How do I combine multiple transformations and compute the relative pose?

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I have the following configuration:

  • Sensor A which gives me at every point in time t a 3D translation vector and a rotation matrix: (R|T)_A_t relative to a static origin
  • Sensor B. The position of sensor B relative to sensor A does not change in time and is statically defined by the rotation and translation matrix: (R|T)_A_to_B
    • Meaning both sensors move together (mounted on the same vehicle)

I compute the relative pose from Sensor A at time t to time 0 like that: (R|T)_A_0_to_t = inverse( (R|T)_A_0 ) * (R|T)_A_t

But how do I get now the relative pose from Sensor B at time t to Sensor A at time 0? Meaning (R|T)_B_0_to_t?