由於傳統覆蓋控制方法之缺陷以及環境估測、多移動機器人系統、致動器網路與彈性控制間整合相關研究的缺乏，本論文基於最大似然函數估測與高斯混合模型去建構出環境的重要性分佈，配合最佳化方法中被廣泛應用的梯度下降法與Lyapunov穩定性定理，提出整合無線感測器網路與致動器之多移動機器人架構及其環境覆蓋與調節系統，並且加入彈性控制讓多機器人系統能夠避免系統中發生機器失效而導致整體系統無法完成環境覆蓋與調節任務。
此架構使用無線感測器來蒐集環境資訊，根據此感測資訊來建構估測密度函數，並以期望最大演算法使實際密度函數與估測密度函數之相似性達到最大化。於獲得環境估測模型後，利用覆蓋控制的方法定義出使多機器人系統達到最佳分布的最佳化問題，同時考慮進環境中的障礙物資訊，以梯度下降法設計控制器，找出機器人移動時最有效率的移動軌跡。利用配置在移動機器人上的致動器，並設計其環境調節控制器之控制輸出，使致動器對環境重要分佈做出影響，並將環境調節至目標分佈。
考慮多機器人系統在執行環境任務的過程中會發生機器人失效的情況，進而導致整體系統無法成功完成環境覆蓋與調節任務，因此將多機器人以責任權重來區分其能力，基於Lyapunov穩定性理論來分析與調整各機器人的責任權重，使失效機器人之責任權重能夠下降，且其他正常機器人能成功將環境任務完成，並定義一指標說明原系統有無加入彈性控制之差異性。最後，本論文以理論分析、數值模擬以及實驗架構，驗證其彈性控制於環境覆蓋與調節任務之穩定性與效能。

This thesis proposes a methodology that combines Wireless Sensor and Actuator Networks (WSANs) with multi-robot control system and enables environmental coverage and regulation control with resilience for existing faulty robots at the control system. Wireless sensor networks are used to collect sensory information to estimate the real environment and the environment model is constructed by Gaussian mixture model and Expectation Maximization algorithm. Subsequently, utilize the gradient method coverage controller to manage mobile robots to cover the higher important region. Then, based on Lyapunov theorem, design a regulating actuator controller to regulate the region to desire distribution. Meanwhile, consider there exists faulty robot in the control system that make the environment not regulated, so propose a resilient control strategy to mitigate the responsibility of faulty robot so that the remaining robots can perform the regulating task. Theoretical analysis, numerical simulations and experiment results are given to demonstrate the effect of the control strategy.

[1] Jennifer Yick, Biswanath Mukherjee, and Dipak Ghosal. Wireless sensor network survey. Computer Networks, 52(12):2292-2330, 2008.
[2] Joseph M Kahn, Randy H Katz, and Kristofer SJ Pister. Next century challenges: mobile networking for "smart dust". In Proceedings of the 5th annual ACM/IEEE International Conference on Mobile Computing and Networking, pages 271-278, 1999.
[3] Xianghui Cao, Jiming Chen, Yan Zhang, and Youxian Sun. Development of an integrated wireless sensor network micro-environmental monitoring system. ISA Transactions, 47(3):247-255, 2008.
[4] Geo rey Werner-Allen, Konrad Lorincz, Mario Ruiz, Omar Marcillo, Je ff Johnson, Jonathan Lees, and Matt Welsh. Deploying a wireless sensor network on an active volcano. IEEE Internet Computing, 10(2):18-25, 2006.
[5] Ian F Akyildiz and Ismail H Kasimoglu. Wireless sensor and actor networks: research challenges. Ad Hoc Networks, 2(4):351-367, 2004.
[6] Tamio Arai, Enrico Pagello, Lynne E Parker, et al. Advances in multi-robot systems. IEEE Transactions on Robotics and Automation, 18(5):655-661, 2002.
[7] Clarence W de Silva. Some issues and applications of multi-robot cooperation. In 2016 IEEE 20th International Conference on Computer Supported Cooperative Work in Design (CSCWD), pages 2-2. IEEE, 2016.
[8] Xu Li, Inria Lille, Rafael Falcon, Amiya Nayak, and Ivan Stojmenovic. Servicing wireless sensor networks by mobile robots. IEEE Communications Magazine, 50(7):147-154, 2012.
