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

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.