A temporal rigid geometry has no similarity distance of its own. Comparing two poses combines a difference of positions with a difference of orientations, which needs a length a pose does not carry, and the distances a rigid body admits, such as the Hausdorff distance of the placed shapes, the largest displacement of a point of the body or the area of their symmetric difference, order pairs of values differently. The trajectories of the reference points of two temporal rigid geometries, the origins of their local frames, are compared with the similarity functions of temporal points over their conversion to tgeompoint.
Compare the trajectories of the reference points of two temporal rigid geometries
SELECT round(frechetDistance(
tgeompoint(trgeometry 'Polygon((0 0,1 0,1 1,0 1,0 0));
[Pose(Point(0 0),0)@2001-01-01, Pose(Point(2 0),0)@2001-01-03]'),
tgeompoint(trgeometry 'Polygon((0 0,1 0,1 1,0 1,0 0));
[Pose(Point(0 0),0)@2001-01-01, Pose(Point(0 2),0)@2001-01-03]')), 6);
-- 2.828427