Model Inversion for Precise Path and Trajectory Tracking in an Underactuated, Non-Minimum Phase, Spatial Overhead Crane

Purpose This paper proposes a motion planning technique for precise path and trajectory tracking in an underactuated, non-minimum phase, spatial overhead crane. Besides having a number of independent actuators that is smaller than the number of degrees of freedom, tip control on this system presents unstable internal dynamics that leads to divergent solution of the inverse dynamic problem. Method The paper exploits the representation of the controlled output as a separable function of the actuated (i.e., the platform translations) and unactuated (i.e., the swing angles) coordinates to easily formulate the internal dynamics, without any approximation, and to study its stability. Then, output redefinition is adopted within the internal dynamics to stabilize it, leading to stable and causal reference commands for the platform translations. Results Besides proposing the theoretical formulation of this novel method, the paper includes the numerical validation and the experimental application on a laboratory setup. Comparison with the state-of-the-art input shaping is also proposed. Conclusion The results, obtained through different reference trajectories, clearly show that almost exact tracking is obtained also in the experiments, by outperforming the benchmarks.