Homework 4: Coordinate Transformations

A point has been measured in the lidar sensor coordinate system as

\[\begin{split}^{lid}P_{1} = \begin{bmatrix} 2.7 \\ -1.5 \\ 23.1 \end{bmatrix} \; \text{m}\end{split}\]

The lidar coordinate system is initially aligned with the vehicle coordinate system. Its origin is translated to the point

\[\begin{split}^{veh}P_{lid0} = \begin{bmatrix} 4.0 \\ 0.0 \\ 0.8 \end{bmatrix} \; \text{m}\end{split}\]

It is then rotated \(85^\circ\) about its Y axis followed by \(10^\circ\) about its modified X axis.

The vehicle coordinate system is initially aligned with a fixed world coordinate system. Its origin is translated to the point

\[\begin{split}^{F}P_{veh0} = \begin{bmatrix} 200.0 \\ 185.4 \\ 0.25 \end{bmatrix} \; \text{m}\end{split}\]

It is then rotated \(75^\circ\) about its Z axis.

Deliverables

Determine the coordinates of point 1 in the fixed world coordinate system. Show your work either handwritten or through a Python script.

A brief powerpoint on the subject, can be found on the class website.

TODO briefly explain the math