Spherical fuzzy Bézier curve approximation for efficient lane-changing trajectories under uncertain data

In real-world problems, acquiring precise information can be challenging, as data points often exhibit vagueness, imprecision, or uncertainty. Dealing with uncertain data, which involves intricate processes due to incomplete information, poses difficulties. This paper presents a spherical fuzzy Bézier curve (SfBC) model for computer-aided geometric design (CAGD) to tackle uncertain data, especially in the context of vehicle lane-changing trajectories. Unlike existing methods that assume exact data and overlook obstacles or uncertainty, SfBC employs spherical fuzzy point relations and control point relations are defined using fuzzy set theory to achieve superior uncertainty modeling and adaptability. An SfBC, illustrated in a lane-changing scenario, produces adaptive, obstacle-avoiding trajectories that outperform crisp Bézier models. Visualization of spherical fuzzy Bézier surfaces (SfBS) is also provided in this paper. The de Casteljau algorithm efficiently calculates curve points, and a dynamic method for trajectory planning improves adaptability. This model demonstrates superior performance compared to traditional crisp Bézier methods, providing valuable solutions for automotive design, 3D modeling, and animation.