Ros By example-第七章 控制移动底座

最新推荐文章于 2020-08-25 09:31:34 发布
最新推荐文章于 2020-08-25 09:31:34 发布
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7.1 单位和坐标系统


7.2 不同层次的移动控制

内部运动数据统称为里程计

7.2.1 电机, 轮子和编码器

7.2.2电机控制器和驱动

ROS 核心包不包括具体电机控制器的驱动。可以找到第三方的包如 Arduino, ArbotiX, Serializer, Element, LEGO® NXT and Rovio.

7.2.3 ROS Base 控制器

PID控制。 PID“比例积分微分”

驱动和PID控制器整合成单个ROS 节点，base controller.

该base controller节点通常发布里程计数据到/odom 主题，并监听监听在/ cmd_vel主题运动命令。同时，控制器节点通常（但不总是）发布从/odom坐标系到/ base_link或/ base_footprint坐标系的转换

7.2.4 使用ROS move_base包基于坐标系运动

7.2.5 使用ROS gmapping 和 amcl 包的 SLAM

amcl -自适应蒙特卡洛定位

7.2.6 语义目标

7.2.7 总结


smach, behavior trees, executive_teer, and knowrob. (smach 和behavior trees讲在第二卷介绍.)

7.3.2 使用 RViz监视机器人运动

$rosmsg show geometry_msgs/Twist

线速度和角速度，都是3维的向量， 线速度的单位是m/s, 角速度的单位是弧度 rad/s.( 1rad= 57°),  在二维平面上，一般只用到线速度的X和角速度的Z。

geometry_msgs/Vector3 linear
float64 x
float64 y
float64 z
geometry_msgs/Vector3 angular
float64 x
float64 y
float64 z


'{linear: {x: 0, y: 0, z: 0}, angular: {x: 0, y: 0, z: 1.0}}'   冒号后面的空格是必须的。


$rostopic pub -r 10 /cmd_vel geometry_msgs/Twist '{linear: {x: 0.1, y: 0, z: 0}, angular: {x: 0, y: 0, z: -0.5}}'

（-r 10 代表 周期发布，频率为10Hz） 


$rostopic pub -1 /cmd_vel geometry_msgs/Twist '{}'

（-1 代表发布一次）

7.4 校准 Robot's Odometry 里程计

没有真实的机器人，所以跳过这节

7.5 发送Twist 信息到真是的机器人

没有真实的机器人，所以跳过这节

7.6 从ROS 节点发布 Twist 信息

$roslaunch rbx1_bringup fake_turtlebot.launch
$rosrun rviz rviz -d `rospack find rbx1_nav`/sim.rviz
<pre name="code" class="html">$rosrun rbx1_nav timed_out_and_back.py
 

</pre><pre name="code" class="html">如果你的包py引入 Twist， 需在你的package.xml加入
 

<run_depend>geometry_msgs</run_depend>
 

 

self.cmd_vel = rospy.Publisher('/cmd_vel', Twist, queue_size=5)
 

 

queue_size ， 如果没设置的话， 发布会表现为同步，如果有多个订阅这个主题，如果有一个被挂起，其他的也会被阻塞，如果设为某个数， 则每个订阅通过不同的线程接收到信息。
 

r.sleep() == rospy.sleep(1/rate) 因为我们定义了变量  r = rospy.Rate(rate).
 
 
 

7.7 机器人是否正确的执行我们的意图， 如果我给机器人发布 0.2m/s 的向前速度， 实际中，机器人有可能是按0.18m/s 速度前进， 那我们怎么来保证这个问题呢
 
 

机器人的base 控制节点使用里程计和PID控制把motion请求转换为真实世界中的速度。该方法的准确度和可靠性取决于机器人的内部传感器，所述校准过程的精度和环境条件。 （例如，某些表面可能允许车轮稍微打滑从而将陷编码器计数和行驶距离之间的映射打乱。）
 
 


 
 

ROS 提供了一个消息类型来存储里程计数据; nav_msgs/Odometry. 里程计信息类型结构大体如下:
 
 

Header header
string child_frame_id
geometry_msgs/PoseWithCovariance pose
geometry_msgs/TwistWithCovariance twist
 

 

 

