  In this paper, we design decentralized control strategies for the
two-dimensional movement of autonomous vehicles on lane-free roads. The bicycle
kinematic model is used to model the dynamics of the vehicles, and each vehicle
determines its control input based only on its own speed and on the distance
from other (adjacent) vehicles and the boundary of the road. Potential
functions and Barbalat's lemma are employed to prove the following properties,
which are ensured by the proposed controller: (i) the vehicles do not collide
with each other or with the boundary of the road; (ii) the speeds of all
vehicles are always positive, i.e., no vehicle moves backwards at any time;
(iii) the speed of all vehicles remain below a given speed limit; (iv) all
vehicle speeds converge to a given longitudinal speed set-point; and (v) the
accelerations, lateral speeds, and orientations of all vehicles tend to zero.
The efficiency of the proposed 2-D cruise controllers is illustrated by means
of numerical examples.
