基于多项式混沌展开的船舶避碰鲁棒轨迹规划

doi:10.12305/j.issn.1001-506X.2025.02.28

摘要/Abstract

摘要：

现有的船舶避碰轨迹规划大部分是以精确的运动模型和环境信息为前提, 难以应对实际环境中存在的多种不确定海况因素, 并导致规划出的轨迹安全可靠性降低。针对以上问题, 提出一种基于多项式混沌展开法的船舶鲁棒轨迹规划方法, 将船舶水动力学模型中的水动力系数视为不确定性参数, 以碰撞危险度及舵角控制量为目标函数, 建立船舶轨迹规划的最优控制模型, 并使用遗传算法求得控制量与优化后的轨迹。仿真实验结果表明, 优化后的轨迹最小距离以及最大会遇距离均提升10%~20%, 平均碰撞危险度降低10%, 实验结果表明考虑不确定性的船舶轨迹规划更加安全可靠。

关键词: 船舶避碰, 多项式混沌展开, 碰撞危险度, 最优控制, 遗传算法

Abstract:

Most of the existing ship collision avoidance trajectory planning is based on accurate motion mo-dels and environmental information, which makes it difficult to cope with various uncertain sea conditions in the actual environment and leads to a decrease in the safety and reliability of the planned trajectory. A robust trajectory planning method for ships based on polynomial chaotic expansion method is proposed to address the above issues. The hydrodynamic coefficients in the ship hydrodynamic model are considered as uncertain parameters, and the collision risk and rudder angle control variables are used as objective functions to establish the optimal control model for ship trajectory planning. Genetic algorithm is used to obtain the control variables and optimized trajectory. The experimental results show that the minimum distance and maximum encounter distance of the optimized trajectory are increased by 10%-20%, and the average collision risk is reduced by 10%. The experimental results prove that the ship trajectory considering uncertainty is more safer and reliable.

Key words: ship collision avoidance, polynomial chaotic expansion, collision risk, optimal control, genetic algorithm

中图分类号:

U675

祁新宇, 张智, 尚晓兵, 张艺琼, 姜立超, 周悦欣. 基于多项式混沌展开的船舶避碰鲁棒轨迹规划[J]. 系统工程与电子技术, 2025, 47(2): 621-632.

Xinyu QI, Zhi ZHANG, Xiaobing SHANG, Yiqiong ZHANG, Lichao JIANG, Yuexin ZHOU. Robust trajectory planning for ship collision avoidance based on polynomial chaotic expansion[J]. Systems Engineering and Electronics, 2025, 47(2): 621-632.

