中英文翻译

Fuzzy Logic Based Autonomous Skid Steering Vehicle Navigation

L.Doitsidis,K.P.Valavanis,N.C.Tsourveloudis

Technical University of Crete

Department of Production Engineering and Management

Chania,Crete,Greece GR-73100

{Idoitsidis ,kimonv,nikost}@dpem.tuc.gr

Abstract-A two-layer fuzzy logic controller has been designed for 2-D autonomous Navigation of a skid steering vehicle in an obstacle filled environment. The first layer of the Fuzzy controller provides a model for multiple sonar sensor input fusion and it is composed of four individual controllers, each calculating a collision possibility in front, back, left and right directions of movement. The second layer consists of the main controller that performs real-time collision avoidance while calculating the updated course to be applicability and implementation is demonstrated through experimental results and case studies performed o a real mobile robot.

Keywords - Skid steering, mobile robots, fuzzy navigation.

Ⅰ.INTRODUCTION

The exist several proposed solutions to the problem of autonomous mobile robot navigation in 2-D uncertain environments that are based on fuzzy logic[1],[2],evolutionary algorithms [3],as well as methods combining fuzzy logic with genetic algorithms[4] and fuzzy logic with electrostatic potential fields[5].

The paper is the outgrowth of recently published results [9],[10],but it studies 2-D environments navigation and collision avoidance of a skid steering vehicle. Skid steering vehicles are compact, light, require few parts to assemble and exhibit agility from point turning to line driving using only the motions, components, and swept volume needed for straight line driving.

Skid steering vehicle motion differs from explicit steering vehicle motion in the way the skid steering vehicle turns. The wheels rotation is limited around one axis and the back of steering wheel results in navigation determined by the speed change in either side of the skid steering vehicle. Same speed in either side results in a straight-line motion. Explicit steering vehicles turn differently since the wheels are moving around two axes. The geometric configuration of a skid steering vehicle in the X-Y plane is shown in Fig1，while a t is the heading angle, W is the robot width, θthe sense of rotation and S1, S2 are the speeds in the either side of the robot.

The derived and implemented planner a two-layer fuzzy logic based controller that provides purely” reactive behavior” of the vehicle moving in a 2-D obstacle filled environment, with inputs readings from a ring of 24 sonar sensors and angle errors, and outputs the updated rotational and translational velocities of the vehicle.

Ⅱ.DESIGN OF THE FUZZY LOGIC CONTROL SYSTEM

The order to the vehicle movement, a two-layer Madman-type controller has been designed and implemented. In the first layer, there are four fuzzy logic controllers repondible for obstacle detection and calculation of the collision possibleilities in the four main directions, front, back, left and right. The possibilities calculated in the first layer are the input to the second layer along with the angle error (the difference between the robot heading angle and the desired target angle), and the output is the updated vehicle’s translational and the rotational speed.

Fig. 1.Geometric configuration of the robot in the X-Y plane.

A .first layer of the fuzzy logic controller

The ATRV-mini is equipped with an array of 24 ultrasonic sensors that are vehicles as shown in Fig.2. The ultrasonic sensors that are used are manufactured by Polaroid.

After experiment with, and testing several methods concerning sonar sensor date grouping and management, it was first decided to follow the sensor grouping in pairs as proposed in [8](considering the ATRV –mini twelve sonar group A is=1,…..,12, have been enumerated as shown in Fig.2) and then divide the sun of the provided pair sensor data by two to determine the distance from the (potential) obstacle. However, this method gave unsatisfactory results due to the ATRV –minis specific sensor unreliability. Even in cases with obstacles present in the vicinity of the vehicle, the sensors were detecting a “free path”. To overcome this problem, a modified, simpler, sensor grouping and data management method was tested that return much better and accurate results: The sensors were again grouped in pairs according to Fig.2, but the minimum of the (potential) obstacle. Each A TRV –mini sonar returns from obstacles at a maximum distance of 4metres (experimentally verified as opposed to different value provided by the sonar sensors manufacturer

Fig.2. Grouping of the Sensors.

The form of each first layer individual fuzzy controller, including the obstacle detection module, is shown in Fig.3.Observing Fig.3, data from group sensors A1, A2, ….,A5(5 inputs) and group sensors A7, A8 , …,A11(5 inputs) serve as inputs to the individual controllers responsible for the calculation of the front and back collision possibilities, respectively. Data from group sensors A5, A6, A7 (3 inputs) serve as input to calculate the left and right possibilities, respectively. The individual fuzzy controllers utilize the same membership functions to calculate the collision possibilities. The linguistic values of the variable distance_from_obstance are defined to be three, near, meium_distance, away with membership functions as shown in Fig.4 reflecting the maximum distance of 4 meters a sonar returns accurate information about potential obstacles.

Fig.3.Obstacle detection module.

