Dynamics and trajectory tracking control of cooperative multiple mobile cranes

This paper addresses the dynamics and trajectory tracking control of cooperative multiple mobile cranes. Compared with a single mobile crane, cooperative cable parallel manipulators for multiple mobile cranes (CPMMC) are more complex in configuration, which have the characters of both series and parallel manipulators. Therefore, for the CPMMC, the forward as well as the inverse kinematics and dynamics include the difficulties of both series and parallel manipulators. However, the closed kinematic chain brings about potential benefits, including sufficient accuracy, higher cost performance, better lifting capacity and security. Firstly, the forward and inverse kinematics of the CPMMC with point mass are derived with elimination method, and the complete dynamic model of the CPMMC is established based on Lagrange equation and the complete kinematics. Secondly, considering the repetitive tasks and high security and precision requirement, a robust iterative learning controller is designed for trajectory tracking on the basis of the linearization of the dynamics. Thirdly, taking the engineering practice into consideration, two case studies are simulated with the same expected trajectory but with different weights of the loads. Finally, the designed controller is compared with traditional PD control algorithm via numerical simulation. The results demonstrate the feasibility and superiority of the CPMMC and designed controller, and provide a theoretical basis for the cooperation of multiple mobile cranes.