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

Geometric Facts Underlying Algorithms of Robot Navigation for Tight Circumnavigation of Group Objects through Singular Inter-Object Gaps