Sampled-Data Controllers for Autonomous Vehicles on Lane-Free Roads

In this paper, we design decentralized control strategies (per vehicle) for the two-dimensional movement of autonomous vehicles on lane-free roads, where each vehicle determines its control input based on its own state and the relative speeds and distances from adjacent vehicles and from the boundaries of the road. It is shown that the vehicles do not collide with each other or with the road boundaries, and all vehicle speeds converge to a given longitudinal speed set-point. Moreover, we present sufficient conditions for the emulated (sampled-data) controllers that ensure collision avoidance between vehicles and with the road boundaries, as well as speed positivity, bounded speed and bounded orientation of the vehicles. Finally, we numerically investigate the maximum allowable sampling period and present periodic and non-periodic sampling algorithms where each vehicle has its own sampling period.