Three-dimensional road models for vehicular minimum-lap-time manoeuvring are typically based on curvilinear coordinates and generalizations of the Frenet–Serret formulae. These models describe the road as a parametrized ‘ribbon’, which can be described in terms of three curvature variables. In this abstraction the road is assumed laterally flat. While this class of road models is appropriate in many situations, this is not always the case. In this research we extend the laterally-flat ribbon-type road model to include lateral curvature. This accommodates the case in which the road camber can change laterally across the track. Lateral-position-dependent camber is introduced as a generalisation that is required for some race tracks. A race track model with lateral curvature is constructed using high-resolution LiDAR measurement data. These ideas are demonstrated on a NASCAR raceway, which is characterized by large changes in lateral camber angle (\(\approx 10^\circ\)) on some parts of the track. A free-trajectory optimization is employed to solve a minimum-lap-time optimal control problem. The calculations highlight the practically observed importance of lateral camber variations.

用于车辆最小圈速机动的三维道路模型通常基于曲线坐标和 Frenet-Serret 公式的推广。这些模型将道路描述为参数化的“带”，可以用三个曲率变量来描述。在这个抽象中，道路被假定为横向平坦的。虽然此类道路模型适用于许多情况，但并非总是如此。在这项研究中，我们将横向平坦的带状道路模型扩展为包括横向曲率。这适应了道路外倾角可以在轨道上横向变化的情况。引入与横向位置相关的外倾角作为某些赛道所需的概括。使用高分辨率 LiDAR 测量数据构建具有横向曲率的赛道模型。\(\approx 10^\circ\) ) 在轨道的某些部分。采用自由轨迹优化来解决最小单圈时间优化控制问题。计算强调了实际观察到的横向外倾角变化的重要性。