A constant-speed nonholonomic robot should pass through an unstructured and unknown 3D tunnel-like cave environment. The sensors provide information about the nearest point of tunnel's surface and the distance to the surface along any ray going from the robot at an upper-limited angle with respect to the direction toward the nearest point. A new navigation law is presented that solves the mission, respects a given safety margin to the surface, drives the robot to the pre-specified distance to it, and then maintains this distance. This law generates the control as a reflex-like reaction to the current observation. Mathematically rigorous justification of this law is provided; its applicability is confirmed by computer simulation tests.