多群組系統中利用位能場之分散式隊型控制

Abstract

近年來，多群組機器人系統已逐漸被廣泛研究。由於機器人間之合作與協調，機器人團隊可完成更困難及更複雜的任務。然而，在多數任務中，如果機器人團隊能夠形成特定隊型，將能夠更有效率的完成任務。因此，多群組機器人系統之隊型控制是個很重要之研究主題。透過各個機器人的軌跡規劃，將可以達到機器人團隊之隊型控制。此外在真實環境中可能存在有障礙物，因此機器人之避障行為也是軌跡規劃之重要課題。 在過去，利用位能場之方法已被廣泛運用於多群組機器人系統之軌跡規劃。由位能場得來之人造力被用來控制機器人之運動。過去研究中已有許多種人造力被提出，其中之一為倒次方形式。然而，過去研究中，皆是直覺地設計此倒次方人造力之係數。此外，流線函數是另一種運用於機器人避障行為之位能場方法。 本論文中研究多群組機器人系統隊型控制之穩定度分析。首先，參考圖形理論之方法定義多群組機器人系統之隊型。接著定義論文中將會使用之位能場方法及倒次方人造力。本論文使Lyapunov方法及Linearization方法分析一個由三個機器人使用倒次方人造力組成之多機器人系統。經由分析可得此多機器人系統隊型穩定度與倒次方人造力係數之關係。此分析結果可作為多機器人系統設計之準則。此外，本論文結合倒次方人造力與流線函數方法應用在此多機器人系統以達到隊型控制與避障之目地。最後，以模擬方式呈現此論文之分析結果。

The research topics of multi-robot systems have attracted much attention in recent years. Due to the ability of cooperation of robots, multiple robots can perform more difficult and complex tasks than one robot can perform. However, formation control problem is an important topic because multiple robots can perform tasks efficiently if the robots are in formation. Some specific formations can be formed by the multiple robots by planning trajectories of all robots. Moreover, when there are some obstacles in the real environment, the trajectories of the robots must be planned to navigate all robots for avoiding the obstacles and forming specific formations in the real environment. In the trajectory planning problems of multi-robot systems, potential field methods are used widely in the past. Artificial forces related to the potential field are used as the controllers of the robots. There are many kinds of the artificial forces proposed previously. One is the inverse power force. However, the coefficients of the inverse power force are designed intuitively in previous research. Moreover, there is another potential field method which is stream function method used to navigate a robot to avoid the obstacles in the environment. In this thesis, the trajectory planning problem of multi-robot systems is focused. The formations of multi-robot systems are defined firstly for the formation control problems. Secondly, the potential field methods and the artificial inverse power forces used in this thesis are defined. Thirdly, a case of three-robot system in is analyzed mathematically. There are two analysis methods used in thesis, that is, Lyapunov’s method and Linearization method. The convergence of these three robots is analyzed by Lyapunov’s method. The relationship between the stability of the formations which formed by these there robots and the coefficients of the artificial inverse power force are analyzed by the linearization method. The analysis results act as a design criterion when using inverse power forces in multi-robot systems. Moreover, the stream function method is combined with the artificial power forces to navigate these three robots to avoid obstacles and move to goal. Furthermore, some simulations demonstrate the analysis results in this thesis.