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Volume 13
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10.3390/machines13090764
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Time-Optimal Trajectory Planning for Industrial Robots Based on Improved Fire Hawk Optimizer

by
Shuxia Ye
1,2,
Bo Jiang
1,
Yongwei Zhang
1,2,
Liwen Cai
1,
Liang Qi
1,2,* and
Siyu Fei
1
1
School of Automation, Jiangsu University of Science and Technology, No. 666 Changhui Road, Zhenjiang 212114, China
2
Jiangsu Shipbuilding and Ocean Engineering Design and Research Institute, Zhenjiang 212100, China
*
Author to whom correspondence should be addressed.
Machines 2025, 13(9), 764; https://doi.org/10.3390/machines13090764
Submission received: 12 July 2025 / Revised: 14 August 2025 / Accepted: 25 August 2025 / Published: 26 August 2025
(This article belongs to the Section Automation and Control Systems)
Versions Notes

Abstract

Focusing on joint-space time-optimal trajectory planning for industrial robots, this study integrates 3-5-3 piecewise polynomial parameterization with an improved Fire Hawk Optimization algorithm (TFHO). Subject to joint position, velocity, and acceleration limits, segment durations are optimized as decision variables. TFHO employs Tent-chaotic initialization to improve the uniformity of initial solutions and a two-phase adaptive Lévy–Gaussian–Cauchy hybrid mutation to balance early global exploration with late local exploitation, mitigating premature convergence and enhancing stability. On benchmark functions, TFHO attains the lowest mean area under the convergence curve (AUC; lower is better). Wilcoxon signed-rank tests show statistically significant improvements over FHO, PSO, GWO, and WOA (p≤0.05). Ablation studies indicate a pronounced reduction in run-to-run variability: the standard deviation decreases from 0.3157 (FHO) to 0.0023 with TFHO, a 99.27% drop. In an ABB IRB-2600 simulation case, the execution time is shortened from 12.00 s to 9.88 s (−17.66%) while preserving smooth and continuous kinematic profiles (position, velocity, and acceleration), demonstrating practical engineering applicability.
Keywords: trajectory planning; time-optimal; adaptive hybrid mutation; 3-5-3 polynomial trajectory planning; time-optimal; adaptive hybrid mutation; 3-5-3 polynomial

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MDPI and ACS Style

Ye, S.; Jiang, B.; Zhang, Y.; Cai, L.; Qi, L.; Fei, S. Time-Optimal Trajectory Planning for Industrial Robots Based on Improved Fire Hawk Optimizer. Machines 2025, 13, 764. https://doi.org/10.3390/machines13090764

AMA Style

Ye S, Jiang B, Zhang Y, Cai L, Qi L, Fei S. Time-Optimal Trajectory Planning for Industrial Robots Based on Improved Fire Hawk Optimizer. Machines. 2025; 13(9):764. https://doi.org/10.3390/machines13090764

Chicago/Turabian Style

Ye, Shuxia, Bo Jiang, Yongwei Zhang, Liwen Cai, Liang Qi, and Siyu Fei. 2025. "Time-Optimal Trajectory Planning for Industrial Robots Based on Improved Fire Hawk Optimizer" Machines 13, no. 9: 764. https://doi.org/10.3390/machines13090764

APA Style

Ye, S., Jiang, B., Zhang, Y., Cai, L., Qi, L., & Fei, S. (2025). Time-Optimal Trajectory Planning for Industrial Robots Based on Improved Fire Hawk Optimizer. Machines, 13(9), 764. https://doi.org/10.3390/machines13090764

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