Time-Optimal Control for High-Order Chain-of-Integrators Systems with Full State Constraints and Arbitrary Terminal States (Extended Version)
Abstract
Time-optimal control for high-order chain-of-integrators systems with full state constraints and arbitrarily given terminal states remains a challenging problem in the optimal control theory domain, yet to be resolved. To enhance further comprehension of the problem, this paper establishes a novel notation system and theoretical framework, providing the switching manifold for high-order problems in the form of switching laws. Through deriving properties of switching laws regarding signs and dimension, this paper proposes a definite condition for time-optimal control. Guided by the developed theory, a trajectory planning method named the manifold-intercept method (MIM) is developed. The proposed MIM can plan time-optimal jerk-limited trajectories with full state constraints, and can also plan near-optimal non-chattering higher-order trajectories with negligible extra motion time compared to optimal profiles. Numerical results indicate that the proposed MIM outperforms all baselines in computational time, computational accuracy, and trajectory quality by a large gap.
Keywords
Cite
@article{arxiv.2311.07039,
title = {Time-Optimal Control for High-Order Chain-of-Integrators Systems with Full State Constraints and Arbitrary Terminal States (Extended Version)},
author = {Yunan Wang and Chuxiong Hu and Zeyang Li and Shize Lin and Suqin He and Yu Zhu},
journal= {arXiv preprint arXiv:2311.07039},
year = {2024}
}