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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
Outline
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Abstract
Introduction
PROBLEM STATEMENT
PATH PLANNING BASED ON IMPROVED ANT
COLONY ALGORITHM
DISTRIBUTED NAVIGATION WITH
COLLISION AVOIDANCE
SIMULATION STUDIES
CONCLUSIONS
REFERENCES
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。
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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。
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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。
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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。
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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。
Introduction
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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。
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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。
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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。
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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。
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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。
PROBLEM STATEMENT
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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。
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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。
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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。
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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。
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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。
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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。
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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。
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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。
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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 。
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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。
PLANNING BASED ON IMPROVED
ANT COLONY ALGORITHM
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To find collision-free path for each robot from its initial
location 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。
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1) Improvement in Selective Strategy:
According to the basic selective strategy, ants usually
choose the edge on which the pheromone is stronger, and
thus the search of ants will tend to several local optimal
paths so that lose the diversity of the solution.
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。
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In order to overcome this difficulty in the searching
process, we propose that create randomly n trial points
between the start and goal, meanwhile n routes planned
by ant colony algorithm go through these points. In this
way, ants can choose more different paths during the
initial stage, so as to 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。
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Ｗe assume that (Sxi,Syi) and (Gxi,Gyi), i=1,‥‥,m ,
represent the initial location and the goal location
respectively. As an example of Robot 1, n points are
created randomly in the region W that is a quadrilateral
area and four points of the area 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)。
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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。
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2) Solution for “Deadlock”:
“Deadlock” problem in robotics means that the robot is
probable not to go forward and loses moveable
possibility. Similarly it is probable to appear the status
of “deadlock” in robot path planning, called as the route
deadlock. The problem of route deadlock also
occurs in the path planning with the basic ant colony
algorithm.
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。
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The definition of “deadlock” in this paper is: Ants
enter into the location which is surrounded by obstacles
during searching a path, thus losing the capability to go
forward. We put forward establishing a dead-corner
table and introducing 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。

The definition of “deadlock” in this paper is: Ants enter into
the location which is surrounded by obstacles during
searching a path, thus losing the capability to go forward. We
put forward establishing a dead-corner table and introducing
a penalty function to solve this problem. The dead-corner is
such a location in which ants come into the status of
deadlock, as shown in Fig.4. If an ant comes into dead-corner
in path searching process, the location of deadcorner is listed
in dead-corner table and the ant returns to the former
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。
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The pheromone of edges around the dead-corner is
increasing so that ants tend to choose these edges in next
iterative search. It is likely to increase the time of finding
optimal path, and even not find the 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。
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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。
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The penalty function assures that pheromone of the
edges around dead-corner decreases, resulting in that
the ant does not choose those edges in next iterative
searching process. Thus, the situation of route deadlock
is avoided, and the efficiency of searching for the
optimal path is improved simultaneously.
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。
DISTRIBUTED NAVIGATION
WITH COLLISION AVOIDANCE
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Each robot has a planned path from its start to its destination.
Then the robot will go to the goal location from the fixed
initial location avoiding the obstacles and the other robots.
There are various methods for dealing with conflicting
between the moving robots, such as selecting a robot to stop
randomly, traffic rules, prioritized planning, and so on. In
order to avoid collision, we use the strategy of “first come and
first service” and prioritized rules to 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。
SIMULATION STUDIES

Let the workspace be divided by square grid with wide of one
meter. Si and Gi represent the start location and the goal
location of robot i , respectively. Consider the path planning
and navigation with collision avoidance of two robots 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。
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The planned paths for individual robots in a simple
workspace and a complex workspace are given in Fig.5 and
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 。
CONCLUSIONS
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The decoupled approach can be effectively applied to a class
of motion planning problem that each robot has its
independent goal in multi-robot systems. The improved ant
colony algorithm is able to plan an optimal or reasonable path
in static environment with different obstacles. The collision
avoidance strategy with “first come and first service” and the
priorities make the robots navigate safely. Extensive
simulations have shown that the proposed approach is very
simple 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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Thank You
!!