本研究旨在建立一個用於動態環境的多機器人系統，考慮環境中有動態障礙物的情形下進行定位、避障及導航。基於雙層的導航框架，利用Dijkstra 演算法找出全域計畫，再藉由結合人工勢場法與Pure-Pursuit 演算法的區域規劃器，找出該時刻控制命令，並引入移動窗口法與障礙物濾波器，以降低於力場中搜尋時陷入區域最小值的可能性，最後加上多機器人間的協調策略，確保機器人相遇時得以化解衝突。系統實現時還需搭配定位與障礙物追蹤系統，本研究採用一組感測器特徵擷取系統處理二維光達的資料，並透過延伸型卡爾曼濾波器進行定位。在模擬環境與動態窗口法(DWA) 及時間彈力帶(TEB)進行比較，本研究所提出的系統在17 個場景中皆能保持93% 以上的成功率，且所需的計算時間皆在5 毫秒以下，同時也在自製的移動機器人平台進行測試，結果表明此系統確實能處理動態環境中的導航問題。

This research aims to establish a Multi-Robot System that is suitable for the dynamic environment. Implementing localization, obstacle avoidance, and navigation systems in an environment with dynamic obstacles. Based on the two-layer navigation framework, the Dijkstra algorithm is used to construct the global plan, and then the control command at each moment is created by combining the artificial potential field and the Pure-Pursuit algorithm. The rolling window method and the obstacle filter are also introduced to reduce the possibility of falling into the local minimum of the potential field. A coordination strategy between multi-robot is introduced to ensure the conflicts can be resolved when robots meet. It's also essential that each robot is equipped with the localization and the obstacle tracking system in the proposed system. In this work, an obstacle detection system is used to process the data from 2D-LiDAR, and the Extended Kalman Filter is used for localization. Compared with Dynamic Window Approach and Timed Elastic Band in the simulated environment, proposed the system in this research can achieve a success rate of at least 93% in 17 different scenarios, and the controller execution time is at most 5 milliseconds. Eventually, the proposed methodology is also tested on the self-made multi-robot platform, and the experiment results prove that the system can handle navigation problems in dynamic environment.

摘要i
Abstract ii
誌謝iii
圖目錄vi
表目錄x
第一章緒論1
1.1 前言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究動機及目的. . . . . . . . . . . . . . . . . . . . . . . 3
1.3 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 本文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . 11
第二章導航問題描述13
2.1 歐洲機器人大賽簡介. . . . . . . . . . . . . . . . . . . . 13
2.2 本研究之簡化場域. . . . . . . . . . . . . . . . . . . . . . 15
2.3 導航系統架構. . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 導航性能指標. . . . . . . . . . . . . . . . . . . . . . . . 18
第三章機器人定位與路徑追蹤系統21
3.1 感測器特徵提取系統. . . . . . . . . . . . . . . . . . . . 22
3.1.1 障礙物偵測. . . . . . . . . . . . . . . . . . . . . 22
3.1.2 障礙物追蹤. . . . . . . . . . . . . . . . . . . . . 24
3.2 機器人定位系統. . . . . . . . . . . . . . . . . . . . . . . 25
3.3 路徑追蹤系統. . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.1 差動運動學. . . . . . . . . . . . . . . . . . . . . 31
3.3.2 軌跡追蹤. . . . . . . . . . . . . . . . . . . . . . . 33
3.3.3 緊急停車系統. . . . . . . . . . . . . . . . . . . . 35
第四章多機器人導航系統37
4.1 基於move_base 之導航架構. . . . . . . . . . . . . . . . 37
4.2 基於人工勢場法的導航系統設計. . . . . . . . . . . . . . 39
4.2.1 人工勢場法. . . . . . . . . . . . . . . . . . . . . 40
4.2.2 移動窗口法. . . . . . . . . . . . . . . . . . . . . 46
4.2.3 障礙物濾波器. . . . . . . . . . . . . . . . . . . . 47
4.2.4 多機器人協調策略. . . . . . . . . . . . . . . . . 48
4.3 模擬方法與場景. . . . . . . . . . . . . . . . . . . . . . . 49
4.3.1 對照組方法簡介. . . . . . . . . . . . . . . . . . . 49
4.3.2 模擬平台與流程. . . . . . . . . . . . . . . . . . . 51
4.3.3 模擬地圖與場景. . . . . . . . . . . . . . . . . . . 51
4.4 導航系統模擬結果. . . . . . . . . . . . . . . . . . . . . . 60
第五章多機器人系統實作與實驗結果83
5.1 硬體設備及配置. . . . . . . . . . . . . . . . . . . . . . . 83
5.2 實驗方法與場景. . . . . . . . . . . . . . . . . . . . . . . 86
5.3 實驗結果與討論. . . . . . . . . . . . . . . . . . . . . . . 90
第六章結論與未來工作103
6.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2 未來工作. . . . . . . . . . . . . . . . . . . . . . . . . . . 105
參考文獻107
附錄A 模擬結果之各項統計量表113

