Optimal orientation for automated vehicles on large lane-free roundabouts

Path planning for vehicles on large, complex, lane-free roundabouts is challenging due to the geometrical features and frequent conflicts among entering, navigating, and exiting vehicles. A key difficulty is to properly determine the desired vehicle orientations on the roundabout so that vehicles enter the roundabout and move towards their corresponding exits smoothly and safely. Specification of vehicle orientations should consider the resulting trip distance, the angle difference from other vehicles, and the exploitation of the available roundabout surface for efficient traffic flow. This paper proposes an optimal control approach to determine optimal vehicle orientations at each point on the roundabout, in dependence of the exit branch, so as to minimize a weighted sum of the trip distance and the deviation from the circular motion. Analytical solutions for two extreme cases, addressing only the shortest path or only the minimum deviation from the circular angle, respectively, are derived. For the general weighted problem solution, a Dynamic Programming-based (backward Dijkstra) algorithm is employed to deliver the optimal orientations in a 2-D space-discretized grid of the roundabout surface. In the light of the optimal solution, a computationally light near-optimal approach is also proposed. As a challenging case study, the methods are applied to the famous roundabout of Place Charles de Gaulle in Paris, which features a road width of 38 m and comprises 12 bidirectional radial streets, hence a total of 144 origin-destination movements for the vehicles.