Fig.4.Input Variable Distance_ From _ Obstacle.

The first layer output is a collision possibility in each direction taking values from 0 to 1.The linguistic variables describing each direction output variable collision possibility (with empirically Derived for best performance) membership functions as shown In Fig.5.A part of the rules base for left collision is presented in TableⅠ.

An example of the rules used to extract front collision possibilities is: IF A1 is near AND A2 is near AND A3 is Near AND A4 is medium_distance AND A5is near THEN collision_possibility is high. Similar for the back collision possibility.For left (equivalently for right collision)possibilities the rule is of the form: If A5 is near And A6 is nearAnd A7 is near THEN collision_possibility is high.

Fig.5.Output Variable collision_possibility

TABLE Ⅰ

PART OF THE RULES BASE FOR LEFT COLLISION

B. Second layer of the fuzzy logic controller

The second layer fuzzy controller recives as inputs the four collision possibilities in the four directions and the angle error, and outputs the translational velocity, which is responsible for moving the vehicle backward or forward and the rotational speed, which is responsible for the vehicle rotation as shown in Fig.6.

The angle error represents the difference between the robot-heading angle and the desired angle the robot should have in order to reach its target. The angle error takes values ranging from-1800to 1800. The linguistic variables that represent the angle error are: Backwards_1, Hard_Left, Left, right, Hard_right, Backwards_2 with (empirically derived from tests) membership functions as shown in Fig.7.

The translational velocity (m/sec) , which is one of the outputs of the second layer controller, is described with the following linguistic variables: back_full, back, back_solw, stop, front_slow, front, frontfull, with membership functions as in Fig.8.

Fig 6.Block diagram of the 2nd layer of the fuzzy logic controller

Fig 7.Input Variable Angle Error.

Fig 8.Output Variable Translational_Velocity.

The rotational_speed (rad/sc) is described with the following linguistic variables: Right_full, right, no_ratation, left, let_full with membership functions as in Fig.9.

An example of the rules that control the vehicle is demonstrated: If front_collision is Not_Possible AND Back_Collision is Not_possible And Left_Collision is Not_possible And Right_Collision is Not_possible And Angle Error is Ahead THEN Translational_velocity is Front_Full AND Rotational_Velocity is No_Ratation.

Fig. 9. Output Variable Rotational_velocity.

Ⅲ. RUSULTS

The fuzzy logic controller has been designed and implemented using C++ in an ATRV-mini manufactured by Real World Interface(RWI). In all experiments the robot is considered to have reached its target when stopping inside a circle with radius of 30 cm. This assumption has been dictated because all calculations have been made relative to the center of the robot. So if the robot stops inside that circle it is assumed that it has reached its target.

Several scenarios in an indoor 2-D obstacle filled environment have been tested to study the robot behavior and the controller’s applicability.

The arrow in Fig.10, Fig.15, Fig.20 is showing the initial direction of the vehicle.

In test case 1 we examine the behavior of the vehicle in an environment with three obstacles. The test case 1 is presented in Fig.10. Fig.11 shows the translational velocity, while the rotational velocity is given in Fig.12.Fig.13 presents the front collision possibility. In Fig.14, the solid line indicates the left collision possibility while the doted the right collision possibility. The behavior of the vehicle is defined from the surrounding obstacles.

In the beginning the left collision possibility is high due to the obstacle in the left. The robot moves forwards and it’s steering right in order to avoid the obstacle. Then it steers left and moves towards its target.

In the second test case presented in Fig.15, a more complicated environment with three obstacles has been tested. Fig.16 shows the translational velocity, while the rotational velocity is given in Fig.17. Fig.18 presents the front collision possibility while in Fig.19 the solid line indicates the left collision possibility while the doted the right collision possibility. In Fig.15 we can see that the path in front of the robot is blocked. The robot uses only the rotational velocity in order to steer and avoid the obstacle. Then it moves in a curve towards its target.

The third test case considers an environment with many small obstacles. The path the vehicle is following is presented in Fig.20. Due to the obstacles that are around the vehicle, the vehicle is forced to make a small right turn an then it escapes from the closed area. Fig.21 shows the translational velocity, while the rotational velocity is given in Fig.22.Fig.23 presents the front collision possibility while in Fig.24 the solid line indicates the left collision possibility while the

doted the right collision possibility.

The behavior of the vehicle in each case can verified by observing the relative figures concerning the collision possibility in each direction.

Fig. 10.Test Case 1. Environment with three obstacles and remote target point.

Fig.11. Translational Velocity in Test Case Fig. 14. Left and right Collision Possibilities in Test Case 1.

Fig.12. Rotational Velocity in Test Case 1. Fig. 15. Test Case 2. Environment with three obstacles.

Fig.13. Front Collision Possibility in Test Case 1. Fig.16. Translational Velocity in Test Case 2.

