A non-holonomic under-actuated planar robot is propelled via interaction of its actuators with a dynamic surrounding medium; a control input is the angular velocity of robot’s self-rotation relative to the medium. Meanwhile, the motion of the medium is unknown and unpredictable; the relative surge speed is time-varying and treated as uncertain. There is an unpredictably varying scalar environmental field. From a remote initial location, the robot should reach the isoline where the field assumes a pre-specified value, and then should repeatedly run its length. Robot measures only the field value at the current location and has no access to the field gradient or parameters of the medium motion. To solve this task, at first conditions are established that are necessary for the mission to be feasible with the given limitations on the robot’s dynamics. Then a navigation law is presented that solves the mission under slight and partly unavoidable enhancement of these conditions. This law is computationally inexpensive and directly converts the current sensory data into the current control in a reflex-like fashion. The performance of the law is rigorously justified by a global convergence result and is confirmed via computer simulation tests.