$rosmsg show nav_msgs/Odometry

Header header
uint32 seq
time stamp
string frame_id
string child_frame_id
geometry_msgs/PoseWithCovariance pose
geometry_msgs/Pose pose
geometry_msgs/Point position
float64 x
float64 y
float64 z
geometry_msgs/Quaternion orientation
float64 x
float64 y
float64 z
float64 w
float64[36] covariance
geometry_msgs/TwistWithCovariance twist
geometry_msgs/Twist twist
geometry_msgs/Vector3 linear
float64 x
float64 y
float64 z
geometry_msgs/Vector3 angular
float64 x
float64 y
float64 z
float64[36] covariance
 

 

 PoseWithCovariance 记录了机器人的位置和方向，TwistWithCovariance 记录了线速度和角速度的值， Pose 和 Twist 可以写成协方差矩阵，用于计算各种测试的不确定。
 

Header 和child_frame_id 是用来定义计算距离和角度的参考坐标系坐标系
 
 

我们通常 把 /odom 作为父坐标系 id ， /base_link (或/base_footprint) 作为子坐标系 id. 而/ base_link坐标系对应于机器人的实际物理部分，/odom 坐标系定义成由封装成里程计数据的平移和旋转。这些转换是相对/odom。
 
 

7.8 使用里程计
 
 

7.8.3 基于里程计的 Out-and-Back 脚本
 
 

需要geometry_msgs 包下的Twist, Point and Quaternion 数据类型
 
 

还需要 tf 库来监听/odom and /base_link (or /base_footprint) 坐标系之间的转换.
 
 

2.5°是允许的误差范围
 

7.8.4 /odom 主题与/odom 坐标系
 
 

读者可能会奇怪，为什么我们在前面的脚本中使用一个TransformListener访问里程计信息，而不仅仅是订阅到/odom 主题。其原因是，在/odom 主题发布的数据并不总是完整的。例如，TurtleBot使用单轴陀螺仪为机器人的旋转提供附加估计。这是用从由robot_pose_ekf节点（这是在TurtleBot启动文件启动）车轮编码器中的数据组合以获得比单独源更好的估计。
 
 

然而，robot_pose_ekf节点不发布数据到保留车轮编码器数据/odom 主题。相反，它发布到 / odom_combined主题。此外，数据发布不是作为一个里程计信息，但作为一个PoseWithCovarianceStamped消息。
 

7.9.4 航位推算问题
 
 

仅利用内部运动数据导航，不参照外部路标被称为航位推算。 误差的累积会导致机器人与预期的不一致， 这时需要用到 下一章的SLAM 
 
 

7.10 遥控机器人
 
 

 

$sudo apt-get install ros-indigo-joystick-drivers ros-indigo-turtlebot-teleop
 

 7.10.1 使用键盘 

 

 

 

$roslaunch rbx1_bringup fake_turtlebot.launch
$rosrun rviz rviz -d `rospack find rbx1_nav`/sim.rviz
$roslaunch rbx1_nav keyboard_teleop.launch

 

 7.10.2使用罗技游戏手柄 

 

 

 

$roslaunch rbx1_nav joystick_teleop.launch
 

 


 
 7.10.3 使用Arbotix GUI 

 

arbotix_gui
 

 7.10.4 使用可交互标记 

 

 

sudo apt-get install ros-indigo-turtlebot-interactive-markers
 

<pre name="code" class="html">$roslaunch rbx1_bringup fake_turtlebot.launch
$rosrun rviz rviz -d `rospack find rbx1_nav`/interactive_markers.rviz
$roslaunch rbx1_nav interactive_markers.launch
 

 

 

 

 

 

 

 

 


 

                

        

    

  



    

      

        

            

              
                
