Constructing Artificial Traffic Fluids by Designing Cruise Controllers

Abstract

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.

Optimal Path Planning for Connected and Automated Vehicles in Lane-free Traffic

“…It is interesting to note that the consideration of a safety gap not only in front, but also behind the ego vehicle is creating a longitudinal "nudging" to the ego vehicle due to a moving obstacle behind it. More generally, due to this gap, vehicle driving is not influenced only by obstacles in front, as in manual driving or in most lanebased automated vehicle concepts, but also by obstacles behind them, something that gives rise to structurally new traffic flow characteristics at the macroscopic level [27], [37]. • Due to the different length of the safety gaps in front and behind the ego vehicle, which depend on the ego vehicle speed and the following obstacle speed, respectively, the positioning of the centre of the symmetric ellipsoid in the longitudinal direction depends on the speed difference of the ego and obstacle vehicles.…”