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2.4 The Relativity of Space

Stage II: The Graph

"Where am I? The answer depends entirely on who you ask."

1. The Transform Tree (TF)​

The robot is a collection of rigid bodies connected by joints. Every sensor measures data in its own coordinate frame.

  • Camera Frame: Z is forward (Optical).
  • Base Frame: X is forward (Mechanical).
  • Map Frame: Inertial World Frame.

The Problem: If the Camera sees an obstacle at (3, 0, 1), where is that obstacle relative to the Wheels? The Solution: The Transform Tree. A distributed graph of frame relationships published by robot_state_publisher.

$$ ^{base}P = ^{base}T_{camera} \times ^{camera}P $$

2. Standard Frames (REP-105)​

To make robots interoperable, we agree on a standard hierarchy:

  1. map: Fixed world frame. Z points up. Discontinuous (can jump if loop closure happens). Use for long-term planning.
  2. odom: Continuous world frame. Smooth local navigation. Drifts over time. Use for PID control.
  3. base_link: The robot's center of mass.
  4. sensor_link: Attached to the robot.

The Golden Rule:

  • Localization: Computes map $\to$ odom.
  • Odometry: Computes odom $\to$ base_link.
  • State Publisher: Computes base_link $\to$ sensor_link.

3. Time Travel (The Buffer)​

TF is not just spatial; it is temporal. "Where was the camera relative to the map 50ms ago when this image was taken?"

The tf2_ros buffer stores the last 10 seconds of transforms. When you ask for a transform, you must specify the Time. buffer.lookup_transform("map", "camera", time_of_image)

If you ask for Time.now(), you will fail. Why? Because Time.now() hasn't happened yet in the TF buffer (latency). You must ask for Time(0) (latest available) or specific timestamp.

Deep FAQ​

Q: Why does my TF tree break? A: It usually breaks because of Timestamp Mismatch. If your computer clock and the robot clock drift by 1 second, TF will reject lookups as "Extrapolation into the Future". Use Chrony/NTP to sync clocks.

Q: Static vs. Dynamic Transforms? A:

  • Static: Camera mount on chassis. Never moves. Published once (latched).
  • Dynamic: Wheel rotation, Arm joint. Moves constantly. Published at 50Hz.