指導教授：邱俊賢 學 生：蔡政育

1. Path Planning Based on Ant Colony Algorithm and Distributed Local Navigation for Multi-Robot Systems Proceedings of the 2006 IEEE International Conference on Mechatronics and Automation June 25 - 28, 2006, Luoyang, China Shirong Liu and Linbo Mao and Jinshou Yu 指導教授：邱俊賢 學　　生：蔡政育

2. Outline • Abstract • Introduction • PROBLEM STATEMENT • PATH PLANNING BASED ON IMPROVED ANT COLONY ALGORITHM • DISTRIBUTED NAVIGATION WITH COLLISION AVOIDANCE • SIMULATION STUDIES • CONCLUSIONS • REFERENCES

3. Abstract • This paper presents a decoupled path planning based on ant colony algorithm and distributed navigation with collision avoidance for multi-robot systems. 本篇文章提出一種基於螞蟻演算法的路徑規畫和多機器人系統中，防止碰撞的分佈式導航。 • An improved ant colony algorithm is proposed to plan a reasonable collision-free path for each mobile robot of multi-robot system in the decoupled path planning scheme in complicated static environment. 一種改良式的螞蟻演算法提出一個在複雜的靜態環境中，多機器人系統彼此間防撞的路徑規畫方法。

4. When an ant explores a dead-corner in path searching, a dead-corner table is established and a penalty function is used for the trail intensity updated. 當一隻螞蟻搜尋到一個死角，會建立一個表格，以及損失函數，用於費洛蒙濃度的更新。 • A behavior strategy on “first come and first service” is adopted to solve the conflict between moving robots. 行為策略採用first come and first service，先到先服務的方式來解決機器人之間的碰撞問題。

5. Simulation results show that the proposed method can effectively improve the performance of the planned path, and the individual robots with collision-free can achieve to reach their goal locations. 模擬結果表示，該方法有效改善路徑規畫方法。機器人能在無碰撞的情形之下到達目標位置。

6. Introduction • Multirobot path planning with collision avoidance is devoted to find an optimal or reasonable path from an initial location to a goal location so that the mobile robot is able to move safely through the workspace with collision avoidance. 多機器人路徑規畫與避撞致力於尋找一個從起始位置到目標位置的最佳路徑，而使機器人能夠安全的通過工作區域，且無碰撞發生。

7. A novel decoupled path planning for multi-robot systems and distributed navigation with collision avoidance is presented in the paper. 本文在多機器人系統中提出一種新型的路徑規畫及避撞分佈式導航。 • In the decoupled path planning phase, we adopted an improved ant colony algorithm (IACA) to plan the motion path for each robot. 在分佈式路徑規畫部份，我們採用一種改善的ACA來規劃每個機器人的運動路徑。

8. Aiming at avoiding the possible collision between robots during movement, a behavior strategy on “first come and first service” and a priority strategy are employed. 在運動過程中，針對可能碰撞的機器人提出先來先服務以及優先權的設定。 • Simulation results show that the proposed method can effectively improve the performance of the planned path, and the individual robots with collision-free can achieve to reach their goal locations. 模擬結果表示，該方法有效改善路徑規畫方法。機器人能在無碰撞的情形之下到達目標位置。

9. PROBLEM STATEMENT • The workspace of mobile robot in 2D environment can be represented by grids with the same size. There are a set of static obstacles with different size and shape in the workspace. The premises and assumptions of our study are stated as follows: 工作區域中的機器人以2D環境，相同的網格大小為例，在工作區域內有一組靜態障礙物，其大小以及形狀皆不相同，我們的研究以下列的假設為前提。

10. 1. The mobile robot is assumed to be point-size and occupies only one grid at a time. 假設機器人為一個點的大小且一次只佔用一個網格。 • 2. Each robot has an assigned goal, and knows its start and goal positions. 每個機器人有一個分配的目標，並且知道它的開始和目標位置。

11. 3. Each robot is in equal level without any priority in path planning. 每個機器人都是平等的，沒有任何優先路徑規劃。 • 4. Collision may be caused because of the cross position of planned paths, not considering the collision generated by too nearer distance between robots. 因為交叉路徑規畫可能發生碰撞，不考慮因為機器人之間距離太近造成的碰撞。

12. 5. Each robot moves in an even speed, and its status can be switched instantaneously between the moving with a fixed speed and halting. 每個機器人移動的速度相等，它的狀態可以在定速與停止之間瞬間切換。 • 6. The mobile robot is equipped with range sensors, target detectors, and communication sets. 機器人配備了一系列的傳感器，包含目標探測器和通訊工具。