Fig.17.Rotational Velocity in Test Case 2. Fig.20. Test Case . Environment with many small obstacles.

Fig.18. Front Collision Possibility in Test Case 2. Fig.16. Translational Velocity in Test Case 3.

Fig.19. Left and right Collision Possibilities in Test Case 2 Fig.22.Rotational Velocity in Test Case 3.

Fig.23. Front Collision Possibility in Test Case 3.

Fig.24. Left and right Collision Possibilities in Test Case 3

Ⅳ.DISCUSSION AND CONCLUSIONS

We have presented a navigation system for a skid steering vehicle with the use of a two-layer fuzzy logic controller. The first layer of the fuzzy logic controller is composed of four fuzzy logic controllers. The rule base of the controllers responsible for front and back collision contains 60 rules and the rule base of the controllers responsible for front and back collision contains 57 rules. The rule base of the second layer fuzzy logic controller responsible for real-time navigation and collision avoidance contains 238 rules.

The fuzzy logic controller has performed satisfactorily. The results show that the vehicle has the ability to move in complicated environments. The controller, which is proposed in this paper, is based in the controller proposed in [9] but it is implemented in a skid steering vehicle.

Future directions of the research include the testing of dynamic environments, and the use of other sources of information.. The goal is to create an autonomous vehicle that will use for navigation and the collision avoidance combined information from visual inputs, sonars and outdoors GPS data that will guide the vehicle in remote target points.

中译文

模糊控制理论在自动引导车智能导航中的应用

L. Doitsidis, K. P. Valavanis, N. C. Tsourveloudis

（克利特科技大学生产过程和管理工程系，克利特岛，希腊，希腊GR-73100，

电子邮箱：{ldoitsidis, kimonv, nikost}@dpem .tuc .gr）

摘要：本文设计了一种双层的基于模糊控制理论的控制器，用来在一个充满障碍物的环境下为自动引导车提供自主领航。控制器的第一层建立了一个复合的声纳传感器的输入端模型，它是由四个独立的控制器组成，这四个控制器分别用来计算自动引导车向前、后、左、右四个方向移动时碰撞可能性。第二层是由一个主控制器构成，它能计算自动引导车的行驶路线，因此能执行相应的程序以避免碰撞。通过对一个移动机器人进行研究证明了这个双层控制器的适用性。

关键词：自动引导，移动机器人，智能导航

1．引言

自主移动的机器人在2维不确定环境下的导航的问题，现存有很多方法，这些建议有的是以模糊控制理论的算法为基础的，还有的是把把模糊控制理论和调优算法结合起来的，以及把模糊控制理论和静电学领域结合起来的方法。

这篇文章是结合最近的一些研究成果而提出的。本文主要研究自动引导车的2维环境下的导航问题。自动引导车是坚实而轻巧的，只要求很少的装配部件，并且它可以很迅速的从点运动转变到线运动时, 本文导论的就是自动引导车的直线驾驶问题[6].

自动引导车和明确指点车的运动的不同在于自动引导车的转弯方式. 轮子的转动被限于绕一条轴, 方向盘的缺陷导致导航由每边的速度变化决定。只要任一方向有相同速度就将导致自动引导车沿直线运动。而明确指点车的轮子绕着两条轴转动。自动引导车在X-Y 平面里的几何结构如图1所示,在这张图里,α表示的是航向角度,w表示的是机器人的宽度,θ自转角和S1、S2时该车在每个方向的速度。.

2.模糊逻辑控制系统的设计

为了控制车的移动，一个双层的Mamdani型的控制器已经设计出来并完成。在第一层，四个模糊控制器负责对障碍物的探测和对前后左右四个方向的碰撞可能性进行计算。这四个控制器接收来自声纳传感器的数据，同时输出前后左右四个方向的碰撞的可能性。这些可能性在第一层中计算出来并和角度误差一起被输入到第二层中，输出量是车的最新的平移和旋转速度。

图1. 自动引导车在X-Y平面上的模型

A.模糊逻辑控制器的第一层

在自动引导车周围装有24个超声波传感器，如图2所示。这里所用到的这些超声波传感器由Polaroid制造。

在测试一些关于声纳传感器数据编组和管理之后，最初决定按照文献[8]的方法对传感器编组(把小测距系统中的十二台生波探侧器的传感器编组为Ai, i=1,4a.., 12,如图2)，然后再把来自两组传感器的一对数据分开来讨论，可以得到潜在障碍物的距离。然而，由于小型测距系统特有的声纳传感器的不可靠性, 这个方法得到的结果不尽如人意，当车附近有障碍时，传感器却探测到一条“自由道路”。为了解决这个问题，本文提出了一个改进的,更简单的传感器编组和数据管理方法，并得到了更好更准确的结果：对图2的传感器再编组，它们的读数的最小数是到障碍物的距离的一个衡量值。每个A TRV生波探侧器传感器以4米作为最大距离，从这个距离处的障碍物返回数据。(这由生波探侧器传感器制造商进行了实验性地核实).

