Time-Optimal Control for High-Order Chain-of-Integrators Systems with Full State Constraints and Arbitrary Terminal States (Extended Version)
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914966058041344 |
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| author | Wang, Yunan Hu, Chuxiong Li, Zeyang Lin, Shize He, Suqin Zhu, Yu |
| author_facet | Wang, Yunan Hu, Chuxiong Li, Zeyang Lin, Shize He, Suqin Zhu, Yu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07039 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Time-Optimal Control for High-Order Chain-of-Integrators Systems with Full State Constraints and Arbitrary Terminal States (Extended Version) Wang, Yunan Hu, Chuxiong Li, Zeyang Lin, Shize He, Suqin Zhu, Yu Systems and Control 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. |
| title | Time-Optimal Control for High-Order Chain-of-Integrators Systems with Full State Constraints and Arbitrary Terminal States (Extended Version) |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2311.07039 |