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.

Jerk-constrained trajectories offer a wide range of advantages that collectively improve the performance of robotic systems, including increased energy efficiency, durability, and safety. In this paper, we present a novel approach to jerk-constrained time-optimal trajectory planning (TOTP), which follows a specified path while satisfying up to third-order constraints to ensure safety and smooth motion. One significant challenge in jerk-constrained TOTP is a non-convex formulation arising from the inclusion of third-order constraints. Approximating inequality constraints can be particularly challenging because the resulting solutions may violate the actual constraints. We address this problem by leveraging convexity within the proposed formulation to form conservative inequality constraints. We then obtain the desired trajectories by solving an $\boldsymbol n$-dimensional Sequential Linear Program (SLP) iteratively until convergence. Lastly, we evaluate in a real robot the performance of trajectories generated with and without jerk limits in terms of peak power, torque efficiency, and tracking capability.