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Contents
Preface................................................................................................................vii
Printed vs PDF Versions of the Book...............................................................ix
1. Scope of this Volume.......................................................................................1
2. Installing the ros-by-example Code...............................................................3
3. Task Execution using ROS.............................................................................7
3.1 A Fake Battery Simulator.....................................................................................8
3.2 A Common Setup for Running the
Examples.....................................................10
3.3 A Brief Review of ROS Actions........................................................................11
3.4 A Patrol Bot Example.........................................................................................12
3.5 The Patrol Bot using a Standard Script...............................................................13
3.6 Problems with the Script Approach....................................................................16
3.7 SMACH or Behavior Trees?..............................................................................17
3.8 SMACH: Tasks as State Machines.....................................................................17
3.8.1 SMACH review.......................................................................................................18
3.8.2 Patrolling a square using SMACH..........................................................................19
3.8.3 Testing SMACH navigation in the ArbotiX simulator............................................23
3.8.4 Accessing results from a SimpleActionState...........................................................26
3.8.5 SMACH Iterators.....................................................................................................27
3.8.6 Executing commands on each transition.................................................................30
3.8.7 Interacting with ROS topics and services................................................................31
3.8.8 Callbacks and Introspection.....................................................................................36
3.8.9 Concurrent tasks: Adding the battery check to the patrol routine...........................36
3.8.10 Comments on the battery checking Patrol Bot......................................................44
3.8.11 Passing user data between states and state machines............................................44
3.8.12 Subtasks and hierarchical state machines..............................................................48
3.8.13 Adding the battery check to the house cleaning robot...........................................54
3.8.14 Drawbacks of state machines................................................................................54
3.9 Behavior Trees...................................................................................................55
3.9.1 Behavior Trees versus Hierarchical State Machines...............................................56
3.1.2 Key properties of behavior
trees..............................................................................57 3.9.3 Building a behavior
tree..........................................................................................58 3.9.4 Selectors
and sequences...........................................................................................60
3.9.5 Customizing behaviors using decorators (meta-behaviors).....................................61
3.10 Programming with Behavior Trees and ROS....................................................63
3.10.1 Installing the pi_trees library.................................................................................63
3.10.2 Basic components of the pi_trees library..............................................................63
3.10.3 ROS-specific behavior tree
classes........................................................................68
3.10.4 A Patrol Bot example using behavior trees..........................................................72
3.10.5 A housing cleaning robot using behavior trees.....................................................79
3.10.6 Parallel tasks..........................................................................................................85
3.10.7 Adding and removing tasks...................................................................................87
4. Creating a URDF Model for your Robot....................................................89
4.1 Start with the Base and Wheels..........................................................................90
4.1.1 The robot_state_publisher and joint_state_publisher
nodes....................................91 4.1.2 The base URDF/Xacro
file......................................................................................92
4.1.3 Alternatives to using the /base_footprint frame......................................................97
4.1.4 Adding the base to the robot model.........................................................................97
4.1.5 Viewing the robot's transform tree..........................................................................98
4.1.6 Using a mesh for the base........................................................................................99
4.2 Simplifying Your Meshes.................................................................................104
4.3 Adding a Torso.................................................................................................104
4.3.1 Modeling the
torso.................................................................................................105 4.3.2 Attaching
the torso to the base..............................................................................106
4.3.3 Using a mesh for the torso.....................................................................................107
4.3.4 Adding the mesh torso to the mesh base...............................................................108
4.4 Measure, Calculate and Tweak.........................................................................110
4.5 Adding a Camera..............................................................................................110
4.5.1 Placement of the
camera........................................................................................111 4.5.2 Modeling the
camera.............................................................................................112
4.5.3 Adding the camera to the torso and base...............................................................114
4.5.4 Viewing the transform tree with torso and camera................................................115
4.5.5 Using a mesh for the camera.................................................................................116
4.5.6 Using an Asus Xtion Pro instead of a Kinect........................................................118
4.6 Adding a Laser Scanner (or other Sensors)......................................................119
4.6.1 Modeling the laser
scanner....................................................................................119
4.6.2 Attaching a laser scanner (or other sensor) to a mesh base...................................120
4.6.3 Configuring the laser node launch
file..................................................................121
4.7 Adding a Pan and Tilt
Head..............................................................................122 4.7.1 Using an Asus
Xtion Pro instead of a Kinect........................................................124
4.7.2 Modeling the pan-and-tilt
head..............................................................................124 4.7.3 Figuring out
rotation axes......................................................................................127
4.7.4 A pan and tilt head using meshes on Pi Robot......................................................128
4.7.5 Using an Asus Xtion Pro mesh instead of a Kinect on Pi Robot...........................129
4.8 Adding One or Two Arms................................................................................129
4.8.1 Placement of the
arm(s).........................................................................................130
4.8.2 Modeling the
arm...................................................................................................130 4.8.3
Adding a gripper frame for
planning.....................................................................133
4.8.4 Adding a second arm.............................................................................................134
4.8.5 Using meshes for the arm servos and brackets......................................................136
4.9 Adding a Telescoping Torso to the Box
Robot.................................................138 4.10 Adding a Telescoping Torso to Pi
