Jerk-limited Traversal of One-dimensional Paths and its Application to Multi-dimensional Path Tracking

TL;DR

This paper introduces an iterative method for fast, jerk-limited traversal of multi-dimensional paths, improving tracking accuracy by adjusting temporal path parameters, and demonstrates its effectiveness on high-dimensional paths.

Contribution

The paper presents a novel iterative approach for multi-dimensional path traversal that optimizes speed and accuracy under jerk constraints, with detailed analysis and comparison to existing methods.

Findings

Method achieves faster traversal times.

Improves path tracking accuracy.

Effective on seven-dimensional paths.

Abstract

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.