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Volume 14
Issue 11
10.3390/act14110513
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Nonlinear Dynamic Modeling of Flexible Cable in Overhead Bridge Crane and Trajectory Optimization Under Full-Constraint Conditions

by
Guangwei Yang
1,
Jiayang Wu
1,
Yutian Lei
2,
Yanan Cui
1,
Yifei Liu
3,
Lin Wan
4,
Gang Li
3,
Chunyan Long
5,6,
Yonglong Zhang
2,* and
Zehua Chen
4,*
1
College of Mechanical Engineering, Taiyuan University of Technology, Taiyuan 030024, China
2
College of Aeronautics and Astronautics, Taiyuan University of Technology, Taiyuan 030024, China
3
College of Electrical and Power Engineering, Taiyuan University of Technology, Taiyuan 030024, China
4
College of Artificial Intelligence, Taiyuan University of Technology, Taiyuan 030024, China
5
Shanxi Keda Automatic Control Co., Ltd., Taiyuan 030006, China
6
Provincial Technology Innovation Center for Special Robots in Mines; Taiyuan 030006, China
*
Authors to whom correspondence should be addressed.
Actuators 2025, 14(11), 513; https://doi.org/10.3390/act14110513
Submission received: 13 August 2025 / Revised: 11 October 2025 / Accepted: 21 October 2025 / Published: 23 October 2025
(This article belongs to the Special Issue Modeling and Nonlinear Control for Complex MIMO Mechatronic Systems)
Versions Notes

Abstract

Gantry cranes play a key role in modern industrial logistics. However, the traditional dynamic model based on the assumption of cable rigidity faces difficulty in accurately describing the complex swing characteristics of flexible cables, resulting in low load positioning accuracy and limited operation efficiency. To address this problem, this paper proposes a cable modeling method that considers the flexible deformation and nonlinear dynamic characteristics of the cable. Based on the theory of continuum mechanics, a flexible cable dynamic model that can accurately describe the flexible deformation and distributed mass characteristics of the cable is established. In order to solve the transportation time optimization and full-state constraint problems, a velocity trajectory optimization algorithm based on a discretization framework is proposed. Through inverse kinematics analysis and numerical integration technology, a reverse angle enumeration reasoning (RAER) method is proposed to suppress the swing of the load. Under the same constraints of distance, velocity, acceleration, cable swing angle, and residual swing angle, RAER requires a longer transportation time but achieves smaller peak swing and residual swing, making it the only algorithm that satisfies full-state constraints. Under the energy criterion, the proposed algorithm also requires the least amount of energy. Comprehensive comparisons through simulations and experiments show that the predicted swing angles of the flexible cable are highly consistent with the experimental results.
Keywords: flexible cable dynamics; anti-sway control; speed optimization algorithm; discrete modeling flexible cable dynamics; anti-sway control; speed optimization algorithm; discrete modeling

Share and Cite

MDPI and ACS Style

Yang, G.; Wu, J.; Lei, Y.; Cui, Y.; Liu, Y.; Wan, L.; Li, G.; Long, C.; Zhang, Y.; Chen, Z. Nonlinear Dynamic Modeling of Flexible Cable in Overhead Bridge Crane and Trajectory Optimization Under Full-Constraint Conditions. Actuators 2025, 14, 513. https://doi.org/10.3390/act14110513

AMA Style

Yang G, Wu J, Lei Y, Cui Y, Liu Y, Wan L, Li G, Long C, Zhang Y, Chen Z. Nonlinear Dynamic Modeling of Flexible Cable in Overhead Bridge Crane and Trajectory Optimization Under Full-Constraint Conditions. Actuators. 2025; 14(11):513. https://doi.org/10.3390/act14110513

Chicago/Turabian Style

Yang, Guangwei, Jiayang Wu, Yutian Lei, Yanan Cui, Yifei Liu, Lin Wan, Gang Li, Chunyan Long, Yonglong Zhang, and Zehua Chen. 2025. "Nonlinear Dynamic Modeling of Flexible Cable in Overhead Bridge Crane and Trajectory Optimization Under Full-Constraint Conditions" Actuators 14, no. 11: 513. https://doi.org/10.3390/act14110513

APA Style

Yang, G., Wu, J., Lei, Y., Cui, Y., Liu, Y., Wan, L., Li, G., Long, C., Zhang, Y., & Chen, Z. (2025). Nonlinear Dynamic Modeling of Flexible Cable in Overhead Bridge Crane and Trajectory Optimization Under Full-Constraint Conditions. Actuators, 14(11), 513. https://doi.org/10.3390/act14110513

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