[1] U. Nations, “World population prospects 2019,” Department of Economic and Social Affairs, vol. 2, 2019.
[2] 廖珮如, “人口老化：勞動力短缺之衝擊與挑戰,” 人文與社會科學簡訊. 科技部人文及社會科學研究發展司, 2020, vol. 21, pp.
74–83.
[3] 國家發展委員會. (2020) 三階段年齡人口變動趨勢. [Online]. Available: https://www.ndc.gov.tw/Content_List.aspx?n= D527207EEEF59B9B, accessed: 2021-12-04.
[4] D. B. Poudel, “Coordinating hundreds of cooperative, autonomous robots in a warehouse,” Jan, vol. 27, no. 1-13, p. 26, 2013.
[5] J. P. Queralta, J. Taipalmaa, B. C. Pullinen, V. K. Sarker, T. N. Gia, H. Tenhunen, M. Gabbouj, J. Raitoharju, and T. Westerlund, “Collaborative multi-robot search and rescue: Planning, coordination, perception, and active vision,” IEEE Access, vol. 8, pp. 191 617– 191 643, 2020.
[6] A. Petitti, A. Franchi, D. Di Paola, and A. Rizzo, “Decentralized motion control for cooperative manipulation with a team of networked mobile manipulators,” 2016 IEEE International Conference on Robotics and Automation (ICRA), pp. 441–446, Stockholm, Sweden, May 16 - 21, 2016.
[7] E. W. Dijkstra et al., “A note on two problems in connexion with graphs,” Numerische mathematik, vol. 1, no. 1, pp. 269–271, 1959.
[8] P. E. Hart, N. J. Nilsson, and B. Raphael, “A formal basis for the heuristic determination of minimum cost paths,” IEEE transactions on Systems Science and Cybernetics, vol. 4, no. 2, pp. 100–107, 1968.
[9] D. Dolgov, S. Thrun, M. Montemerlo, and J. Diebel, “Practical search techniques in path planning for autonomous driving,” Ann Arbor, vol. 1001, no. 48105, pp. 18–80, 2008.
[10] K. Daniel, A. Nash, S. Koenig, and A. Felner, “Theta*: Any-angle path planning on grids,” Journal of Artificial Intelligence Research, vol. 39,
pp. 533–579, 2010.
[11] S. M. Lavalle, “Rapidly-exploring random trees: A new tool for path planning,” Iowa State University, Department of Computer Science, Tech. Rep., 1998.

[12] S. Karaman and E. Frazzoli, “Sampling-based algorithms for optimal motion planning,” The international journal of robotics research, vol. 30, no. 7, pp. 846–894, 2011.
[13] L. Palmieri, S. Koenig, and K. O. Arras, “Rrt-based nonholonomic motion planning using any-angle path biasing,” 2016 IEEE International Conference on Robotics and Automation (ICRA),
pp. 2775–2781, Stockholm, Sweden, May 16 - 21, 2016.
[14] J. Yu and S. M. LaValle, “Structure and intractability of optimal multi- robot path planning on graphs,” Twenty-Seventh AAAI Conference on Artificial Intelligence,” Washington, USA, July 14–18, 2013.
[15] M. Čáp, P. Novák, A. Kleiner, and M. Seleckỳ, “Prioritized planning algorithms for trajectory coordination of multiple mobile robots,” IEEE transactions on automation science and engineering, vol. 12, no. 3, pp. 835–849, 2015.
[16] R. Luna and K. E. Bekris, “Efficient and complete centralized multi- robot path planning,” 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3268–3275, San Francisco, USA, September 25 - 30, 2011.
[17] R. Stern, “Multi-agent path finding–an overview,” Artificial Intelligence, pp. 96–115, 2019.
[18] G. Wagner and H. Choset, “Subdimensional expansion for multirobot path planning,” Artificial Intelligence, vol. 219, pp. 1–24, 2015.
[19] G. Sharon, R. Stern, M. Goldenberg, and A. Felner, “The increasing cost tree search for optimal multi-agent pathfinding,” Artificial Intelligence, vol. 195, pp. 470–495, 2013.
[20] G. Sharon, R. Stern, A. Felner, and N. R. Sturtevant, “Conflict-based search for optimal multi-agent pathfinding,” Artificial Intelligence, vol. 219, pp. 40–66, 2015.
[21] P. Fiorini and Z. Shiller, “Motion planning in dynamic environments using velocity obstacles,” The International Journal of Robotics Research, vol. 17, no. 7, pp. 760–772, 1998.
[22] J. Van den Berg, M. Lin, and D. Manocha, “Reciprocal velocity obstacles for real-time multi-agent navigation,” 2008 IEEE International Conference on Robotics and Automation, pp. 1928–1935, California, USA, May 19 - 23, 2008.

