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Motion control of vehicles under uncertain, noisy, and discontinuous positioning is essential in autonomous navigation in unknown environments. This article suggests two methods for motion control, where the initial parameters of the on-line control are physically explainable, the resulting trajectory as well as the control parameters are asymptotically converging and glitches in the localization are handled robustly. The differences to a known method based on Lyapunov functions are discussed theoretically as well as in terms of actual motion measurements. Physical experiments with landbound vehicles show the reliability and limitations of these different methods in setups employing static attractors, systematically moving targets and fast, unpredictable moving targets in highly dynamical environments. Mainly due to the physical meaning of the control parameters the adaptation to actual kinematics and dynamics is significantly simplified.