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Lyapunov-based two-dimensional cruise control of autonomous vehicles on lane-free roads

Karafyllis Iason, Theodosis Dionysios, Papageorgiou Markos

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Summary

In this paper, we design decentralized control strategies for the two-dimensional movement of autonomous vehicles on lane-free roads. The behavior of the autonomous vehicles resembles that of self-driven particles that individually produce their driving force and steering, while interacting with each other, giving rise to an emerging particle traffic flow. 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 state and on the relative displacement vector from other (adjacent) vehicles and the boundary of the road. The resulting control system is nonlinear and evolves on a specific open set. Therefore, the feedback design is challenging and is accomplished by means of a control Lyapunov function methodology. Potential functions and Barbălat’s lemma are employed to prove the following properties, which are ensured by the proposed nonlinear 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.

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