Robot........................................................139
4.11 A Tabletop One-Arm Pi Robot.......................................................................140
4.12 Testing your Model with the ArbotiX Simulator............................................142
4.12.1 A fake Box Robot................................................................................................142
4.12.2 A fake Pi Robot...................................................................................................145
4.13 Creating your own Robot Description Package..............................................145
4.13.1 Using rosbuild......................................................................................................145
4.13.2 Using catkin.........................................................................................................146
4.13.3 Copying files from the rbx2_description
package...............................................147
4.13.4 Creating a test launch file....................................................................................147
5. Controlling Dynamixel Servos: Take
2......................................................149
5.1 Installing the ArbotiX Packages.......................................................................149
5.2 Launching the ArbotiX
Nodes..........................................................................150
5.3 The ArbotiX Configuration File.......................................................................154
5.4 Testing the ArbotiX Joint Controllers in Fake
Mode........................................160
5.5 Testing the Arbotix Joint Controllers with Real
Servos....................................162
5.6 Relaxing All Servos..........................................................................................165
5.7 Enabling or Disabling All Servos.....................................................................168
6. Robot
Diagnostics........................................................................................169
6.1 The DiagnosticStatus
Message.........................................................................170
6.2 The Analyzer Configuration
File......................................................................171
6.3 Monitoring Dynamixel Servo Temperatures....................................................172
6.3.1 Monitoring the servos for a pan-and-tilt
head.......................................................172
6.3.2 Viewing messages on the /diagnostics
topic.........................................................175
6.3.3 Protecting servos by monitoring the /diagnostics
topic.........................................177
6.4 Monitoring a Laptop Battery............................................................................181
6.5 Creating your Own Diagnostics
Messages.......................................................182
6.6 Monitoring Other Hardware States...................................................................188
7. Dynamic
Reconfigure..................................................................................191
7.1 Adding Dynamic Parameters to your own
Nodes.............................................192
7.1.1 Creating the .cfg file..............................................................................................192
7.1.2 Making the .cfg file executable.............................................................................193
7.1.3 Configuring the CMakeLists.txt file......................................................................194
7.1.4 Building the package.............................................................................................194
7.2 Adding Dynamic Reconfigure Capability to the Battery Simulator
Node........194 7.3 Adding Dynamic Reconfigure Client Support to a ROS
Node.........................198
7.4 Dynamic Reconfigure from the Command Line...............................................201
8. Multiplexing Topics with mux & yocs.......................................................203
8.1 Configuring Launch Files to Use mux
Topics..................................................204
8.2 Testing mux with the Fake TurtleBot...............................................................205
8.3 Switching Inputs using mux
Services...............................................................206
8.4 A ROS Node to Prioritize mux Inputs..............................................................207
8.5 The YOCS Controller from Yujin
Robot..........................................................210
8.5.1 Adding input sources.............................................................................................213
9. Head Tracking in 3D...................................................................................215
9.1 Tracking a Fictional 3D Target.........................................................................216
9.2 Tracking a Point on the
Robot..........................................................................217
9.3 The 3D Head Tracking Node............................................................................220
9.3.1 Real or fake head tracking.....................................................................................220
9.1.2 Projecting the target onto the camera
plane...........................................................221
9.4 Head Tracking with Real Servos......................................................................224
9.4.1 Real servos and fake target....................................................................................225
9.4.2 Real servos, real target...........................................................................................226
9.4.3 The nearest_cloud.py node and launch
file...........................................................228
10. Detecting and Tracking AR Tags.............................................................233
10.1 Installing and Testing the ar_track_alvar Package..........................................234
10.1.1 Creating your own AR
Tags................................................................................234 10.1.2 Generating and
printing the AR tags...................................................................236
10.1.3 Launching the camera driver and ar_track_alvar node.......................................236
10.1.4 Testing marker detection.....................................................................................238
10.1.5 Understanding the /ar_pose_marker topic...........................................................238
10.1.6 Viewing the markers in RViz..............................................................................240
10.2 Accessing AR Tag Poses in your Programs....................................................240
10.2.1 The ar_tags_cog.py script....................................................................................240
10.2.2 Tracking the tags with a pan-and-tilt head..........................................................244
10.3 Tracking Multiple Tags using Marker Bundles..............................................245
10.4 Following an AR Tag with a Mobile Robot....................................................245
10.4.1 Running the AR follower script on a TurtleBot .................................................248
10.5 Exercise: Localization using AR Tags............................................................249
11. Arm Navigation using MoveIt!.................................................................251
11.1 Do I Need a Real Robot with a Real Arm?.....................................................252
11.2 Degrees of Freedom.......................................................................................252
11.3 Joint
Types.....................................................................................................253
11.4 Joint Trajectories and the Joint Trajectory Action Controller.........................254
11.5 Forward and Inverse Arm Kinematics............................................................257
11.6 Numerical versus Analytic Inverse Kinematics..............................................258
11.7 The MoveIt! Architecture...............................................................................258
11.8 Installing MoveIt!...........................................................................................260
11.9 Creating a Static URDF Model for your Robot .............................................261
11.10 Running the MoveIt! Setup Assistant...........................................................262
11.10.1 Load the robot's URDF model...........................................................................263
11.2.2 Generate the collision matrix.............................................................................264
11.10.3 Add the base_odom virtual
joint.......................................................................264
11.10.4 Adding the right arm planning group................................................................265
