The article considers the problem of moving and stabilizing underactuated wheeled robot on the visual curve in the motion plane. The curve is detected by the video camera mounted on the robot. The task is solved with the help of the approach named visual servoing which uses the visual information in the feedback. The aim of the visual serving is to minimize the difference between desired and the actual position of the set of the points on the image. The main feature of the proposed solution is considering a number of requirements to the robot’s dynamic including the reaction on the presence of the external disturbances. Thereby the regulators of special kind called multipurpose structure are used which makes possible to decompose the basic set of requirements into smaller independent tasks. Additional complication is the underactuated nature of the considered robot. Efficiency of the derived regulator is shown through the experiments with computer model.