The computation of time-optimal velocity profiles along prescribed paths, subject to generic acceleration constraints, is a crucial problem in robot trajectory planning, with particular relevance to autonomous racing. However, the existing methods either support arbitrary acceleration constraints at high computational cost or use conservative box constraints for computational efficiency. We propose FBGA, a new \underline{F}orward-\underline{B}ackward algorithm with \underline{G}eneric \underline{A}cceleration constraints, which achieves both high accuracy and low computation time. FBGA operates forward and backward passes to maximize the velocity profile in short, discretized path segments, while satisfying user-defined performance limits. Tested on five racetracks and two vehicle classes, FBGA handles complex, non-convex acceleration constraints with custom formulations. Its maneuvers and lap times closely match optimal control baselines (within $0.11\%$-$0.36\%$), while being up to three orders of magnitude faster. FBGA maintains high accuracy even with coarse discretization, making it well-suited for online multi-query trajectory planning. Our open-source \texttt{C++} implementation is available at: https://anonymous.4open.science/r/FB_public_RAL.

翻译：在给定路径上计算时间最优速度剖面，同时满足通用加速度约束，是机器人轨迹规划中的一个关键问题，在自主竞速领域尤为重要。然而，现有方法要么以高计算成本支持任意加速度约束，要么为了计算效率而采用保守的箱型约束。我们提出了FBGA，一种具有通用加速度约束的新型前向-后向算法，它同时实现了高精度和低计算时间。FBGA通过前向和后向传递，在短离散化路径段上最大化速度剖面，同时满足用户定义的性能限制。在五条赛道和两类车辆上的测试表明，FBGA能够处理具有自定义公式的复杂非凸加速度约束。其机动轨迹和圈速与最优控制基准线高度吻合（误差在$0.11\%$-$0.36\%$以内），同时计算速度提升了高达三个数量级。即使采用粗离散化，FBGA仍能保持高精度，使其非常适合在线多查询轨迹规划。我们的开源\texttt{C++}实现可在以下网址获取：https://anonymous.4open.science/r/FB_public_RAL。