Determination of image transformations from lidar

Question

Do it yourself

Hello.

I have a lidar that scans in a circle in the same plane, along which a certain robot will navigate (assuming, however, that there is no odometric data). From the lidar, we get an array consisting of azimuths and distances to a point in the corresponding direction. Further, using simple trigonometry, the data is converted to a rectangular coordinate system.

I have a need, comparing two consecutive measurements, to determine the rotation and movement of the lidar relative to a stationary environment.

I have a question for the public: what algorithms can be used for this, are there open implementations of such algorithms, or at least where can I read about it?