  An underactuated nonholonomic Dubins-vehicle-like robot with a lower-limited
turning radius travels with a constant speed in a plane, which hosts unknown
complex objects. The robot has to approach and then circumnavigate all objects,
with maintaining a given distance to the currently nearest of them. So the
ideal targeted path is the equidistant curve of the entire set of objects. The
focus is on the case where this curve cannot be perfectly traced due to
excessive contortions and singularities. So the objective shapes into that of
automatically finding, approaching and repeatedly tracing an approximation of
the equidistant curve that is the best among those trackable by the robot. The
paper presents some geometric facts that are in demand in research on reactive
tight circumnavigation of group objects in the delineated situation.
