ABSTRACT

A method to solve minimum-lap-time problems using quasi-steady-state models and free (i.e. not predetermined) trajectory on two-dimensional tracks has been recently proposed. This work describes the extension of the method to three-dimensional tracks and builds upon g–g–g diagrams (instead of the standard g–g), to account for the effects of three-dimensionality. The main features of car and motorcycle g–g–g diagrams are discussed, to get insight into the main effects of three-dimensionality and to suggest a convenient parametrisation for the subsequent optimal control problem (OCP), whose size is not affected by the complexity of the vehicle model employed to generate the g–g–g diagrams. The application of the method to the Mugello and Barcelona–Catalunya circuits is given, with vehicle datasets resembling those of a race motorcycle (MotoGP) and a race car (Formula One). The results obtained are in line with those reported in the literature using full-dynamic models, yet such dynamic models are generally associated with the solution of much larger OCP.

摘要

最近提出了一种使用准稳态模型和二维轨道上的自由（即非预定）轨迹来解决最小单圈时间问题的方法。这项工作描述了该方法对三维轨道的扩展，并建立在 g-g-g 图（而不是标准 g-g）的基础上，以考虑三维度的影响。讨论了汽车和摩托车 g-g-g 图的主要特征，以深入了解三维的主要影响，并为随后的最优控制问题 (OCP) 提出方便的参数化，其大小不受用于生成 g-g-g 图的车辆模型的复杂性。给出了该方法在穆杰罗和巴塞罗那-加泰罗尼亚赛道上的应用，具有类似于赛车（MotoGP）和赛车（一级方程式）的车辆数据集。获得的结果与文献中使用全动态模型报告的结果一致，但这种动态模型通常与更大的 OCP 的解决方案相关联。