Transform Velocity data from sensor frame to world frame

Question

I am new to Robotics and transformation topics. I need help in understanding and solving the below problem.

1. I have data (surrounding obstacle position, orientation and velocity) which are in sensor frame. Basically it gives the relative speed of the surrounding obstacles (v_rx, v_ry)
2. I have converted the obstacle position and orientation to UTM coordinates (WCS) using Translation and Rotation matrix.
3. How the velocity can be converted to WCS if the received data (Vx, Vy, Vz) is in sensor frame?

Thank you,
KK

Answer 1

You can use the rotation matrix.

linear_v= R*sensor_linear_v + p X sensor_angular_v p is the translation vector and the X is the cross operator

angular_v=R*sensor_angular_v