[9] Wolfram Burgard, Mark Moors, Cyrill Stachniss, and Frank E Schneider. Coordinated multi-robot exploration. IEEE Transactions on Robotics, 21(3):376-386, 2005.
[10] Nikhil Chopra, Dusan M Stipanovic, and Mark W Spong. On synchronization and collision avoidance for mechanical systems. In 2008 American Control Conference, pages 3713-3718. IEEE, 2008.
[11] J Cortes, S Martinez, T Karatas, and F Bullo. Coverage control for mobile sensing networks. In Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No. 02CH37292), volume 2, pages 1327-1332. IEEE, 2002.
[12] T. Hatanaka, T. Ibuki, A. Gusrialdi, and M. Fujita. Coverage control for camera sensor networks: Its implementation and experimental veri cation. In Proc. of the 17th Mediterranean Conference on Control and Automa-
tion(MED), pages 446-451, June 2009.
[13] M. Schwager, D. Rus, and J.-J. Slotine. Decentralized, adaptive coverage control for networked robots. The International Journal of Robotics Research, 28(3):357-375, 2009.
[14] Jorge Cort es. Coverage optimization and spatial load balancing by robotic sensor networks. IEEE Transactions on Automatic Control, 55(3):749-754, 2010.
[15] Kelsey Saulnier, David Saldana, Amanda Prorok, George J Pappas, and Vijay Kumar. Resilient
flocking for mobile robot teams. IEEE Robotics and Automation Letters, 2(2):1039-1046, 2017.
[16] Jacopo Panerati, Marco Minelli, Cinara Ghedini, Lucas Meyer, Marcel Kaufmann, Lorenzo Sabattini, and Giovanni Beltrame. Robust connectivity maintenance for fallible robots. Autonomous Robots, 43(3):769-787, 2019.
[17] Wente Zeng and Mo-Yuen Chow. Resilient distributed control in the presence of misbehaving agents in networked control systems. IEEE Transactions on Cybernetics, 44(11):2038-2049, 2014.
[18] P. Wu, J. Li, and T. Cheng. Distributed coverage control with dependent density functions. In 2018 IEEE Conference on Decision and Control (CDC), pages 1299-1304, Dec 2018.
[19] 林沐泰. 環境估測與調節之多移動機器人系統. Master's thesis, 國立成功大學, 2018.
[20] Stuart Lloyd. Least squares quantization in pcm. IEEE Transactions on Information Theory, 28(2):129-137, 1982.
[21] 林岑璋. 基於最大似然估計之直接學習覆蓋控制. Master's thesis, 國立成功大學, 2017.
[22] ROBOTIS. Speci cations of Turtlebot3. http://emanual.robotis.com/docs/en/platform/turtlebot3/specifications/#specifications.
[23] Mehmet Dogar, Ross A Knepper, Andrew Spielberg, Changhyun Choi, Henrik I Christensen, and Daniela Rus. Multi-scale assembly with robot teams. The International Journal of Robotics Research, 34(13):1645-1659, 2015.
[24] Bruno Siciliano and Oussama Khatib. Springer handbook of robotics. Springer, 2016.
[25] Tucker Balch and Ronald C Arkin. Behavior-based formation control for multirobot teams. IEEE Transactions on Robotics and Automation, 14(6):926-939, 1998.
[26] Reza Olfati-Saber. Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Transactions on Automatic Control, 51(3):401-420, 2006.
[27] Yen-Chen Liu and Nikhil Chopra. Synchronization of networked robotic systems on strongly connected graphs. In 49th IEEE Conference on Decision and Control (CDC), pages 3194-3199. IEEE, 2010.
[28] Takeshi Hatanaka, Yuji Igarashi, Masayuki Fujita, and Mark W Spong. Passivity-based pose synchronization in three dimensions. IEEE Transactions on Automatic Control, 57(2):360-375, 2011.
[29] Silvia Mastellone, Du san M Stipanovi c, Christopher R Graunke, Koji A Intlekofer, and Mark W Spong. Formation control and collision avoidance for multi-agent non-holonomic systems: Theory and experiments. The International Journal of Robotics Research, 27(1):107-126, 2008.
[30] Sung G Lee, Yancy Diaz-Mercado, and Magnus Egerstedt. Multirobot control using time-varying density functions. IEEE Transactions on Robotics, 31(2):489-493, 2015.
