We propose an online planning approach for racing that generates the time-optimal trajectory for the upcoming track section. The resulting trajectory takes the current vehicle state, effects caused by \acl{3D} track geometries, and speed limits dictated by the race rules into account. In each planning step, an optimal control problem is solved, making a quasi-steady-state assumption with a point mass model constrained by gg-diagrams. For its online applicability, we propose an efficient representation of the gg-diagrams and identify negligible terms to reduce the computational effort. We demonstrate that the online planning approach can reproduce the lap times of an offline-generated racing line during single vehicle racing. Moreover, it finds a new time-optimal solution when a deviation from the original racing line is necessary, e.g., during an overtaking maneuver. Motivated by the application in a rule-based race, we also consider the scenario of a speed limit lower than the current vehicle velocity. We introduce an initializable slack variable to generate feasible trajectories despite the constraint violation while reducing the velocity to comply with the rules.

翻译：我们提出一种面向赛车的在线规划方法，可生成即将行驶赛道段的时间最优轨迹。所得轨迹综合考虑当前车辆状态、三维赛道几何结构引起的效应以及比赛规则限定的速度限制。在每个规划步骤中，通过求解一个最优控制问题，采用基于gg图约束的质点模型进行准稳态假设。为实现在线实时应用，我们提出gg图的高效表示方法，并通过识别可忽略项来降低计算复杂度。实验表明，在单车竞赛场景下，该在线规划方法可复现离线生成赛车线的单圈时间。当需要偏离原始赛车线时（例如超车操作），该方法能计算出新的时间最优解。针对基于规则的赛事场景，我们还考虑了车速高于规则限速的特殊情况，通过引入可初始化的松弛变量，在满足约束违规时生成可行轨迹，同时将车速降至合规范围。