Mastering Robot Control: Building an Autonomous TurtleBot3 Node

Introduction

Overview: Setting Up Your Control Node

Key Concepts and Mathematics

Building the Control Node in ROS 2

Challenges in Mobile Robot Control

Conclusion

References

1 Introduction

If you’re exploring robotics, understanding how to control a mobile robot to move towards a target

is a fundamental skill. In this tutorial, we’ll dive into the creation of a custom control node for the

popular TurtleBot3 using ROS 2, focusing on the high-level logic and mathematical foundations

that guide the robot from its current location to a user-defined goal. By the end of this guide, you’ll

grasp how to work with topics in ROS 2, leverage sensor data for odometry, calculate goal-directed

movement, and publish commands to the robot.

2 Overview: Setting Up Your Control Node

The control node we’ll develop allows you to set a goal position (x, y coordinates) for the TurtleBot3.

The robot will continuously update its position based on odometry data and adjust its motion until

it reaches the target.

We’ll achieve this by following these key steps:

1. Receive Real-Time Odometry Data: Gather the robot’s current position and orientation.

2. Calculate Distance and Angular Error to Goal: Use mathematical formulas to compute the

distance and angle between the robot’s position and the goal.

3. Publish Control Commands: Send velocity commands to drive the robot forward and adjust

its heading toward the goal.

3 Key Concepts and Mathematics

3.1 Odometry: Getting the Robot’s Current Position

Odometry data from the /odom topic provides the current position and orientation of the robot,

which we store in a Pose message. This message contains:

• Position (x, y): The robot’s coordinates in the map.

• Orientation (quaternion): The robot’s orientation in quaternion form, which we convert

to a usable angle.

3.2 Calculating the Euclidean Distance to the Goal

The Euclidean distance gives the shortest path between two points in a plane. For a goal located

at (goalx, goaly), and the current robot position (x, y), the formula is:

This distance serves as our error term, guiding the robot’s forward speed.

3.3 Calculating the Angular Error to Goal

To move toward the target, the robot must adjust its heading to point directly at the goal. We

calculate the angular error using the arctangent function:

The difference between the robot’s current heading and the desired angle is the angular error.

In practice, we use the quaternion data from the odometry message to calculate the robot’s heading

and compare it to desired angle to determine how much to rotate.

3.3.1 Challenges with Euler Angles

Interpolating directly between Euler angles can create problems:

• Gimbal Lock: When two rotational axes align, you lose a degree of freedom, making it

impossible to represent all rotations correctly.

• Angle Wrapping: Multiple sets of Euler angles can represent the same orientation due to

the wrapping of angles (e.g., 0◦ and 360◦).

3.3.2 Using Rotation Matrices

3.3.3 Using Quaternions

3.4 Control Law: Adjusting Linear and Angular Velocity

A proportional controller adjusts both linear and angular velocities:

linear velocity = kd × distance

angular velocity = kθ × angular error

Here, kd and kθ are tuning parameters that adjust the sensitivity of the control response. You

can see in the code that depending on the how close we are to the goal i have varied the parameters

because otherwise it will always overshoot the desired position.

4 Building the Control Node in ROS 2

Node Overview

Our control node:

• Publishes Twist messages to /cmd vel to control movement.

• Subscribes to /odom for position feedback.

• Calculates control commands using the distance and angular error, derived from real-time

odometry.

5 Challenges in Mobile Robot Control

• Tuning Parameters: Proper selection of kd and kθ is essential for smooth motion.

• Coordinate Transformations: Converting quaternions to angles is nontrivial.

• Thread Management: Ensuring the control loop and input handling work concurrently.

• Settling Time: In the video you can see that settling time to the goal is high, so in future

we can try PID control where we are able to minimize the settling time without damping.

6 Conclusion

Creating a control node in ROS 2 for TurtleBot3 provides foundational knowledge in mobile robot

control and ROS-based programming. By grasping the concepts of odometry, goal setting, and

error correction with control laws, you’re well on your way to building more complex autonomous

systems in ROS 2.

7 References

1. Turtlebot3

2. ROS2 Wiki 3. Robotics Control Theory

4. Robotics and Control by RK Mittal and IJ Nagrath