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In this paper, we design decentralized control strategies for thetwo-dimensional movement of autonomous vehicles on lane-free roads. The bicyclekinematic model is used to model the dynamics of the vehicles, and each vehicledetermines its control input based only on its own speed and on the distancefrom other (adjacent) vehicles and the boundary of the road. Potentialfunctions and Barbalat's lemma are employed to prove the following properties,which are ensured by the proposed controller: (i) the vehicles do not collidewith each other or with the boundary of the road; (ii) the speeds of allvehicles 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) allvehicle speeds converge to a given longitudinal speed set-point; and (v) theaccelerations, lateral speeds, and orientations of all vehicles tend to zero.The efficiency of the proposed 2-D cruise controllers is illustrated by meansof numerical examples.

Two-Dimensional Cruise Control of Autonomous Vehicles on Lane-Free Roads