13. 7. The robot may has eight moveable directions (North, East, South, West, NE, NW, SE, SW), and the range detected by the sensors cover the area with eight grids, as shown in Fig.1. 機器人有 8 個可移動的方向（北，東，南，西，東北，西北，東南，西南），範圍檢測使用感測器，包含 8 個網格，如圖1。

14. The decoupled approach first computes separate paths for the individual robots and then the strategy of local navigation resolves possible conflicts of paths. The decoupled planning scheme for the individual robots is shown in Fig. 2. 該方法首先計算每個機器人個體的路徑，然後在局部導航策略中解決可能碰撞的路徑。如圖2 。

15. The robot use reactive strategy to avoid local collision in motion. The distributed local navigation scheme of the mobile robot with coordination mechanism is given in Fig. 3. The strategy of “first come and first service” and prioritized rules are employed in coordinating the motion of robots so that the robots are able to reach their goals safely. 機器人使用應對策略以避免局部碰撞，分佈式導航方法與協調機制，如圖3 。“first come and first service”，先到先服務策略和優先權規則協調機器人的運動，使機器人能夠安全的到達自己的目標。

16. PLANNING BASED ON IMPROVED ANT COLONY ALGORITHM • To find collision-free path for each robot from its initiallocation to its goal location in multi-robot system, there have been various methods, such as genetic algorithm, neural network, and so forth. We have developed an improved ant colony algorithm to find optimal or reasonable paths for mobile robots. 在多機器人系統中，要找到避免碰撞的路徑規畫有各種方法，例如，基因演算法，類神經網路等等。我們已經發現一種改良式的螞蟻演算法可以找到最佳路徑。

17. 1) Improvement in Selective Strategy: According to the basicselective strategy, ants usually choose the edge on which thepheromone is stronger, and thus the search of ants will tend toseveral local optimal paths so that lose the diversity of thesolution. 在選擇策略方面的改良，根據基本的選擇策略，螞蟻通常選擇費洛蒙濃度較高的地方。因此，螞蟻將侷限於幾個 局部最佳路徑，進而失去了其他可能的解。

18. In order to overcome this difficulty in the searching process, we propose that create randomly n trial pointsbetween the start and goal, meanwhile n routes planned byant colony algorithm go through these points. In this way, antscan choose more different paths during the initial stage, so asto obtain diversified solutions. 為了克服此問題，在搜尋過程中，我們建議在起點以及終點之間隨機設立 n 個試驗點，同時，ACA 將經過這些點，產生 n 條路徑，這樣一來，螞蟻在初始階段可以選擇更多不同的路徑，從而獲得不同的解決方法。

19. Ｗeassume that (Sxi,Syi) and (Gxi,Gyi), i=1,‥‥,m ,represent theinitial location and the goal location respectively. As anexample of Robot 1, n points are created randomly in theregion W that is a quadrilateral area and four points of thearea are denoted as (Sx1,Sy1), (Sx1,Gy1), (Gx1,Sy1), (Gx1,Gy1). 我們假設(Sxi,Syi)及(Gxi,Gyi)分別代表初始位置和目標位置。例如機器人 1，在四邊形的 W 區域隨機設立 n 個點，且四個點表示為(Sx1,Sy1), (Sx1,Gy1), (Gx1,Sy1), (Gx1,Gy1)。

20. Using the basic ant colony algorithm n paths through n random points in the region W can be obtained. Obviously, the shortest path from the start to the destination can be easily found among these paths, and the shortest path is chosen to update the global pheromone. In this way, the diversity of solution is increased during the initial stage, and the tendency of the solution falling in local optimum is ecreased. 使用基本的 ACA ，在 W 區域中， n 條路徑通過 n 個隨機點，很明顯的，從開始點到目標點的最短路徑很容易被找到，最短路徑的選擇靠全域的費洛蒙，此種方法多樣性的解增加了，而且傾向局部最佳解的情況也減少了。

21. 2) Solution for “Deadlock”: “Deadlock” problem inrobotics means that the robot is probable not to go forwardand loses moveable possibility. Similarly it is probable toappear the status of “deadlock” in robot path planning, calledas the route deadlock. The problem of route deadlock also occurs in the path planning with the basic ant colonyalgorithm. Deadlock 問題是指機器人可能無法前進，失去了移動的可能性。在路徑規畫也可能出現此問題，稱為路徑 Deadlock。也會發生在基於 ACA 的路徑規劃。

