資訊軌跡規劃 (IPP) 是無人機的關鍵應用之一。它可以重新定義為在軌跡限制下的次模性最大化問題。然而，尋找最佳搜索軌跡包括兩個NP-hard問題，即最大覆蓋問題和最小路徑問題。此研究提出成 本效益生成樹(CBST) ，以提高IPP 的效能。理論說明樹的總曲率影響了理論保證值。實驗表明，所提出的 CBST 演算法的效能比其他演算法的效能更好。

Informative path planning (IPP) is one of key applications for unmanned aerial vehicles (UAVs). It can be formulated as the submodular maximization problem with routing constraints. However, finding an optimal search path includes two NP-hard problems, the covering problem and routing problem. In this research, the proposed algorithm generates the cost-benefit spanning tree (CBST) to boost the IPP performance. The proofs show the theoretical guarantees depends on the total curvatures of the trees. The experiments demonstrate that the proposed method outperforms the benchmark approaches.

[1] Marija Popovi¢, Teresa Vidal-Calleja, Gregory Hitz, Inkyu Sa, Roland Siegwart, and Juan Nieto. Multiresolution mapping and informative path planning for uav-based terrain monitoring. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 1382-1388, 2017.
[2] Marija Popovi¢, Teresa Vidal-Calleja, Gregory Hitz, Jen Jen Chung, Inkyu Sa, Roland Siegwart, and Juan Nieto. An informative path planning framework for uav-based terrain monitoring. Autonomous Robots, 44(6):889-911, 2020.
[3] George L Nemhauser, Laurence A Wolsey, and Marshall L Fisher. An analysis of approximations for maximizing submodular set functions i. Mathematical programming, 14(1):265-294, 1978.
[4] Samir Khuller, Anna Moss, and Joseph Se Naor. The budgeted maximum coverage problem. Information processing letters, 70(1):39-45, 1999.
[5] Haifeng Zhang and Yevgeniy Vorobeychik. Submodular optimization with routing constraints. Proceedings of the AAAI conference on articial intelligence, 30(1), 2016.
[6] Uriel Feige. A threshold of ln n for approximating set cover. Journal of the ACM (JACM), 45(4):634-652, 1998.
[7] Merrill M Flood. The traveling-salesman problem. Operations research, 4(1):61-75, 1956.
[8] Tal Grossman and Avishai Wool. Computational experience with approximation algorithms for the set covering problem. European journal of operational research, 101(1):8192, 1997.
[9] Shen Lin and Brian W Kernighan. An effective heuristic algorithm for the traveling-salesman problem. Operations research, 21(2):498-516, 1973.
[10] Pao-Te Lin and Kuo-Shih Tseng. Improvement of submodular maximization problems with routing constraints via submodularity and fourier sparsity. IEEE Robotics and Automation Letters, 8(4):1927-1934, 2023.
[11] Lawrence D Stone. Theory of optimal search. Elsevier, 1976.
[12] Frederic Bourgault, Tomonari Furukawa, and Hugh F DurrantWhyte. Coordinated decentralized search for a lost target in a bayesian world. Proceedings IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 1:48-53, 2003.
[13] KE Trummel and JR Weisinger. The complexity of the optimal searcher path problem. Operations Research, 34(2):324-327, 1986.
[14] Timothy H Chung and Joel W Burdick. A decision-making framework for control strategies in probabilistic search. Proceedings IEEE International Conference on Robotics and Automation, pages 4386-4393, 2007.
[15] Timothy H Chung and Joel W Burdick. Analysis of search decision making using probabilistic search strategies. IEEE Transactions on Robotics, 28(1):132-144, 2011.
[16] Alberto Elfes. Using occupancy grids for mobile robot perception and navigation. Computer, 22(6):46-57, 1989.
[17] Kuo-Shih Tseng and Bérénice Mettler. Near-optimal probabilistic search via submodularity and sparse regression. Autonomous Robots, 41(1):205-229, 2017.
[18] Haye Lau, Shoudong Huang, and Gamini Dissanayake. Discounted mean bound for the optimal searcher path problem with nonuniform travel times. European journal of operational research, 190(2):383-397, 2008.
[19] Eva Besada-Portas, Luis de la Torre, Jesus M de la Cruz, and Bonifacio de Andrés-Toro. Evolutionary trajectory planner for multiple uavs in realistic scenarios. IEEE Transactions on Robotics, 26(4):619-634, 2010.
[20] Enric Galceran and Marc Carreras. A survey on coverage path planning for robotics. Robotics and Autonomous systems, 61(12):1258-1276, 2013.
[21] Marina Torres, David A Pelta, José L Verdegay, and Juan C Torres. Coverage path planning with unmanned aerial vehicles for 3d terrain reconstruction. Expert Systems with Applications, 55:441-451, 2016.
[22] Chao Qian, Jing-Cheng Shi, Yang Yu, and Ke Tang. On subset selection with general cost constraints. IJCAI, 17:2613-2619, 2017.
[23] Chao Bian, Chao Feng, Chao Qian, and Yang Yu. An efficient evolutionary algorithm for subset selection with general cost constraints. Proceedings of the AAAI Conference on Artificial Intelligence, 34(04):3267-3274, 2020.