[23] J. Van Den Berg, S. J. Guy, M. Lin, and D. Manocha, “Reciprocal n- body collision avoidance,” Robotics research, 2011, pp. 3–19.

[24] O. Khatib, “Real-time obstacle avoidance for manipulators and mobile robots,” Autonomous robot vehicles, 1986, pp. 396–404.

[25] S. S. Ge and Y. J. Cui, “New potential functions for mobile robot path planning,” IEEE Transactions on robotics and automation, vol. 16, no. 5, pp. 615–620, 2000.

[26] T. Weerakoon, “Artificial potential field and feature extraction method for mobile robot path planning in structured environments,” Kyushu Institute of Technology, 2016.

[27] Y. Yongjie and Z. Yan, “Collision avoidance planning in multi-robot based on improved artificial potential field and rules,” 2008 IEEE International Conference on Robotics and Biomimetics, pp. 1026– 1031, Bangkok, Thailand, December 14 - 17, 2009.

[28] Z. Pan, D. Li, K. Yang, and H. Deng, “Multi-robot obstacle avoidance based on the improved artificial potential field and pid adaptive tracking control algorithm,” Robotica, vol. 37, no. 11, pp. 1883–1903, 2019.

[29] Y. F. Chen, M. Liu, M. Everett, and J. P. How, “Decentralized non-communicating multiagent collision avoidance with deep reinforcement learning,” arXiv preprint arXiv:1609.07845, 2016.

[30] W. Ding, S. Li, H. Qian, and Y. Chen, “Hierarchical reinforcement learning framework towards multi-agent navigation,” 2018 IEEE International Conference on Robotics and Biomimetics (ROBIO), pp. 237–242, Kuala Lumpur, Malaysia, December 12 - 15, 2018.

[31] T. Fan, P. Long, W. Liu, and J. Pan, “Distributed multi-robot collision avoidance via deep reinforcement learning for navigation in complex scenarios,” The International Journal of Robotics Research, vol. 39, no. 7, pp. 856–892, 2020.

[32] L. Jetto, S. Longhi, and G. Venturini, “Development and experimental validation of an adaptive extended kalman filter for the localization of mobile robots,” IEEE Transactions on Robotics and Automation, vol. 15, no. 2, pp. 219–229, 1999.