图2. 传感器组

第一层的每个独立的模糊控制器的模型，即障碍物探测模块，如图3所示。从图3可知，对前、后方向的碰撞可能性的测定由传感器A1,A2,…A5（5个输入数据）和传感器A7,A8,…A11（5个输入数据）完成，而对左、右方向的碰撞可能性的测定由传感器A5,A6,A7（3个输入数据）和传感器A11,A12,A13（3个输入数据）完成，每个独立的模糊控制器利用隶属度函数来计算碰撞的可能性。距离障碍物的距离按照隶属度函数分为三个标准：近、中等距离、远，如图4，反映了关于潜在障碍物在4 米内的准确信息。

图3.障碍物探测模块。

图4.输入变量：距离障碍物的距离

第一层的输出结果是各个方向的碰撞可能性，取从0 到1的值来表示，.描述各个方向撞击可能性按照隶属度函数的标准有：不可能、可能、非常可能性，如图5。基于左碰撞可能性的输出结果如表1。

图5. 输出变量：碰撞可能性。

以前碰为类: 如果A1、A2、A3、A5是近的、A4 是中等距离，那麽碰撞可能性高的。后面碰撞与此相似。为左边(等效为右碰)碰撞可能性是: 如果A5 、A6、A7

都是近的，那碰撞的可能性是高的。

表1.

一部分的规则基地为左碰撞。

B.模糊逻辑控制器的第二层

模糊控制器的第二层输入的是四个方向的碰撞可能性和角度误差，输出的是使车子前后移动的移动速度和转动速度，如图6所示。角度误差描述的是机器人航向角度和机器人要达到它的目的地的目标角度之间的差距。角度误差的范围是-180度到180度之间。按照隶属度函数描述角度误差的词有：偏后1、正左方、左边、前面、正右面、偏后2，如图7.

可平移速度(m/sec), 作为第二层的输出结果,按照隶属度函数用以下词描述: 向后加速, 向后、向后减速、停止, 向前减速、向前、向前加速，如图8.

按照隶属度函数转动速度(rad/sec)用以下词汇描述:向右加速,、向右、不转、向左、向左加速，如图9.

图6. 模糊控制器的第2 层模型

图7. 输入变量：角度误差

图8. 输出变量：平移速度

控制车运动的例子: 如果前面碰撞、后面碰撞、左面碰撞、右面碰撞都是不可能的，则角度误差是前面，平移速度是向前加速、加速度是不旋转

图9. 输出变量：旋转速度。

3.结论

模糊控制器已经被设计出来，并在一个由R W I制造的小型测距系统中运用，而且利用C++语言进行了设计并执行。在所有的实验中，当机器人能在一个半径为30厘米的圆圈中停下来的时候，就可以认为它达到了它的目标。这个假设是成立的，因为所有的计算都已经被验证。所以，如果机器人在假定的圆圈内停下来，它的目标就实现了。

通过研究该机器在有障碍的2维环境中的一些情况，来测定它的运行情况和控制器的适用性。

图10、图15、图20的箭头显示的是车的初始方向。

在测试情形1中，我们检查了车在一个有三个障碍物的环境下的运行情况，具体如图10所示。图11显示了平移速度以及图12显示的是转速。图13介绍的是前撞的可能性。在图14中，实线表示的是左撞的可能性，而虚线表示右撞的可能性。车的运行情况是由周围的障碍所决定的。

一开始，左撞的可能性是由左边的障碍物决定的。机器向前移动，然后向右行驶避开障碍，然后再向左驶向其目标运动。

图15所示的测试情形2，显示的是一个更加复杂的三个障碍物的测试环境。图16 显示了平移速度，图17显示了转动速度。图18表示的是前撞的可能性，图19 中的实线代表的是左撞的可能性，而虚线代表的是右撞的可能性。在图15中，我们可以发现机器人前面的路是被封锁的。机器仅仅利用转动速度来行驶并避开障碍物。然后它以曲线行驶向着目标前进。车

的行使路线如图20所示。由于周围的障碍物，车不得不稍稍向右转了一个弯，然后逃离了

这个封闭的区域。

图21显示了平移速度，图22显示了转动速度。图23表示的是前撞的可能性，图24 中的

实线代表的是左撞的可能性，而虚线代表的是右撞的可能性。每种情形中的车的运行情况可

以通过各个方向的碰撞可能性的相关数据得到检验。

图10. 判例1 ：三个障碍并且目标点较远

图11. 判例1中平移速度。图14. 判例1中左右碰撞可能性

图12. 判例1中旋转速度图15 判例2：较复杂的三个障碍

图13. 判例1中前面碰撞可能性图16. 判例2中平移速度