[24] Ioannis K Nikolos, Kimon P Valavanis, Nikos C Tsourveloudis, and Anargyros N Kostaras. Evolutionary algorithm based offline/online path planner for uav navigation. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 33(6):898-912, 2003.
[25] Gregory Hitz, Enric Galceran, Marie-Ève Garneau, François Pomerleau, and Roland Siegwart. Adaptive continuous-space informative path planning for online environmental monitoring. Journal of Field Robotics, 34(8):1427-1449, 2017.
[26] Shervin Javdani, Matthew Klingensmith, J Andrew Bagnell, Nancy S Pollard, and Siddhartha S Srinivasa. Efficient touch based localization through submodularity. IEEE International Conference on Robotics and Automation, pages 18281835, 2013.
[27] Amarjeet Singh. Nonmyopic adaptive informative path planning for multiple robots. 2009.
[28] Joseph B Kadane and Herbert A Simon. Optimal strategies for a class of constrained sequential problems. The Annals of Statistics, 5(2):237-255, 1977.
[29] Marija Popovic, Gregory Hitz, Juan Nieto, Inkyu Sa, Roland Siegwart, and Enric Galceran. Online informative path planning for active classication using uavs. arXiv preprint arXiv:1609.08446, 2016.
[30] Brian Yamauchi. Frontier-based exploration using multiple robots. Proceedings of the second international conference on Autonomous agents, pages 47-53, 1998.
[31] Nikolaus Hansen. The cma evolution strategy: a comparing review. Towards a new evolutionary computation, pages 75-102, 2006.
[32] Micah Corah and Nathan Michael. Distributed matroid-constrained submodular maximization for multi-robot exploration: Theory and practice. Autonomous Robots, 43:485-501, 2019.
[33] Bing-Xian Lu and Kuo-Shih Tseng. 3d map exploration via learning submodular functions in the fourier domain. International Conference on Unmanned Aircraft Systems (ICUAS), pages 1199-1205, 2020.
[34] Georey Hollinger and Sanjiv Singh. Proofs and experiments in scalable, near-optimal search by multiple robots. Proceedings of Robotics: Science and Systems, 1, 2008.
[35] Andreas Krause, Carlos Guestrin, Anupam Gupta, and Jon Kleinberg. Near-optimal sensor placements: Maximizing information while minimizing communication cost. Proceedings of the 5th international conference on Information processing in sensor networks, pages 2-10, 2006.
[36] Peter Stobbe and Andreas Krause. Learning fourier sparse set functions. Artificial Intelligence and Statistics, pages 1125-1133, 2012.
[37] Robert Clay Prim. Shortest connection networks and some generalizations. The Bell System Technical Journal, 36(6):1389-1401, 1957.
[38] EW Dijkstra. A note on two problems in connexion with graphs. Numerische Math., 1:269-271, 1959.
[39] Charles J Alpert, TC Hu, Jen-Hsin Huang, and Andrew B Kahng. A direct combination of the prim and dijkstra constructions for improved performance-driven global routing. IEEE International Symposium on Circuits and Systems, pages 1869-1872, 1993.
[40] Charles J Alpert, Wing-Kai Chow, Kwangsoo Han, Andrew B
Kahng, Zhuo Li, Derong Liu, and Sriram Venkatesh. Prim-dijkstra revisited: Achieving superior timing-driven routing trees. Proceedings of the International Symposium on Physical Design, pages 10-17, 2018.
[41] Michele Conforti and Gérard Cornuéjols. Submodular set functions, matroids and the greedy algorithm: tight worst-case bounds and some generalizations of the rado-edmonds theorem. Discrete applied mathematics, 7(3):251-274, 1984.
[42] Kuo-Shih Tseng. Learning in human and robot search: Subgoal, submodularity, and sparsity. PhD thesis, University of Minnesota, 2016.
[43] Rei-Shu Shieh. Map explorations via dynamic tree-structured graph. Master's thesis, National Central University, 2023.
[44] Kurt Schütte and Bartel Leendert van der Waerden. Das problem der dreizehn kugeln. Mathematische Annalen, 125(1):325-334, 1952.
[45] Daniel J Rosenkrantz, Richard E Stearns, and Philip M Lewis, II. An analysis of several heuristics for the traveling salesman problem. SIAM journal on computing, 6(3):563-581, 1977.
[46] Glenn Jocher, Ayush Chaurasia, Alex Stoken, Jirka Borovec, NanoCode012, Yonghye Kwon, Kalen Michael, TaoXie, Jiacong Fang, imyhxy, Lorna, Zeng Yifu, Colin Wong, Abhiram V, Diego Montes, Zhiqiang Wang, Cristi Fati, Jebastin Nadar, Laughing, UnglvKitDe, Victor Sonck, tkianai, yxNONG, Piotr Skalski, Adam Hogan, Dhruv Nair, Max Strobel, and Mrinal Jain. ultralytics/yolov5: v7.0 - YOLOv5 SOTA Realtime Instance Segmentation, November 2022.