Lett. 6, 4528–4535 (2021).
Wang, J. & Zheng, E. Path planning of a mobile robot based on the improved rapidly exploring random trees star algorithm. Electronics 13, 2340 (2024).
Zhu, H. et al. Dsvp: Dual-stage viewpoint planner for rapid exploration by dynamic expansion. In 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 7623–7630, https://doi.org/10.1109/IROS51168.2021.9636473 (2021).
Cao, C., Zhu, H., Choset, H. & Zhang, J. Tare: A hierarchical framework for efficiently exploring complex 3d environments. Robot. Sci. Syst. 5, 2 (2021).
Yamauchi, B. A frontier-based approach for autonomous exploration. In Proceedings 1997 IEEE International Symposium on Computational Intelligence in Robotics and Automation CIRA’97.’Towards New Computational Principles for Robotics and Automation’, 146–151 (IEEE, 1997).
Faigl, J. & Kulich, M. On determination of goal candidates in frontier-based multi-robot exploration. In 2013 European Conference on Mobile Robots, 210–215 (IEEE, 2013).
Applegate, D. L., Bixby, R. E., Chvátal, V. & Cook, W. J. The traveling salesman problem: a computational study. In The Traveling Salesman Problem (Princeton university press, 2011).
González-Banos, H. H. & Latombe, J.-C. Navigation strategies for exploring indoor environments. Int. J. Robot. Res. 21, 829–848 (2002).
Bircher, A., Kamel, M., Alexis, K., Oleynikova, H. & Siegwart, R. Receding horizon“ next-best-view” planner for 3d exploration. In 2016 IEEE international conference on robotics and automation (ICRA), 1462–1468 (IEEE, 2016).
LaValle, S. Rapidly-exploring random trees: A new tool for path planning. Res. Rep. 9811 (1998).
Dang, T. et al. Graph-based subterranean exploration path planning using aerial and legged robots. J. Field Robot. 37, 1363–1388 (2020).
Selin, M., Tiger, M., Duberg, D., Heintz, F. & Jensfelt, P. Efficient autonomous exploration planning of large-scale 3-d environments. IEEE Robot. Autom. Lett. 4, 1699–1706 (2019).
Zhang, J. & Singh, S. Loam: Lidar odometry and mapping in real-time. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), 3917–3923, https://doi.org/10.1109/ICRA.2014.6907231 (IEEE, 2014).
Wurm, K. M., Hornung, A., Bennewitz, M., Stachniss, C. & Burgard, W. Octomap: A probabilistic, flexible, and compact 3d map representation for robotic systems. In Proc. of the ICRA 2010 workshop on best practice in 3D perception and modeling for mobile manipulation, vol. 2, 3 (2010).
Li, Y. et al. Voxel field fusion for 3d object detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 1120–1129 (2022).
Dharmadhikari, M. et al. Motion primitives-based path planning for fast and agile exploration using aerial robots. In 2020 IEEE International Conference on Robotics and Automation (ICRA), 179–185, https://doi.org/10.1109/ICRA40945.2020.9196964 (2020).
Funding
This work was supported in part by the Henan Province Key Research and Development Project (Grant No. 241111213000), in part by the Scientific Research Team Plan of Zhengzhou University of Aeronautics (Grant Nos. 23ZHTD01007, 24ZHTD01001), in part by the Zhengzhou University of Aeronautics Research Platform Open Fund Project (Grant No. ZHKF-230204), in part by the Henan Provincial Key Technology Research and Development Program (Grant Nos. 232102220025, 252102210023), in part by the Henan Key Laboratory of General Aviation Technology, in part by the Henan Province Collaborative Innovation Center of Aeronautics and Astronautics Electronic Information Technology, and in part by the Henan Province Special and Urgent Subject Group of Aeronautical and Astronautical Intelligent Engineering.
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Z.Z. developed the methodology, performed the simulations, and drafted the main text of the manuscript. L.X. and Y.Z. reviewed and edited the manuscript and evaluated the simulation results. G.Z. and Y.C. organized the data and managed the project. The final manuscript was reviewed and approved by all authors.
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Zhai, Z., Xu, L., Zhang, Y. et al. Multi-resolution field-based algorithm for autonomous robot exploration. Sci Rep (2026). https://doi.org/10.1038/s41598-026-46119-3
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DOI: https://doi.org/10.1038/s41598-026-46119-3


