We prove the existence of a P-type (proportional-type) space-learning control, which, on the basis of a kinematic third order nonlinear model of an autonomous nonholonomic vehicle and by a proper choice of the proportional control gain, guarantees asymptotic tracking of planar curves whose uncertain curvature is L-periodic in the curvilinear abscissa. The behavior of a human driver, who repetitively learns the correct action from the past experience in the space, is mathematically reproduced. A stability analysis is presented while simulation results demonstrate the effectiveness of the presented approach. (C) 2014 Elsevier Ltd. All rights reserved.