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

Abstract

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.

8 pages, 6 figures, ICRA 2017

References in corpus (1)

• A General, Fast, and Robust Implementation of the Time-Optimal Path Parameterization Algorithm

Cited by in corpus (4)

• A Dynamic Programming Framework for Optimal Planning of Redundant Robots Along Prescribed Paths With Kineto-Dynamic Constraints
• On the Performance of Jerk-Constrained Time-Optimal Trajectory Planning for Industrial Manipulators
• When to make a step? Tackling the timing problem in multi-contact locomotion by TOPP-MPC
• A sequential approach for speed planning under jerk constraints