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. In its local frame, the robot has sensorial access only to the part of the scene that is within a finite zone of visibility and in direct line of sight. It is required to approach and then circumnavigate the objects, with maintaining a given distance to the currently nearest of them, so that the ideal targeted path is the equidistant curve of the set of the objects. The focus is on the case where this curve cannot be perfectly traced due to excessive contortions and singularities. So the objective is restated as that of automatically finding, approaching and repeatedly tracing an approximation of the equidistant curve that is the best among those trackable by the robot with respecting safety concerns. Though pre-computation of this approximation is a hard problem of computational geometry, we show that autonomously seeking and tracking this approximation can be performed on-the-fly at a miserable computational cost via implementation of the proposed navigation law. This law is hybrid and operates in only a few discrete modes; within any mode, it is reactive, i.e., it directly converts the current observation into the current control. Nonlocal convergence of this law is justified by mathematically rigorous results and is confirmed by computer simulations and real-world experiments. © 2024 Elsevier B.V.