Jonathan Brookshire

Non-Degenerate Motion

The following video shows a 2D calibration when the sensors have traveled a non-degenerate path. The red and blue frames are the true positions of sensors r and s, respectively. The magenta frame shows how various calibrations affect the pose of s. On the middle and lower right, two axes show the observed incremental poses. Notice how the expected incremental poses for sensor s (magenta, lower right) only match the observed incremental poses (blue, lower right) when the calibration is correct (i.e., the blue and magenta frames match, upper right).

Degenerate Translation Only

Here, the robot does not rotate. Notice that all the shown calibrations result in the same observations (i.e., the magenta and blue observations in the lower right plot are always the same). In this case, the calibration cannot be recovered. In practice, the robot must rotate to recover the calibration.

Degenerate Concentric Circles

Here, the robot travels such that the sensors travel in concentric circles. Again, all the shown calibrations explain the observations, and the calibration cannot be recovered.

Non-Degenerate Circles

In general, circular motion is non-degenerate, as illustrated here. Only the special case above of concentric circles, is problematic.