Trajectory retiming is the task of computing a feasible time parameterization to traverse a path. It is commonly used in the decoupled approach to trajectory optimization whereby a path is first found, then a retiming algorithm computes a speed profile that satisfies kino-dynamic and other constraints. While trajectory retiming is most often formulated with the minimum-time objective (i.e. traverse the path as fast as possible), it is not always the most desirable objective, particularly when we seek to balance multiple objectives or when bang-bang control is unsuitable. In this paper, we present a novel algorithm based on factor graph variable elimination that can solve for the global optimum of the retiming problem with quadratic objectives as well (e.g. minimize control effort or match a nominal speed by minimizing squared error), which may extend to arbitrary objectives with iteration. Our work extends prior works, which find only solutions on the boundary of the feasible region, while maintaining the same linear time complexity from a single forward-backward pass. We experimentally demonstrate that (1) we achieve better real-world robot performance by using quadratic objectives in place of the minimum-time objective, and (2) our implementation is comparable or faster than state-of-the-art retiming algorithms.

翻译：轨迹重定时是计算一条路径的可通行时间参数化的任务。它常用于轨迹优化的解耦方法中：首先找到一条路径，然后通过重定时算法计算满足运动学和动力学及其他约束的速度曲线。虽然轨迹重定时通常以最小时间目标（即尽可能快地通过路径）来构建，但这并不总是最理想的目标，尤其是在需要平衡多个目标或当 bang-bang 控制不适用时。本文提出了一种基于因子图变量消除的新算法，该算法能够求解具有二次目标（例如，通过最小化平方误差来最小化控制代价或匹配标称速度）的重定时问题的全局最优解，并且可以通过迭代扩展到任意目标函数。我们的工作扩展了现有方法，这些方法仅能找到可行域边界上的解，同时保持了单次前向-后向遍历的线性时间复杂度。我们通过实验证明：（1）使用二次目标替代最小时间目标可以在实际机器人任务中获得更优性能；（2）我们的实现与最先进的重定时算法相比性能相当或更快。