  We propose a global constructibility analysis for a vehicle moving on a
planar surface. Assuming that the vehicle follows a trajectory that can be
uniquely identified by the sequence of control inputs and by some intermittent
ranging measurements from known points in the environment, we can model the
trajectory as a rigid body subject to rotation and translation in the plane.
This way, the localisation problem can be reduced to finding the conditions for
the existence of a unique roto-translation of the trajectory from a known
reference frame to the world reference frame, given the collected measurements.
As discussed in this paper, such conditions can be expressed in terms of the
shape of the trajectory, of the layout of the ranging sensors, and of the
numbers of measurements collected from each of them. The approach applies to a
large class of kinematic models. Focusing on the special case of unicycle
kinematics, we provide additional local constructibility results.