22. The definition of “deadlock” in this paper is: Antsenter into the location which is surrounded by obstaclesduring searching a path, thus losing the capability to goforward. We put forward establishing a dead-corner table andintroducing a penalty function to solve this problem. Deadlock 在本文定義為：螞蟻在搜尋過程中進入一個周圍皆有障礙物的位置，而失去了前進的能力。我們提出一個死角表，並採用損失函數來解決此問題。

23. The definition of “deadlock” in this paper is: Antsenter into the location which is surrounded by obstaclesduring searching a path, thus losing the capability to goforward. We put forward establishing a dead-corner table andintroducing a penalty function to solve this problem. Thedead-corner is such a location in which ants come into thestatus of deadlock, as shown in Fig.4. If an ant comes intodead-corner in path searching process, the location of deadcorneris listed in dead-corner table and the ant returns to theformer location, and then searches the next location newly. 死角為螞蟻進入 deadlock 狀態的位置。如圖4。如果一隻螞蟻在搜尋過程中進入死角，該位置將被列入死角表中，且螞蟻將返回原來的位置，接著搜尋下一個新的位置。

25. The pheromone of edges around the dead-corner is increasing so that ants tend tochoose these edges in next iterative search. It is likely toincrease the time of finding optimal path, and even not findthe optimal path. 費洛蒙附近出現死角，使螞蟻傾向選擇這些地方。很可能花更多時間搜尋，甚至找不到最佳路徑。

26. We take use of a penalty function to prevent this situation occur. If an ant encounters a dead-corner, we use a penalty function instead of local updating rule. The penalty function is defined below τ(i,j)=λ． τ(i,j)0< λ <1 我們採用損失函數來防止這種情況。如果螞蟻遇到死角，我們使用損失函數而非使用局部更新規則。 該函數定義如上。

27. The penalty function assures that pheromone of the edgesaround dead-corner decreases, resulting in that the ant doesnot choose those edges in next iterative searching process.Thus, the situation of route deadlock is avoided, and theefficiency of searching for the optimal path is improvedsimultaneously. 損失函數確保費洛蒙周圍圍繞的死角減少，使螞蟻不選擇那些地方進行搜尋。因此，此路徑 deadlock是可以避免的，同時，有效率的尋找最佳路徑。

28. DISTRIBUTED NAVIGATION WITH COLLISION AVOIDANCE • Each robot has a planned path from its start to itsdestination. Then the robot will go to the goal location fromthe fixed initial location avoiding the obstacles and the otherrobots. There are various methods for dealing with conflictingbetween the moving robots, such as selecting a robot to stoprandomly, traffic rules,prioritized planning,and so on. In order to avoid collision, we use thestrategy of “first come and first service” and prioritized rulesto coordinate the motion of robots. 每個機器人有一個從開始到目的地的規劃路徑。然後機器人將從固定的初始位置前往目標位置，且避開障礙物和其他機器人。有多種方法處理機器人之間的碰撞問題，比如選擇一個機器人隨機停止，交通規則，優先規劃等等。為了避免相撞，我們使用“先來先服務”的策略及優先權規則，來協調機器人間的運動。

29. SIMULATION STUDIES • Let the workspace be divided by square grid withwide of one meter. Si and Gi represent the start location andthe goal location of robot i , respectively. Consider the pathplanning and navigation with collision avoidance of tworobots in the same workspace. 將工作區域切割成寬 1 米的正方形網格，Si 和 Gi 分別代表機器人 i 的起始位置和目標位置。考慮路徑規畫和導航與避障，將兩機器人置於同一工作區域。 • The planned paths for individual robots in asimple workspace and a complex workspace are given in Fig.5and Fig.6, respectively. 機器人的路徑規劃分成簡單的工作區域，如圖 5 。以及複雜的工作區域，如圖 6 。

32. CONCLUSIONS • The decoupled approach can be effectively applied to aclass of motion planning problem that each robot has itsindependent goal in multi-robot systems. The improved antcolony algorithm is able to plan an optimal or reasonable pathin static environment with different obstacles. The collisionavoidance strategy with “first come and first service” and thepriorities make the robots navigate safely. Extensivesimulations have shown that the proposed approach is verysimple and efficient. 該方法可以有效地應用於一流的運動規劃問題，在多機器人系統，每個機器人都有其獨立的目標。改進的螞蟻演算法能在靜態環境規劃一個最佳路徑。先來先服務和優先權設定的避撞策略讓機器人導航安全。模擬表示，該方法非常簡單而有效。

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36. Thank You !!