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参考文献 32

1	LI X P , ZHAO X Y , BAI D L . Marine transport efficiency evaluation of cross-border logistics based on AHP-TOPSIS method[J]. Journal of Coastal Research, 2020, 110 (SI): 95- 99.
2	LIU R Z , WANG T , LI J D , et al. Simulation of seasonal transport of microplastics and influencing factors in the China Seas based on the ROMS model[J]. Water Research, 2023, 244, 120493. doi: 10.1016/j.watres.2023.120493
3	HUANG Y , COLIN C , LIU Z F , et al. Impacts of nepheloid layers and mineralogical compositions of oceanic margin sediments on REE concentrations and Nd isotopic compositions of seawater[J]. Geochimica et Cosmochimica Acta, 2023, 359, 57- 70. doi: 10.1016/j.gca.2023.08.026
4	LIANG X Y , WANG L Z , DU W , et al. Emission factors of oxygenated polycyclic aromatic hydrocarbons from ships in China[J]. Environmental Pollution, 2023, 337, 122483. doi: 10.1016/j.envpol.2023.122483
5	LI L L, WANG J K. SAR image ship detection based on ant co-lony optimization[C]//Proc. of the 5th International Congress on Image and Signal Processing, 2012: 1100-1103.
6	夏悠然, 管军, 易文俊. 基于改进粒子群优化极限学习机的弹丸参数辨识[J]. 系统工程与电子技术, 2023, 45 (2): 521- 529. doi: 10.12305/j.issn.1001-506X.2023.02.24
	XIA Y R , GUAN J , YI W J . Projectile parameter identification: extreme learning machine optimized by improved particle swarm[J]. Systems Engineering and Electronics, 2023, 45 (2): 521- 529. doi: 10.12305/j.issn.1001-506X.2023.02.24
7	CHEN Y Q, LI T X. Collision avoidance of unmanned ships based on artificial potential field[C]//Proc. of the Chinese Automation Congress, 2017: 4437-4440.
8	REN L , ZHANG W X . Matching optimization of ship engine and propeller based on PSO-GA algorithm[J]. Applied Mechanics and Materials, 2012, 121, 4503- 4507.
9	CHEN X J, LIU Y X, HONG X B, et al. Unmanned ship path planning based on RRT[C]//Proc. of the International Conference on Intelligent Computing, 2018.
10	杨荣武, 许劲松, 王鑫. 船舶自主避碰的慎思型轨迹规划[J]. 上海交通大学学报, 2019, 53 (12): 1411- 1419.
	YANG R W , XU J S , WANG X . Deliberative trajectory planning for autonomous collision avoidance of ships[J]. Journal of Shanghai Jiao Tong University, 2019, 53 (12): 1411- 1419.
11	徐杨, 陆丽萍, 褚端峰, 等. 无人车辆轨迹规划与跟踪控制的统一建模方法[J]. 自动化学报, 2019, 45 (4): 799- 807.
	XU Y , LU L P , CHU D F , et al. An unified modeling method for trajectory planning and tracking control of unmanned vehicles[J]. Journal of Automation, 2019, 45 (4): 799- 807.
12	姚绪梁, 王峰, 王景芳, 等. 不确定海流环境下水下机器人最优时间路径规划[J]. 控制理论与应用, 2020, 37 (6): 1302- 1310.
	YAO X L , WANG F , WANG J F , et al. Optimal time path planning for underwater robots in uncertain ocean current environments[J]. Control Theory & Applications, 2020, 37 (6): 1302- 1310.
13	汪萌, 诸兵. 不确定性建模在2D和3D目标检测中的应用[J]. 系统工程与电子技术, 2023, 45 (8): 2370- 2376. doi: 10.12305/j.issn.1001-506X.2023.08.10
	WANG M , CHU B . Application of uncertainty modeling in 2D and 3D object detection[J]. Systems Engineering and Electro-nics, 2023, 45 (8): 2370- 2376. doi: 10.12305/j.issn.1001-506X.2023.08.10
14	CHAUDHURI A , WAYCASTER G , PRICE N , et al. NASA uncertainty quantification challenge: an optimization-based methodology and validation[J]. Journal of Aerospace Information Systems, 2015, 12 (1): 10- 34. doi: 10.2514/1.I010269
15	GHANEM R , YADEGARAN I , THIMMISETTY C , et al. Pro-babilistic approach to NASA Langley research center multidisciplinary uncertainty quantification challenge problem[J]. Journal of Aerospace Information Systems, 2015, 12 (1): 170- 188. doi: 10.2514/1.I010271
16	BAI Y L , HUANG Z Y , LAM H . Model calibration via distributionally robust optimization: on the NASA Langley uncertainty quantification challenge[J]. Mechanical Systems and Signal Processing, 2022, 164, 108211. doi: 10.1016/j.ymssp.2021.108211
17	SEPKA S A , WRIGHT M . Monte Carlo approach to FIAT uncertainties with applications for Mars science laboratory[J]. Journal of Thermophysics and Heat Transfer, 2011, 25 (4): 516- 522. doi: 10.2514/1.49804
18	HALDER A . Probabilistic methods for model validation[M]. College Station, Texas: Texas A&M University, 2014.
19	FEISCHL M , SCAGLIONI A . Convergence of adaptive stochastic collocation with finite elements[J]. Computers & Mathematics with Applications, 2021, 98, 139- 156.
20	ZENG P , LI T B , CHEN Y , et al. New collocation method for stochastic response surface reliability analyses[J]. Engineering with Computers, 2020, 36, 1751- 1762. doi: 10.1007/s00366-019-00793-2
21	JIA B , XIN M . Short-arc orbital uncertainty propagation with arbitrary polynomial chaos and admissible region[J]. Journal of Guidance, Control, and Dynamics, 2020, 43 (4): 715- 728. doi: 10.2514/1.G004548
22	WANG M J, HUANG Q B, LI S D. A subinterval response surface method for frequency response analysis of structural-acoustic system with uncertain-but-bounded parameters[C]//Proc. of the 4th International Conference on Industrial Engineering and Applications, 2017: 327-330.
23	LUO Y Z , YANG Z . A review of uncertainty propagation in orbital mechanics[J]. Progress in Aerospace Sciences, 2017, 89, 23- 39. doi: 10.1016/j.paerosci.2016.12.002
24	YIN S W , YU D J , LUO Z , et al. An arbitrary polynomial chaos expansion approach for response analysis of acoustic systems with epistemic uncertainty[J]. Computer Methods in Applied Mechanics and Engineering, 2018, 332, 280- 302. doi: 10.1016/j.cma.2017.12.025
25	VITTALDEV V , RUSSELL R P , LINARES R . Spacecraft uncertainty propagation using Gaussian mixture models and polynomial chaos expansions[J]. Journal of Guidance, Control, and Dynamics, 2016, 39 (12): 2615- 2626. doi: 10.2514/1.G001571
26	HOSDER S , WALTERS R W , BALCH M . Point-collocation nonintrusive polynomial chaos method for stochastic computational fluid dynamics[J]. AIAA Journal, 2010, 48 (12): 2721- 2730. doi: 10.2514/1.39389
27	谢朔. 基于天牛须优化的船舶运动建模与避碰方法研究[D]. 武汉: 武汉理工大学, 2022.
	XIE S. Research on ship motion modeling and collision avoidance methods based on optimization of longhorn whiskers[D]. Wuhan: Wuhan University of Technology, 2022.
28	郑中义, 吴兆麟. 船舶碰撞危险度的新模型[J]. 大连海事大学学报, 2002, 28 (2): 1- 5. doi: 10.3969/j.issn.1006-7736.2002.02.001
	ZHENG Z Y , WU Z L . A new model of ship collision risk[J]. Dalian Maritime University Journal, 2002, 28 (2): 1- 5. doi: 10.3969/j.issn.1006-7736.2002.02.001
29	VARELA J M , GUEDES SOARES C . Geometry and visual realism of ship models for digital ship bridge simulators[J]. Journal of Engineering for the Maritime Environment, 2017, 231 (1): 329- 341.
30	CHEN L Y , HUANG Y M , ZHENG H R , et al. Cooperative multi-vessel systems in urban waterway networks[J]. IEEE Trans.on Intelligent Transportation Systems, 2019, 21 (8): 3294- 3307.
31	GAO H , ZOU Z J , XIA L , et al. Application of the NIPC-based uncertainty quantification in prediction of ship maneuverability[J]. Journal of Marine Science and Technology, 2021, 26, 555- 572. doi: 10.1007/s00773-020-00754-1
32	KIM H J , KIM Y T , YOON D K . Dependence of polynomial chaos on random types of forces of KdV equations[J]. Applied Mathematical Modelling, 2012, 36 (7): 3080- 3093. doi: 10.1016/j.apm.2011.09.086

