  In this paper, we apply a Control Lyapunov Function methodology to design two
families of cruise controllers for the two-dimensional movement of autonomous
vehicles on lane-free roads using the bicycle kinematic model. The control
Lyapunov functions are based on measures of the energy of the system with the
kinetic energy expressed in ways similar to Newtonian or relativistic
mechanics. The derived feedback laws (cruise controllers) are decentralized, as
each vehicle determines its control input based on its own speed and on the
relative speeds and distances from adjacent vehicles and from the boundary of
the road. Moreover, the corresponding macroscopic models are derived, obtaining
fluid-like models that consist of a conservation equation and a momentum
equation with pressure and viscous terms. Finally, we show that, by selecting
appropriately the parameters of the feedback laws, we can determine the
physical properties of the "traffic fluid", i.e. we get free hand to create an
artificial fluid that approximates the emerging traffic flow.
