Coordinate Frames 2D — Robotics TF Simulation

This mini-project is part of my daily robotics and autonomous systems learning practice.
It implements a simple 2D simulation of robot coordinate frames and transform chaining using pure Python:

• map → odom → base_link → camera frame chain
• A robot moving in the map frame
• A camera mounted on the robot (base_link → camera)
• A ball detected in the camera frame, converted to the map frame
• Real-time 2D visualization using matplotlib

This is a minimal, ROS-free version of what tools like ROS2 TF and RViz do with transforms.

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🎬 Coordinate Frames 2D Simulation (Animation Preview)

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📂 Project Structure

coordinate-frames-2d/ │

├── frames_math.py # Core 2D rotation + transform + composition utilities

├── sim_frames.py # Main simulation + visualization (map, odom, base_link, camera, ball)

└── README.md

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🚀 How to Run

Requirements:

• Python 3.x
• matplotlib

Install:

• pip install matplotlib

Run:

• python sim_frames.py

You will see:

• map origin (black)
• odom origin (blue)
• base_link origin (red)
• camera origin (green)
• ball shown in the global map frame (yellow)
• Colored axes showing each frame’s orientation over time

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🔧 Core Math Concepts (used in this project)

Rotation Matrix [ R(\theta) = \begin{bmatrix} \cos\theta & -\sin\theta \ \sin\theta & \cos\theta \end{bmatrix} ]

Apply Transform [ p' = R p + t ]

Compose Transforms [ (R_1, t_1) \circ (R_2, t_2) = (R_1 R_2, ; R_1 t_2 + t_1) ]

These are the same operations used in SLAM, TF2, odometry, and kinematics — here implemented in clear 2D.

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🧠 What the Code Actually Does (in simple words)

1️⃣ Robot pose updated in the map frame

The robot moves a little forward and rotates slightly each frame:

• robot_theta += omega
• robot_x += v * cos(robot_theta)
• robot_y += v * sin(robot_theta)

→ simulates wandering motion.

2️⃣ Building the transform chain

• map → odom (identity in this project)
• odom → base_link (robot’s pose)
• base_link → camera (camera mounted on robot)
• Composed to get:
• map → base_link → map → camera (robot’s pose + camera’s pose)
• map → camera (robot’s pose + camera’s pose)

3️⃣ Convert ball from CAMERA frame → MAP frame

Ball is defined relative to the camera:

• p_ball_camera = (0.6, -0.2) Robot needs it in map frame:
• p_map = R_map_camera * p_ball_camera + t_map_camera This is exactly what real navigation stacks need for planning.

4️⃣ Visualization

• Each frame origin drawn as a point
• Each frame axes drawn using columns of the rotation matrix
• A yellow dashed line from camera to ball shows the camera ray

You literally see transforms, not just compute them.

🔍 What this code does step-by-step

• p_ball_camera is the direction to the ball as seen by the camera.
• We transform that direction into the map frame using R_map_camera only (no translation).
• This gives us a point in the map frame that lies along the camera’s viewing direction.
• We draw a yellow dashed line from the camera origin toward that transformed direction.
• Visually, that dashed ray tells us:
  “The camera is looking in this direction — and the ball lies somewhere along this ray.”

The ball marker (yellow circle) is the true ball position in the map.
The dashed line is the visual cone / ray — like what real robots draw.

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🧩 What I Learned from Building This

From this simulation I now clearly understand:

✔ How to model a robot pose as (x, y, θ) in the world (map frame).

✔ How to build a full frame chain using transforms:

• map → odom → base_link → camera

✔ How to compose transforms to compute new frames:

• map → camera = (map → base_link) ∘ (base_link → camera)

✔ How to transform a sensor point into world coordinates:

• p_map = R_map_camera * p_camera + t_map_camera

✔ How a camera “ray” is just a direction vector rotated into the global frame.

✔ How to use matplotlib + FuncAnimation to visualize moving frames and transforms in 2D.

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🔥 Why This Matters in Real Robotics

This knowledge directly applies to:

• ROS2 TF trees
• RViz frame visualization
• SLAM and localization
• Odometry correction
• Camera / LiDAR object detection to world mapping
• Navigation and motion planning

In real robots:

• Sensors speak in their own frame
• Control & planning require the map frame
• TF converts between them using exactly the math built in this project

This simulation is a visible and simplified version of TF2, helping me understand transforms at a mathematical and conceptual level before working with ROS2.

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