We introduce a new control law for robots that explore unknown environments and configuration spaces. Unlike numerical continuation methods, which produce a jagged path because of the predictor-corrector approach, the control law, introduced in this paper, performs sensor based planning by directing the head of a robot to follow continuously a roadmap. Recall that a roadmap is a one-dimensional representation of a robot's environment. Once the robot exhaustively traces out the roadmap using this control law, it has in essence explored an environment. Experiments on a mobile robot validate the control law.