README.md

Turtlebot3 simulation

Project description:

1. Simulating Turtlebot3 using Gazebo.
2. LiDAR and IMU Sensor Data Visualization in RViz.
3. Unit Conversion Node Implementation in C++.
4. Uni-dimensional Kalman filter node implemented in python.
5. Testing filtered data in comparison with raw data using rqt_multiplot.

---

Deploying Turtlebot 3:

For deploying Turtlebot3, follow Turtlebot3 gazebo instructions. In our example, we used the Turtlebot3 world. In the root directory of the workspace:

catkin_make
source devel/setup.bash
export TURTLEBOT3_MODEL=waffle
roslaunch turtlebot3_gazebo turtlebot3_world.launch

To control the robot using the keyboard, in a new terminal window:

source devel/setup.bash
export TURTLEBOT3_MODEL=waffle
roslaunch turtlebot3_teleop turtlebot3_teleop_key.launch

---

Visualizing LiDar Data on RVIZ

On a new terminal window:

source devel/setup.bash
export TURTLEBOT3_MODEL=waffle
roslaunch turtlebot3_gazebo turtlebot3_gazebo_rviz.launch

Unit conversion node

Quaternion is a four-dimensional vector used to represent object orientation in 3D space.

$$ q=w+xi+yj+zk $$

The conversion to Euler's RPY can be done on several steps: 1- Conversionn to rotation matrix:

$$ R= \begin{bmatrix} ​1−2(y2+z2) & 2(xy+wz) & 2(xz−wy)​ \cr 2(xy−wz) & 1−2(x2+z2) & 2(yz+wx) \cr ​2(xz+wy) & 2(yz−wx) & 1−2(x2+y2)​ \end{bmatrix} $$

From the rotation Matrix:

$$ \text{Yaw} = \text{atan2}(R_{21}, R_{11}) $$

$$ \text{Pitch} = \text{atan2}\left(-R_{31}, \sqrt{R_{32}^2 + R_{33}^2}\right) $$

$$ \text{Roll} = \text{atan2}(R_{32}, R_{33}) $$

Luckily, this can be done by using the tf2 library, which provides a Matrix3x3 function which calculates the rotation matrix, and getRPY function to extract the Euler Angles. The library provides other similar functions, so to choose carefully we first needed to check the library's documentation and source code

The unit conversion node is based on the OOP principles, following pure i/o functions, each class has its own precise purpose and deals with specific type of data.

AxisRot class, responsible for Unit conversion,

struct AxisRot {
    double yaw =0, pitch=0, roll=0;
    AxisRot() {};
    AxisRot(double yaw, double pitch, double roll): yaw(yaw), pitch(pitch), roll(roll) {}
    AxisRot(tf2::Quaternion q) {
        tf2::Matrix3x3 matrix(q);
        matrix.getRPY(roll, pitch, yaw);
    }
};

FetchQuaternion: contains the call back function, fetches data and stores it appropriate variable.

class FetchQuaternion {
    tf2::Quaternion q;

public:
    tf2::Quaternion get() {
        return q;
    }

    void fetch_data(const sensor_msgs::Imu::ConstPtr& msg) {
        q.setX(msg->orientation.x);
        q.setY(msg->orientation.y);
        q.setZ(msg->orientation.z);
        q.setW(msg->orientation.w);
    }

};

The call back functions cannot return a type. To solve this issue, we can use an object method to store data:

    ros::Subscriber sub = nh.subscribe("/imu", 1000, &FetchQuaternion::fetch_data, &fq);

---

Kalman filter

Base terms for Kalman filter:

• Process variance: How much uncertainty in the system.
• Measurement variance: How much uncertainty in the measurements.
• Initail estimate: A guess for the value being estimated.
• Initial error estimate: A guess for how uncertain the that initial estimate is.

Uni dimensional Kalman filter is based on the following equation:

$$ P_{k∣k−1}​=P_{k−1∣k−1}​+Q $$

• $P_{k∣k−1​}$: predicted estimate covariance (error estimate) at time kk.
• $P_{k−1∣k−1}$: the updated error estimate from the previous step.
• $Q$: process variance.

This can be eaily implemented:

def predict(self):
    self.error_estimate += self.process_variance

The Kalman gain determines how much the new measurement should adjust the estimate. It balances the trust between the prediction and the measurement.

$$ K_k = \frac{P_{K|k-1}}{P_{K|k-1}+R} $$

• $R$: measurement variance.

In our code, this translates to:

def update(self, measurement):
    kalman_gain = self.error_estimate / (self.error_estimate + self.measurement_variance)
    self.estimate += kalman_gain * (measurement - self.estimate)
    self.error_estimate *= (1 - kalman_gain)

Updated estimation:

$$ X_{k|k} = X_{k|k-1} + K_k * (Z_k - X_{k|k-1}) $$

• $X_{k|k}$: The updated state estimate after incorporating the new measurement.
• $X_{k|k-1}$: The predicted state estimate.
• $Z_k$: The new measurement.
• $K_k$: The Kalman gain.

self.estimate += kalman_gain * (measurement - self.estimate)

Updating the error estimate:

$$ P_{k∣k​}=(1−K_k​)P_{k∣k−1} $$

  self.error_estimate *= (1 - kalman_gain)

• The node reads the Yaw value from the /imu_degree topic (Float64MultiArray) and republish it on /filtered_yaw topic (Float64)

---

Testing the kalman Filter:

After installing rqt_multiplot and dependenies, on a new terminal window:

Setup rqt_multiplot:

rosrun rqt_multiplot rqt_multiplot

Visualize the curves:

In the src directory:

mkdir imu_sensor data $$ cd imu_sensor_data
git clone https://github.com/minawashere/MIA-Team-8-task-10.1 #clone our repo
cd ~/catkin_ws
catkin_make

Launch the converter and the filtering nodes:

rosrun imu_sensor_data quaternion_to_degree & #to run it in the backgroung
rosrun imu_sensor_data kalman_filter.py &

To add noise to the gazebo environment, we have to check the configuration files of turtlebot3. To be sure of what value we are changing, we will check their source code , in line 85, it states that the imu plugin for our model is libgazebo_ros_imu.so. Googling it, we find it's source code scroll down:

<gaussianNoise>0.0</gaussianNoise> #this is the value we are looking to change

To add noise to our moodel:

cd /opt/ros/noetic/share/turtlebot3_description/urdf && nvim turtlebot3_waffle.gazebo.xacro

scroll down to the imu_plugin configuration, and change the gaussian noise value to <0.5>

Open rqt_multiplot tab, On the top right part click settings > add new curve. On the x-axis check the time receipt, on the y-axis choode the /imu_degree topic, make sure you are printing the data/0 field. repeat the same steps for the /filtered_yaw topic.