# On the Structure of the Time-Optimal Path Parameterization Problem with Third-Order Constraints

arXiv: https://arxiv.org/abs/1609.05307 · HTML: https://mlsanity.com/paper/1609.05307/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2016.

## Built on by (most cited first, 1 of 1)

- [Learning Time-optimized Path Tracking with or without Sensory Feedback](https://mlsanity.com/paper/2203.01968/) (2022)

## Abstract (arXiv)

Finding the Time-Optimal Parameterization of a Path (TOPP) subject to second-order constraints (e.g. acceleration, torque, contact stability, etc.) is an important and well-studied problem in robotics. In comparison, TOPP subject to third-order constraints (e.g. jerk, torque rate, etc.) has received far less attention and remains largely open. In this paper, we investigate the structure of the TOPP problem with third-order constraints. In particular, we identify two major difficulties: (i) how to smoothly connect optimal profiles, and (ii) how to address singularities, which stop profile integration prematurely. We propose a new algorithm, TOPP3, which addresses these two difficulties and thereby constitutes an important milestone towards an efficient computational solution to TOPP with third-order constraints.