Abstract:Time-optimal control for triple integrator under full box constraints is a fundamental problem in the field of optimal control, which has been widely applied in the industry. However, scenarios involving asymmetric constraints, non-stationary boundary conditions, and active position constraints pose significant challenges. This paper provides a complete characterization of time-optimal switching surfaces for the problem, leading to novel insights into the geometric structure of the optimal control. The active condition of position constraints is derived, which is absent from the literature. An efficient algorithm is proposed, capable of planning time-optimal trajectories under asymmetric full constraints and arbitrary boundary states, with a 100% success rate. Computational time for each trajectory is within approximately 10$\mu$s, achieving a 5-order-of-magnitude reduction compared to optimization-based baselines.
| Comments: | This paper has been accepted by American Control Conference, 2026 |
| Subjects: | Optimization and Control (math.OC); Systems and Control (eess.SY) |
| Cite as: | arXiv:2601.16003 [math.OC] |
| (or arXiv:2601.16003v3 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2601.16003 arXiv-issued DOI via DataCite |
From: Yunan Wang [view email]
[v1]
Thu, 22 Jan 2026 14:28:37 UTC (2,804 KB)
[v2]
Fri, 23 Jan 2026 13:44:49 UTC (2,802 KB)
[v3]
Mon, 25 May 2026 22:15:24 UTC (3,295 KB)
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