11.10.5 Adding the right gripper planning group...........................................................269
11.10.6 Defining robot poses..........................................................................................271
11.10.7 Defining end effectors.......................................................................................273
11.10.8 Defining passive joints......................................................................................273
11.10.9 Generating the configuration files.....................................................................273
11.11 Configuration Files Created by the MoveIt! Setup Assistant........................275
11.11.1 The SRDF file (robot_name.srdf)......................................................................275
11.11.2 The fake_controllers.yaml file...........................................................................276
11.11.3 The joint_limits.yaml
file..................................................................................277
11.11.4 The kinematics.yaml file...................................................................................278
11.12 The move_group Node and Launch File.......................................................280
11.13 Testing MoveIt! in Demo Mode...................................................................280
11.13.1 Exploring additional features of the Motion Planning
plugin...........................284
11.13.2 Re-running the Setup Assistant at a later time..................................................285
11.14 Testing MoveIt! from the Command Line....................................................286
11.15 Determining Joint Configurations and End Effector Poses...........................289
11.16 Using the ArbotiX Joint Trajectory Action Controllers................................292
11.16.1 Testing the ArbotiX joint trajectory action controllers in
simulation...............292
11.16.2 Testing the ArbotiX joint trajectory controllers with real servos......................300
11.17 Configuring MoveIt! Joint Controllers.........................................................301
11.17.1 Creating the controllers.yaml file......................................................................302
11.17.2 Creating the controller manager launch file......................................................304
11.18 The MoveIt! API..........................................................................................305
11.19 Forward Kinematics: Planning in Joint Space..............................................306
11.20 Inverse Kinematics: Planning in Cartesian
Space.........................................314
11.21 Pointing at or Reaching for a Visual Target..................................................322
11.22 Setting Constraints on Planned Trajectories.................................................324
11.22.1 Executing Cartesian
Paths.................................................................................324
11.22.2 Setting other path constraints............................................................................330
11.23 Adjusting Trajectory Speed..........................................................................333
11.24 Adding Obstacles to the Planning Scene......................................................337
11.25 Attaching Objects and Tools to the Robot....................................................346
11.26 Pick and Place..............................................................................................348
11.27 Adding a Sensor Controller..........................................................................360
11.28 Running MoveIt! on a Real Arm..................................................................363
11.28.1 Creating your own launch files and
scripts.......................................................364 11.28.2 Running the robot's launch
files........................................................................364
11.2.3 Forward kinematics on a real arm.....................................................................365
11.28.4 Inverse kinematics on a real
arm.......................................................................366
11.28.5 Cartesian paths on a real arm.............................................................................367
11.28.6 Pick-and-place on a real arm.............................................................................367
11.28.7 Pointing at or reaching for a visual target..........................................................367
11.29 Creating a Custom Fast IK Plugin................................................................368
12. Gazebo: Simulating Worlds and Robots.................................................375
12.1 Installing Gazebo............................................................................................376
12.2 Hardware Graphics
Acceleration....................................................................377
12.3 Installing the ROS Gazebo Packages..............................................................378
12.4 Installing the Kobuki ROS Packages..............................................................379
12.5 Installing the UBR-1 Files..............................................................................379
12.6 Using the Gazebo
GUI...................................................................................379
12.7 Missing Model Bug in Gazebo 1.9.................................................................381
12.8 Testing the Kobuki Robot in Gazebo..............................................................383
12.8.1 Accessing simulated sensor
data.........................................................................385 12.8.2 Adding safety control to
the Kobuki...................................................................389
12.8.3 Running the nav_square.py script from Volume 1..............................................391
12.9 Loading Other Worlds and Objects................................................................392
12.10 Testing the UBR-1 Robot in Gazebo............................................................393
12.10.1 UBR-1 joint
trajectories.....................................................................................394
12.1.2 The UBR-1 and MoveIt!....................................................................................395
12.11 Real Pick-and-Place using the UBR-1 Perception Pipeline..........................397
12.11.1 Limitations of depth
cameras............................................................................398
12.11.2 Running the
demo..............................................................................................399
12.11.3 Understanding the real_pick_and_place.py
script.............................................404
12.12 Running Gazebo Headless + RViz...............................................................407
13. Rosbridge: Building a Web GUI for your Robot...................................411
13.1 Installing the rosbridge Packages...................................................................411
13.2 Installing the mjpeg_sever
Package................................................................412
13.3 Installing a Simple Web Server (mini-httpd)..................................................415
13.4 Starting mini-httpd, rosbridge and mjpeg_server............................................416
13.5 A Simple rosbridge HTML/Javascript GUI....................................................417
13.6 Testing the GUI with a Fake TurtleBot..........................................................420
13.7 Testing the GUI with a Real Robot.................................................................420
13.8 Viewing the Web GUI on another Device on your Network..........................421
13.9 Using the Browser Debug Console.................................................................421
13.10 Understanding the Simple GUI.....................................................................423
13.10.1 The HTML layout:
simple_gui.html.................................................................423
13.1.2 The JavaScript code: simple_gui.js...................................................................428
13.11 A More Advanced GUI using jQuery, jqWidgets and KineticJS..................438
13.12 Rosbridge Summary.....................................................................................443
Appendix: Plug and Play USB Devices for ROS: Creating udev Rules......445
13.13 Adding yourself to the dialout Group...........................................................445
13.14 Determining the Serial Number of a
Device.................................................446
13.15 UDEV Rules.................................................................................................447
13.16 Testing a UDEV Rule...................................................................................448
13.17 Using a UDEV Device Name in a ROS Configuration
File..........................448

