  In this paper, we present an iterative method to quickly traverse
multi-dimensional paths considering jerk constraints. As a first step, we
analyze the traversal of each individual path dimension. We derive a range of
feasible target accelerations for each intermediate waypoint of a
one-dimensional path using a binary search algorithm. Computing a trajectory
from waypoint to waypoint leads to the fastest progress on the path when
selecting the highest feasible target acceleration. Similarly, it is possible
to calculate a trajectory that leads to minimum progress along the path. This
insight allows us to control the traversal of a one-dimensional path in such a
way that a reference path length of a multi-dimensional path is approximately
tracked over time. In order to improve the tracking accuracy, we propose an
iterative scheme to adjust the temporal course of the selected reference path
length. More precisely, the temporal region causing the largest position
deviation is identified and updated at each iteration. In our evaluation, we
thoroughly analyze the performance of our method using seven-dimensional
reference paths with different path characteristics. We show that our method
manages to quickly traverse the reference paths and compare the required
traversing time and the resulting path accuracy with other state-of-the-art
approaches.
