This paper presents a new motion planning primitive to be used for the iterative steering of vision-based autonomous vehicles. This primitive is a parameterized quintic spline, denoted as n-spline, that allows interpolating an arbitrary sequence of points with overall second-order geometric continuity. Issues such as completeness, minimality, regularity, symmetry, and flexibility of these 2 -splines are addressed in the exposition. The development of the new primitive is tightly connected to the inversion control of nonholonomic car-like vehicles. The paper also exposes a supervisory strategy for iterative steering that integrates feedback vision data processing with the feedforward inversion control.