[31] James Bruce and Manuela M Veloso. Real-time randomized path planning for robot navigation. In Robot Soccer World Cup, pages 288-295. Springer, 2002.
[32] Michel Bruneau, Stephanie E Chang, Ronald T Eguchi, George C Lee, Thomas D O'Rourke, Andrei M Reinhorn, Masanobu Shinozuka, Kathleen Tierney, William A Wallace, and Detlof Von Winterfeldt. A framework to quantitatively assess and enhance the seismic resilience of communities. Earthquake Spectra, 19(4):733-752, 2003.
[33] Jorge Cortes, Sonia Martinez, Timur Karatas, and Francesco Bullo. Coverage control for mobile sensing networks. IEEE Transactions on Robotics and Automation, 20(2):243-255, 2004.
[34] Luciano CA Pimenta, Vijay Kumar, Renato C Mesquita, and Guilherme AS Pereira. Sensing and coverage for a network of heterogeneous robots. In 2008 47th IEEE Conference on Decision and Control, pages 3947-3952. IEEE, 2008.
[35] Andreas Breitenmoser, Mac Schwager, Jean-Claude Metzger, Roland Siegwart, and Daniela Rus. Voronoi coverage of non-convex environments with a group of networked robots. In 2010 IEEE International Conference on Robotics and Automation, pages 4982-4989. IEEE, 2010.
[36] Yiannis Stergiopoulos, Michalis Thanou, and Anthony Tzes. Distributed collaborative coverage-control schemes for non-convex domains. IEEE Transactions on Automatic Control, 60(9):2422-2427, 2015.
[37] Wei Li and Christos G Cassandras. Distributed cooperative coverage control of sensor networks. In Proceedings of the 44th IEEE Conference on Decision and Control, pages 2542-2547. IEEE, 2005.
[38] Islam I Hussein and Dusan M Stipanovic. E ective coverage control for mobile sensor networks with guaranteed collision avoidance. IEEE Transactions on Control Systems Technology, 15(4):642-657, 2007.
[39] Mac Schwager, Daniela Rus, and Jean-Jacques Slotine. Decentralized, adaptive coverage control for networked robots. The International Journal of Robotics Research, 28(3):357-375, 2009.
[40] Jaeyong Lee, Avinash D Dharne, and Suhada Jayasuriya. Potential field based hierarchical structure for mobile sensor network deployment. In 2007 American Control Conference, pages 5946-5951. IEEE, 2007.
[41] Farshid Abbasi, Afshin Mesbahi, and Javad Mohammadpour. Team-based coverage control of moving sensor networks. In 2016 American Control Conference (ACC), pages 5691-5696. IEEE, 2016.
[42] Alyssa Pierson and Mac Schwager. Controlling noncooperative herds with robotic herders. IEEE Transactions on Robotics, 34(2):517-525, 2017.
[43] Yuan Yuan, Huanhuan Yuan, Lei Guo, Hongjiu Yang, and Shanlin Sun. Resilient control of networked control system under dos attacks: A uni ed game approach. IEEE Transactions on Industrial Informatics, 12(5):1786-1794, 2016.
[44] Luis Guerrero-Bonilla, Amanda Prorok, and Vijay Kumar. Formations for resilient robot teams. IEEE Robotics and Automation Letters, 2(2):841-848, 2017.
[45] Hassan K. Khalil and Jessy W. Grizzle. Nonlinear systems, volume 3. Prentice hall New Jersey, 1996.
[46] Stephen Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge Univ. Press, Cambridge, U.K., 2003.
[47] Tsen-Chang Lin and Yen-Chen Liu. Direct learning coverage control based on expectation maximization in wireless sensor and robot network. In 2017 IEEE Conference on Control Technology and Applications (CCTA), pages 1784-1790. IEEE, 2017.
[48] Du san M Stipanovi c, Peter F Hokayem, Mark W Spong, and Dragoslav D Siljak. Cooperative avoidance control for multiagent systems. 2007.
[49] NOAA Satellite and Information Service. http://emanual.robotis.com/docs/en/platform/turtlebot3/specifications/#specifications.
[50] Optitrack. https://optitrack.com/.
[51] Ros Wiki. https://www.ros.org/.