The self-localization of a mobile robot within a known environment, by means of an orientable range finder, is considered. The problem of the determination of the sensor orientation which minimizes the position uncertainty of the mobile robot is addressed. An efficient technique is proposed to determine the optimal sensor exploration, given the current robot position estimate and its uncertainty. Once a tentative exploration is given, the technique avoids to take any worst exploration into account, allowing to efficiently determine the optimal one. Both location accuracy and efficiency have been analyzed in the paper. The time needed to plan the exploration is found to be well below the time needed for the sensor activation. The technique is demonstrated by experimental results on environments containing curvilinear parts.Index Terms-Curvilinear environments, nonlinear environments, odometric navigation, pose estimate updating, range measurements, range scanning, robot navigation, robot selflocalization, sensor exploration, sensor planning, uncertaintydriven exploration, uncertainty minimization.