I have a robot (gray box in the picture) that I can rotate in 3D (x, y, z) relative to a center of rotation.
Let's say that this robot has two sensors with fixed poses in the robot:
- One IMU that can measure an angular velocity and acceleration
- One sensor that can measure a velocity Both sensors send values in their own coordinate frame. The center of mass is not know
The goal is to find the pose (position and rotation) of the velocity sensor relative to the IMU.
By rotating the robot with a constant angular velocity, I can find the radius vector of the IMU relative to the center of rotation. Since every point in a rigid body has the same angular velocity, I can use the angular velocity measured by the IMU to find the radius of the other sensor (with the formula of the angular velocity ). So in the end I can find the position of the center of rotation relative to both sensors in their own coordinate frame.