A novel path planning and smoothing method for autonomous vehicles at roundabouts

The rapid expansion of Autonomous vehicles (AVs) into urban environments, particularly at roundabout scenarios lacking complete and smooth reference paths, necessitates advanced path generation strategies. Piecewise curve interpolation methods have been utilised for path planning in complex scenarios, but challenges have been faced in ensuring the smoothness at the segmented path connection points and the overall path's fairness. To address these obstacles, this paper introduces a new approach using Non-Uniform Rational B-Splines (NURBS) curves to generate piecewise reference paths at roundabouts. It involves fitting reference paths with known lane centre discrete points and interpolating unknown reference paths based on high-order continuity with connection points of fitted paths. The study employs the Non-dominated Sorting Genetic Algorithm II (NSGA II) for multi-objective optimisation, enhancing path smoothness and fairness. The manuscript validates this method using CitySim data sets, focussing on standard as well as non-standard roundabout scenarios. The results indicate that while polynomial, Bézier and NURBS curves can all generate smooth reference paths, NURBS outperforms the others in fitting and building fair paths. The standard deviation of the curvature change rate of NURBS is reduced by 10.40% compared to Bézier curves and 8.36% compared to polynomial curves, demonstrating a more uniform curvature transition. This research provides a comprehensive and innovative approach for AVs to path planning, smoothing, and fairing, and overcoming the complex geometrical challenges at roundabouts.