			
		

	





	

		

			

				
					
【仿真】Ros by example1 控制底座、导航、路径规划、SLAM

				
			

			

				

					try_again_later的博客
				

				

					10-02
					
					1267
					
				

			

		

		

			
				
为了快速浏览教程，先从ArbotiX虚拟器开始。具体代码看ros-by-example 1,主要讲述实现过程。

首先要启动一个虚拟的Turtlebot


$ roslaunch rbx1_bringup fake_turtlebot.launch

另一个终端，打开RViz可视化机器人运动


$ rosrun rviz rviz -d `rospack find rbx1_nav`/sim....

			
		

	





	

		

			

				
					
Ros By example-第八章 导航，路劲规划和SLAM

				
			

			

				

					damifeng2018的博客
				

				

					07-26
					
					968
					
				

			

		

		

			
				
SLAM 一般使用昂贵的激光传扫描器来收集数据， 但是现在可以使用 Kinect或者Asus Xtion 等深度相机来使用点云的方式来模拟激光扫描。

			
		

	





	

		

			

				
					
ros_by_example的安装

				
			

			

				

					lzw508170827的博客
				

				

					08-25
					
					407
					
				

			

		

		

			
				
环境：ubuntu14
sudo apt-get install -y ros-indigo-turtlebot-bringup \
ros-indigo-turtlebot-create-desktop ros-indigo-openni-* \
ros-indigo-openni2-* ros-indigo-freenect-* ros-indigo-usb-cam \
ros-indigo-laser-* ros-indigo-hokuyo-node \
ros-indigo-audio-common

			
		

	





	

		

			

				
					

				
			

			

				

					
				

			

		

		

			
				

			
		

	



              




          




        



    





    



      

      

        
      

      





	

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