Motion Trajectory-Based Transportation Control for 3-D Boom Cranes: Analysis, Design, and Experiments

Boom crane systems with high practicality, the control problems of which are more complex than those of most other underactuated systems due to their strongly nonlinear dynamical coupling characteristics, are widely applied in various places. In addition to the basic control objectives of accurate boom positioning and payload swing suppression, another challenging aspect is how to improve the transient performance of the state variables while ensuring time (sub)optimality during transportation. In this paper, to address the two aforementioned issues, i.e., complicated nonlinear dynamics and ensuring transient performance, a new nonlinear time suboptimal trajectory planning approach, which does not require linearizing the original nonlinear dynamics, is proposed to achieve efficient control results for the boom crane system. After performing an in-depth analysis, we find a transformation relationship between four tip signals and the state variables. Then, by planning proper trajectories for the tip signals based on the original nonlinear boom crane dynamics, we obtain swing-free time suboptimal trajectories for the boom pitch and yaw movements; hence, the boom can reach its destination accurately, and the payload swing can be suppressed. Moreover, the state variables can be restricted within specified ranges as required. The presented trajectory planner can be considered as the first solution for generating trajectories for the boom crane system, respecting various state constraints without the need for any linearization operations. Finally, some hardware experiments are introduced to verify the effectiveness of the presented control strategy.