参数	均值	方差
X_u	-0.047 644	0.005
Y_v	-0.145 3	0.020
Y_r	0.366 66	0.020
N_v	-0.161 65	0.020

会遇态势	船舶	初始横坐标/m	初始纵坐标/m	初始速度/(m/s)	初始艏向/rad
对遇	本船	0	0	7	2π
对遇	来船	0	350	7	$-\frac{1}{2} \mathsf{π} $
小角度右舷交叉	本船	0	0	7	$\frac{1}{2}\mathsf{π} $
小角度右舷交叉	来船	50	210	7	$-\frac{2}{3}\mathsf{π} $
大角度右舷交叉	本船	0	0	7	$\frac{1}{2}\mathsf{π} $
大角度右舷交叉	来船	160	80	7	π
追越	本船	0	0	7	$\frac{1}{2}\mathsf{π} $
追越	来船	0	80	7	$\frac{1}{2}\mathsf{π} $

参数名称	取值
a₁	0.9
a₂	0.1
k_g	3
δ_max/rad	0.2π
Ψ_min/rad	$-\frac{1}{3}\mathsf{π} $
Ψ_max/rad	$\frac{1}{3}\mathsf{π} $

指标	方法	对遇	小角度右舷交叉	大角度右舷交叉	追越
R_Tmin/m	确定性	43.5	46.8	34.0	33.4
R_Tmin/m	鲁棒优化	77.9	72.2	37.1	42.2
DCPA_max/m	确定性	52.6	75.6	62.2	46.4
DCPA_max/m	鲁棒优化	84.9	98.1	67.3	83.9
F_CRI	确定性	0.81	0.74	0.71	0.82
F_CRI	鲁棒优化	0.52	0.51	0.61	0.70

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