[33] F. Dellaert, D. Fox, W. Burgard, and S. Thrun, “Monte carlo localization for mobile robots,” Proceedings 1999 IEEE International Conference on Robotics and Automation, vol. 2, pp. 1322–1328, Michigan, USA, May 10 - 15, 1999.
[34] D. Fox, “Kld-sampling: Adaptive particle filters and mobile robot localization,” Advances in Neural Information Processing Systems (NIPS), vol. 14, no. 1, pp. 26–32, 2001.
[35] G. Grisetti, C. Stachniss, and W. Burgard, “Improved techniques for grid mapping with rao-blackwellized particle filters,” IEEE transactions on Robotics, vol. 23, no. 1, pp. 34–46, 2007.
[36] W. Hess, D. Kohler, H. Rapp, and D. Andor, “Real-time loop closure in 2d lidar slam,” 2016 IEEE International Conference on Robotics and Automation (ICRA), pp. 1271–1278, Stockholm, Sweden, May 16 - 21, 2016.
[37] N. H. Amer, H. Zamzuri, K. Hudha, and Z. A. Kadir, “Modelling and control strategies in path tracking control for autonomous ground vehicles: a review of state of the art and challenges,” Journal of intelligent & robotic systems, vol. 86, no. 2, pp. 225–254, 2017.
[38] O. Amidi and C. E. Thorpe, “Integrated mobile robot control,” Mobile Robots V, vol. 1388, pp. 504–523, 1991.
[39] S. F. Campbell, “Steering control of an autonomous ground vehicle with application to the darpa urban challenge,” Ph.D. dissertation, Massachusetts Institute of Technology, 2007.
[40] O. Bittel and M. Blaich, “Mobile robot localization using beacons and the kalman filter technique for the eurobot competition,” Research and Education in Robotics - EUROBOT 2011, pp. 55–67, 2011.
[41] A. Halvorsen, “Eurobot ntnu 2012: Treasure island,” Master’s thesis, Institutt for teknisk kybernetikk, 2012.
[42] L. C. BURKODI, T. G. KISS, P. KARKUS, D. VARGA, and V. Istvän,
“Team organization and participation in the eurobot 2012 contest,”
IFAC Proceedings Volumes, vol. 46, no. 17, pp. 180–185, 2013.
[43] G. Granosik, K. Andrzejczak, M. Kujawinski, R. Bonecki,
L. Chlebowicz, B. Krysztofiak, K. Mirecki, and M. Gawryszewski, “Using robot operating system for autonomous control of robots in

eurobot, erc and robotour competitions,” Acta Polytechnica CTU Proceedings, vol. 6, pp. 11–17, 2016.

[44] M. Quigley, K. Conley, B. Gerkey, J. Faust, T. Foote, J. Leibs,
R. Wheeler, A. Y. Ng et al., “Ros: an open-source robot operating system,” ICRA workshop on open source software, vol. 3, p. 5, Kobe, Japan, May 12 - 13, 17, 2009.

[45] R. Siegwart, I. R. Nourbakhsh, and D. Scaramuzza, Introduction to autonomous mobile robots. MIT press, 2011.

[46] Eurobot. (2022) International robotics contest. [Online]. Available: https://www.eurobot.org/, accessed: 2022-07-14.

[47] Eurobot. (2022) Age of bots –2022. [Online]. Available: https:
//www.eurobot.org/eurobot-contest/eurobot-2022/, accessed: 2022-
07-14.

[48] B. Gerkey, R. T. Vaughan, A. Howard et al., “The player/stage project: Tools for multi-robot and distributed sensor systems,” Proceedings of the 11th international conference on advanced robotics, vol. 1, pp. 317–323, 2003.

[49] J. Jiang and K. Wu, “Cooperative pathfinding based on memory- efficient multi-agent rrt,” IEEE Access, vol. 8, pp. 168 743–168 750,
2020.

[50] F. Zafari, A. Gkelias, and K. K. Leung, “A survey of indoor localization systems and technologies,” IEEE Communications Surveys & Tutorials, vol. 21, no. 3, pp. 2568–2599, 2019.

[51] M. Przybyła, “Detection and tracking of 2d geometric obstacles from lrf data,” 2017 11th International Workshop on Robot Motion and Control (RoMoCo), pp. 135–141, Wąsowo, Poland, July 3 - 5, 2017.

[52] S. Thrun, “Probabilistic robotics,” Communications of the ACM, vol. 45, no. 3, pp. 52–57, 2002.

[53] E. Marder-Eppstein, E. Berger, T. Foote, B. Gerkey, and K. Konolige, “The office marathon: Robust navigation in an indoor office environment,” 2010 IEEE international conference on robotics and automation, pp. 300–307, Alaska, USA, May 3 - 8, 2010.

[54] D. Fox, W. Burgard, and S. Thrun, “The dynamic window approach to collision avoidance,” IEEE Robotics & Automation Magazine, vol. 4, no. 1, pp. 23–33, 1997.
[55] S. Quinlan and O. Khatib, “Elastic bands: Connecting path planning and control,” [1993] Proceedings IEEE International Conference on Robotics and Automation, pp. 802–807, Atlanta, USA, May 2 - 6, 1993.
[56] C. Rösmann, F. Hoffmann, and T. Bertram, “Timed-elastic-bands for time-optimal point-to-point nonlinear model predictive control,” 2015 european control conference (ECC), pp. 3352–3357, Linz, Austria, July 15 - 17, 2015.
[57] O. Robotics. (2020) move_base. [Online]. Available: http://wiki.ros. org/move_base, accessed: 2022-07-22.