A nonholonomic constant speed underactuated robot with a bounded control range travels in three dimensions. A group of targets unpredictably moves in all three dimensions. The robot measures only the distances to the targets and also has access to a certain spatial direction and its own coordinate (termed 'altitude') along it. We present a new navigation law that drives the robot to the locus of points at a prespecified root-mean-square distance from the targets and ensures dense sweep coverage of this locus within a given range of 'altitudes.' This law is rigorously justified by a nonlocal convergence result supported by recommendations on controller tuning; its applicability and performance are confirmed by extensive computer simulations.