Robotics Math Basics

This mini-project is part of my daily robotics and autonomous systems learning practice.

It implements the core 2D math utilities used everywhere in robotics:

• Degrees ↔ radians conversion
• 2D rotation matrices
• Rotating a point in space
• Translation (shifting a point)
• Combining rotation + translation → 2D transform
• Composing two transforms (frame chaining)

The demos are shown in main.py.

---

📂 Project Structure

robotics-math-basics/
│
├── robotics_math.py — Core robotics math utilities
├── main.py — Demo / usage examples
└── README.md

---

🚀 How to Run

Requirements: Python 3.x

Run the demo:

python main.py

---

🔥 Key Concepts Learned

1️⃣ Degrees vs Radians

Humans use degrees.
Robots and mathematics use radians because trigonometry becomes smooth and natural.

Conversion formulas:

degrees → radians = deg × π / 180 radians → degrees = rad × 180 / π

---

2️⃣ Rotation (changing direction)

Rotation changes direction, not position.

Example:
Point (1, 0) rotated 45° → (0.707, 0.707)

---

3️⃣ Rotation Matrix

A rotation matrix is a tool that rotates a point in 2D:

[ cosθ −sinθ ] [ sinθ cosθ ]

Multiplying this matrix by a point rotates the point in space.

---

4️⃣ Translation (changing position)

Translation changes position, not direction.

Example:
(x, y) translated by (2, 1) → (x + 2, y + 1)

---

5️⃣ Rotation + Translation = Transform

When you rotate first and then translate, you get a 2D transform:

orientation + position = robot pose rotation + translation = transform

This is how robots represent where they are.

---

6️⃣ Coordinate Frames (why transforms matter)

Robots never work in a single coordinate system.

Examples:

• map → world reference
• odom → wheel-based motion estimation
• base_link → robot body center
• camera → camera location
• gripper → end-effector

To convert points between frames:

• apply a transform (rotation + translation)
• Apply the inverse of the transform from the target frame to the source frame.
• Apply the transform from the source frame to the target frame.

This mathematical concept is the foundation of:

• ROS2 tf2
• SLAM
• Odometry
• Navigation
• EKF
• Kinematics

---

📌 Why This Repo Matters

This project helped me understand:

• How robots represent direction and movement
• How rotation and translation combine into a transform
• How coordinate frames relate to each other in robotics

These fundamentals support every robotics topic I will learn next.

---

📚 References

• Robotics: Modelling, Planning and Control
• Robot Operating System (ROS) Tutorials